keyword stringclasses 7 values | repo_name stringlengths 8 98 | file_path stringlengths 4 244 | file_extension stringclasses 29 values | file_size int64 0 84.1M | line_count int64 0 1.6M | content stringlengths 1 84.1M ⌀ | language stringclasses 14 values |
|---|---|---|---|---|---|---|---|
3D | febiosoftware/FEBio | FEBioMech/FEViscoElasticDamage.cpp | .cpp | 9,547 | 263 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "FEViscoElasticDamage.h"
#include <FECore/log.h>
#include <FECore/FEModel.h>
//-----------------------------------------------------------------------------
BEGIN_FECORE_CLASS(FEViscoElasticDamage, FEElasticMaterial)
// material parameters
ADD_PARAMETER(m_t[0], "t1")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_t[1], "t2")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_t[2], "t3")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_t[3], "t4")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_t[4], "t5")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_t[5], "t6")->setUnits(UNIT_TIME);
ADD_PARAMETER(m_g0 , "g0");
ADD_PARAMETER(m_g[0], "g1");
ADD_PARAMETER(m_g[1], "g2");
ADD_PARAMETER(m_g[2], "g3");
ADD_PARAMETER(m_g[3], "g4");
ADD_PARAMETER(m_g[4], "g5");
ADD_PARAMETER(m_g[5], "g6");
// define the material properties
ADD_PROPERTY(m_pDmg, "elastic");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! constructor
FEViscoElasticDamage::FEViscoElasticDamage(FEModel* pfem) : FEElasticMaterial(pfem)
{
m_g0 = 1;
for (int i=0; i<MAX_TERMS; ++i)
{
m_t[i] = 1;
m_g[i] = 0;
}
m_pDmg = nullptr;
}
//-----------------------------------------------------------------------------
//! data initialization
bool FEViscoElasticDamage::Init()
{
if (dynamic_cast<FEDamageMaterial*>(m_pDmg) == 0) {
feLogError("elastic component of viscoelastic damage material must be of type elastic damage!");
return false;
}
return m_pDmg->Init();
}
//-----------------------------------------------------------------------------
//! Create material point data for this material
FEMaterialPointData* FEViscoElasticDamage::CreateMaterialPointData()
{
return new FEViscoElasticMaterialPoint(m_pDmg->CreateMaterialPointData());
}
//-----------------------------------------------------------------------------
//! Stress function
mat3ds FEViscoElasticDamage::Stress(FEMaterialPoint& mp)
{
double dt = GetFEModel()->GetTime().timeIncrement;
if (dt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
// get the elastic part
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// get the viscoelastic point data
FEViscoElasticMaterialPoint& pt = *mp.ExtractData<FEViscoElasticMaterialPoint>();
// Calculate the new elastic Cauchy stress
mat3ds se = m_pDmg->GetElasticMaterial()->Stress(mp);
// pull-back to get PK2 stress
mat3ds Se = pt.m_Se = ep.pull_back(se);
// get elastic PK2 stress of previous timestep
mat3ds Sep = pt.m_Sep;
// calculate new history variables
// terms are accumulated in S, the total PK2-stress
mat3ds S = Se*m_g0;
double g, h;
for (int i=0; i<MAX_TERMS; ++i)
{
g = exp(-dt/m_t[i]);
h = (1 - g)/(dt/m_t[i]);
pt.m_H[i] = pt.m_Hp[i]*g + (Se - Sep)*h;
S += pt.m_H[i]*m_g[i];
}
// return the total Cauchy stress,
// which is the push-forward of S
double D = m_pDmg->Damage(mp);
return ep.push_forward(S)*(1-D);
}
//-----------------------------------------------------------------------------
//! Material tangent
tens4ds FEViscoElasticDamage::Tangent(FEMaterialPoint& pt)
{
double dt = GetFEModel()->GetTime().timeIncrement;
// calculate the spatial elastic tangent
tens4ds C = m_pDmg->GetElasticMaterial()->Tangent(pt);
if (dt == 0.0) return C;
// calculate the visco scale factor
double f = m_g0, g, h;
for (int i=0; i<MAX_TERMS; ++i)
{
g = exp(-dt/m_t[i]);
h = ( 1 - exp(-dt/m_t[i]) )/( dt/m_t[i] );
f += m_g[i]*h;
}
double D = m_pDmg->Damage(pt);
// multiply tangent with visco-factor
return C*(f*(1-D));
}
//-----------------------------------------------------------------------------
//! Strain energy density function
double FEViscoElasticDamage::StrainEnergyDensity(FEMaterialPoint& mp)
{
// get the viscoelastic point data
FEViscoElasticMaterialPoint& pt = *mp.ExtractData<FEViscoElasticMaterialPoint>();
FEElasticMaterialPoint& et = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d Fsafe = et.m_F; double Jsafe = et.m_J;
// Calculate the new elastic strain energy density
pt.m_sed = m_pDmg->GetElasticMaterial()->StrainEnergyDensity(mp);
double sed = pt.m_sed;
double sedt = sed*m_g0;
if (SeriesStretchExponent(mp)) {
// get the elastic point data and evaluate the right-stretch tensor
for (int i=0; i<MAX_TERMS; ++i)
{
if (m_g[i] > 0) {
mat3ds C = et.RightCauchyGreen();
double l2[3], l[3];
vec3d v[3];
C.eigen2(l2, v);
l[0] = sqrt(l2[0]); l[1] = sqrt(l2[1]); l[2] = sqrt(l2[2]);
mat3ds Ua = dyad(v[0])*pow(l[0],pt.m_alpha[i])
+ dyad(v[1])*pow(l[1],pt.m_alpha[i]) + dyad(v[2])*pow(l[2],pt.m_alpha[i]);
et.m_F = Ua; et.m_J = Ua.det();
sedt += m_g[i]*m_pDmg->GetElasticMaterial()->StrainEnergyDensity(mp);
}
}
}
else
throw std::runtime_error("FEViscoElasticDamage::strain energy density calculation did not converge!");
et.m_F = Fsafe; et.m_J = Jsafe;
double D = m_pDmg->Damage(mp);
// return the total strain energy density
return sedt*(1-D);
}
//-----------------------------------------------------------------------------
//! calculate exponent of right-stretch tensor in series spring
bool FEViscoElasticDamage::SeriesStretchExponent(FEMaterialPoint& mp)
{
const double errrel = 1e-6;
const double almin = 0.001;
const int maxiter = 50;
// get the elastic point data and evaluate the right-stretch tensor
FEElasticMaterialPoint& et = *mp.ExtractData<FEElasticMaterialPoint>();
// get the right stretch tensor
mat3ds C = et.RightCauchyGreen();
double l2[3], l[3];
vec3d v[3];
C.eigen2(l2, v);
l[0] = sqrt(l2[0]); l[1] = sqrt(l2[1]); l[2] = sqrt(l2[2]);
mat3ds U = dyad(v[0])*l[0] + dyad(v[1])*l[1] + dyad(v[2])*l[2];
double gamma = 0;
for (int i=0; i<MAX_TERMS; ++i) gamma += m_g[i];
// get the viscoelastic point data
FEViscoElasticMaterialPoint& pt = *mp.ExtractData<FEViscoElasticMaterialPoint>();
// use previous time solution as initial guess for the exponent
mat3ds Se = pt.m_Se;
mat3ds S = et.pull_back(et.m_s);
double fmag = Se.dotdot(U);
mat3d Fsafe = et.m_F; double Jsafe = et.m_J;
for (int i=0; i<MAX_TERMS; ++i) {
if (m_g[i] > 0) {
double alpha = pt.m_alphap[i];
bool done = false;
int iter = 0;
do {
mat3ds Ua = dyad(v[0])*pow(l[0],alpha) + dyad(v[1])*pow(l[1],alpha) + dyad(v[2])*pow(l[2],alpha);
et.m_F = Ua; et.m_J = Ua.det();
mat3ds Sea = et.pull_back(m_pDmg->GetElasticMaterial()->Stress(mp));
double f = (Sea*m_g[i] - S + Se).dotdot(U);
tens4ds Cea = et.pull_back(m_pDmg->GetElasticMaterial()->Tangent(mp));
mat3ds U2ap = dyad(v[0])*(pow(l[0],2*alpha)*log(l[0]))
+ dyad(v[1])*(pow(l[1],2*alpha)*log(l[1]))
+ dyad(v[2])*(pow(l[2],2*alpha)*log(l[2]));
double fprime = (Cea.dot(U2ap)).dotdot(U)*m_g[i];
if (fprime != 0) {
double dalpha = -f/fprime;
alpha += dalpha;
if (fabs(f) < errrel*fmag) done = true;
else if (fabs(dalpha) < errrel*fabs(alpha)) done = true;
else if (alpha > 1) { alpha = 1; done = true; }
else if (alpha < almin) { alpha = 0; done = true; }
else if (++iter > maxiter) done = true;
}
else
done = true;
} while (!done);
if (iter > maxiter) {
et.m_F = Fsafe; et.m_J = Jsafe;
return false;
}
pt.m_alpha[i] = alpha;
}
}
et.m_F = Fsafe; et.m_J = Jsafe;
return true;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEIdealGasPressure.cpp | .cpp | 4,158 | 140 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEIdealGasPressure.h"
#include "FEBioMech.h"
#include <FECore/log.h>
BEGIN_FECORE_CLASS(FEIdealGasPressure, FESurfaceLoad)
ADD_PARAMETER(m_initialPressure, "P0")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_bsymm, "symmetric_stiffness");
ADD_PARAMETER(m_bshellb, "shell_bottom");
END_FECORE_CLASS()
FEIdealGasPressure::FEIdealGasPressure(FEModel* pfem) : FESurfaceLoad(pfem)
{
m_initialPressure = 0.0;
m_bsymm = true;
m_bshellb = false;
m_currentPressure = 0;
m_currentVolume = 0;
}
bool FEIdealGasPressure::Init()
{
FESurface& surf = GetSurface();
surf.SetShellBottom(m_bshellb);
// get the degrees of freedom
m_dof.Clear();
if (m_bshellb == false)
{
m_dof.AddVariable(FEBioMech::GetVariableName(FEBioMech::DISPLACEMENT));
}
else
{
m_dof.AddVariable(FEBioMech::GetVariableName(FEBioMech::SHELL_DISPLACEMENT));
}
if (m_dof.IsEmpty()) return false;
return FESurfaceLoad::Init();
}
void FEIdealGasPressure::Activate()
{
m_initialVolume = CalculateSurfaceVolume(GetSurface());
m_currentVolume = m_initialVolume;
m_currentPressure = m_initialPressure;
feLogDebug("initial volume: %lg\n", m_initialVolume);
FESurfaceLoad::Activate();
}
void FEIdealGasPressure::Update()
{
m_currentVolume = CalculateSurfaceVolume(GetSurface());
m_currentPressure = m_initialPressure * (m_initialVolume / m_currentVolume);
feLogDebug("volume: %lg, pressure: %lg\n", m_currentVolume, m_currentPressure);
FESurfaceLoad::Update();
}
void FEIdealGasPressure::LoadVector(FEGlobalVector& R)
{
// evaluate the integral
FESurface& surf = GetSurface();
surf.LoadVector(R, m_dof, false, [&](FESurfaceMaterialPoint& pt, const FESurfaceDofShape& dof_a, std::vector<double>& val) {
// evaluate pressure at this material point
double P = m_currentPressure;
if (m_bshellb) P = -P;
double J = (pt.dxr ^ pt.dxs).norm();
// force vector
vec3d N = (pt.dxr ^ pt.dxs); N.unit();
vec3d t = N * P;
double H_u = dof_a.shape;
val[0] = H_u * t.x * J;
val[1] = H_u * t.y * J;
val[2] = H_u * t.z * J;
});
}
void FEIdealGasPressure::StiffnessMatrix(FELinearSystem& LS)
{
// evaluate the integral
FESurface& surf = GetSurface();
surf.LoadStiffness(LS, m_dof, m_dof, [&](FESurfaceMaterialPoint& mp, const FESurfaceDofShape& dof_a, const FESurfaceDofShape& dof_b, matrix& kab) {
// evaluate pressure at this material point
double P = m_currentPressure;
if (m_bshellb) P = -P;
double H_i = dof_a.shape;
double Gr_i = dof_a.shape_deriv_r;
double Gs_i = dof_a.shape_deriv_s;
double H_j = dof_b.shape;
double Gr_j = dof_b.shape_deriv_r;
double Gs_j = dof_b.shape_deriv_s;
vec3d vab(0, 0, 0);
if (m_bsymm)
vab = (mp.dxr * (H_j * Gs_i - H_i * Gs_j) - mp.dxs * (H_j * Gr_i - H_i * Gr_j)) * 0.5 * P;
else
vab = (mp.dxs * Gr_j - mp.dxr * Gs_j) * (P * H_i);
mat3da K(vab);
kab.set(0, 0, K);
});
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FETendonMaterial.h | .h | 2,266 | 64 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEUncoupledMaterial.h"
//-----------------------------------------------------------------------------
//! Tendon Material
//! This material uses the constitutive model developed by Blemker et.al. to model tendons
class FETendonMaterial : public FEUncoupledMaterial
{
public:
FETendonMaterial(FEModel* pfem);
public:
// transverse constants
FEParamDouble m_G1; //!< along-fiber shear modulus
FEParamDouble m_G2; //!< cross-fiber shear modulus
// along fiber constants
FEParamDouble m_L1; //!< tendon fiber constant L1
FEParamDouble m_L2; //!< tendon fiber constant L2
FEParamDouble m_lam1; //!< max exponential fiber stretch
FEVec3dValuator* m_fiber;
public:
//! calculate deviatoric stress at material point
virtual mat3ds DevStress(FEMaterialPoint& pt) override;
//! calculate deviatoric tangent stiffness at material point
virtual tens4ds DevTangent(FEMaterialPoint& pt) override;
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEMaxDamageCriterion.cpp | .cpp | 1,853 | 50 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEMaxDamageCriterion.h"
#include "FEElasticMaterial.h"
BEGIN_FECORE_CLASS(FEDamageAdaptorCriterion, FEMeshAdaptorCriterion)
END_FECORE_CLASS();
FEDamageAdaptorCriterion::FEDamageAdaptorCriterion(FEModel* fem) : FEMeshAdaptorCriterion(fem)
{
}
bool FEDamageAdaptorCriterion::GetMaterialPointValue(FEMaterialPoint& mp, double& value)
{
// TODO: What about mixtures?
FEDamageMaterialPoint* dp = mp.ExtractData<FEDamageMaterialPoint>();
if (dp == nullptr) return false;
// evaluate the damage at this point
value = dp->m_D;
return true;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEKinematicGrowth.h | .h | 3,464 | 94 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2019 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEGrowthTensor.h"
#include "FEElasticMaterial.h"
#include <FECore/FEMaterialPoint.h>
#include <FECore/FEModelComponent.h>
//-----------------------------------------------------------------------------
//! Define a material point that stores the multiplicative decomposition
//! of the deformation gradient and the solid referential density
//
class FEKinematicMaterialPoint : public FEMaterialPointData
{
public:
FEKinematicMaterialPoint(FEMaterialPointData *pt) : FEMaterialPointData(pt) {}
FEMaterialPointData* Copy() override;
void Init() override;
void Update(const FETimeInfo& timeInfo) override;
void Serialize(DumpStream& ar) override;
public:
mat3d m_Fe; //!< elastic deformation
double m_Je; //!< elastic relative volume
mat3d m_Fg; //!< growth deformation
double m_rhor; //!< solid referential density
};
//-----------------------------------------------------------------------------
//! Material class that implements Kinematic growth model.
//
class FEKinematicGrowth : public FEElasticMaterial
{
public:
FEKinematicGrowth(FEModel* pfem);
//! Initialization routine
bool Init() override;
//! get the elastic base material
FEElasticMaterial* GetBaseMaterial() { return m_pBase; }
//! get the elastic base material
FEGrowthTensor* GetGrowthMaterial() { return m_pGrowth; }
//! Returns the Cauchy stress
mat3ds Stress(FEMaterialPoint& mp) override;
//! Returns the spatial tangent
tens4ds Tangent(FEMaterialPoint& mp) override;
//! Returns the strain energy density
double StrainEnergyDensity(FEMaterialPoint& mp) override;
// returns a pointer to a new material point object
FEMaterialPointData* CreateMaterialPointData() override;
// update material point at each iteration
void UpdateSpecializedMaterialPoints(FEMaterialPoint& mp, const FETimeInfo& tp) override;
private:
FEElasticMaterial* m_pBase; //!< pointer to elastic solid material
FEGrowthTensor* m_pGrowth; //!< pointer to growth tensor
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEVolumeConstraint.h | .h | 3,367 | 111 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESurfaceConstraint.h>
#include <FECore/FESurface.h>
//-----------------------------------------------------------------------------
class FEVolumeSurface : public FESurface
{
public:
//! constructor
FEVolumeSurface(FEModel* fem);
//! Initialization
bool Init();
//! copy data
void CopyFrom(FEVolumeSurface& s);
//! serialization
void Serialize(DumpStream& ar);
public:
double m_Lp; //!< Lagrange multipler pressure
double m_p; //!< applied pressure (= Lp + eps*DV)
double m_V0; //!< Initial volume
double m_Vt; //!< current volume
};
//-----------------------------------------------------------------------------
// This class implements a constraint that tries to maintain the volume of the
// enclosed space using an isochoric pressure.
class FEVolumeConstraint : public FESurfaceConstraint
{
public:
//! constructor
FEVolumeConstraint(FEModel* pfem);
~FEVolumeConstraint();
void Activate() override;
void LoadVector(FEGlobalVector& R, const FETimeInfo& tp) override;
void StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) override;
bool Augment(int naug, const FETimeInfo& tp) override;
void Serialize(DumpStream& ar) override;
void CopyFrom(FENLConstraint* plc) override;
// update state
void Reset() override;
void Update() override;
//! Unpack surface element data
void UnpackLM(FEElement& el, vector<int>& lm);
//! build connectivity for matrix profile
void BuildMatrixProfile(FEGlobalMatrix& M) override;
// get the surface
FESurface* GetSurface() override;
public:
double EnclosedVolume() const;
double Pressure() const;
public:
double m_eps; //!< penalty parameter
double m_atol; //!< augmented Lagrangian tolerance
bool m_blaugon; //!< augmentation flag
private:
bool m_binit; //!< flag indicating whether the constraint is initialized
// degrees of freedom
// (TODO: find a better way of defining this.
// I don't want to have to do this in each class)
int m_dofX;
int m_dofY;
int m_dofZ;
FEVolumeSurface* m_s; //!< the bounding surface
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEBioMechPlot.cpp | .cpp | 162,146 | 5,213 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEBioMechPlot.h"
#include "FEDamageNeoHookean.h"
#include "FEDamageTransIsoMooneyRivlin.h"
#include "FEKinematicGrowth.h"
#include "FEReactiveMaterialPoint.h"
#include "FEReactiveFatigue.h"
#include "FEReactivePlasticity.h"
#include "FEReactivePlasticDamage.h"
#include "FERemodelingElasticMaterial.h"
#include "FERigidSolidDomain.h"
#include "FERigidShellDomain.h"
#include "FEElasticShellDomainOld.h"
#include "FEElasticEASShellDomain.h"
#include "FEElasticANSShellDomain.h"
#include "FEElasticMixture.h"
#include "FEElasticMultigeneration.h"
#include "FEUT4Domain.h"
#include "FEContactSurface.h"
#include "FERigidBody.h"
#include <FECore/FESPRProjection.h>
#include "FEUncoupledElasticMixture.h"
#include "FERigidMaterial.h"
#include "FEVolumeConstraint.h"
#include "FEFacet2FacetSliding.h"
#include "FEMortarSlidingContact.h"
#include "FEMechModel.h"
#include "FEPreStrainElastic.h"
#include <FECore/writeplot.h>
#include <FECore/FEDomainParameter.h>
#include <FECore/FEModel.h>
#include "FEDiscreteElasticMaterial.h"
#include "FEDiscreteElasticDomain.h"
#include "FEContinuousElasticDamage.h"
#include <FECore/FEMeshAdaptor.h> // for projectToNodes
#include "FESlidingInterface.h"
#include "FESlidingElasticInterface.h"
#include "FETiedContactSurface.h"
#include "FEStickyInterface.h"
#include "FEReactiveVEMaterialPoint.h"
#include "FELinearTrussDomain.h"
#include <FECore/FESurface.h>
#include <FECore/FESurfaceLoad.h>
#include <FECore/FETrussDomain.h>
#include <FECore/FEElement.h>
#include <FEBioMech/FEElasticBeamDomain.h>
#include <FEBioMech/FEElasticBeamMaterial.h>
#include <FEBioMech/FEEdgeToSurfaceSlidingContact.h>
#include "FEIdealGasPressure.h"
#include "FEBodyForce.h"
//=============================================================================
// N O D E D A T A
//=============================================================================
//-----------------------------------------------------------------------------
bool FEPlotNodeDisplacement::Save(FEMesh& m, FEDataStream& a)
{
FEModel* fem = GetFEModel();
const int dof_X = fem->GetDOFIndex("x");
const int dof_Y = fem->GetDOFIndex("y");
const int dof_Z = fem->GetDOFIndex("z");
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return node.get_vec3d(dof_X, dof_Y, dof_Z);
});
return true;
}
bool FEPlotNodeRotation::Save(FEMesh& m, FEDataStream& a)
{
FEModel* fem = GetFEModel();
const int dof_U = fem->GetDOFIndex("u");
const int dof_V = fem->GetDOFIndex("v");
const int dof_W = fem->GetDOFIndex("w");
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return node.get_vec3d(dof_U, dof_V, dof_W);
});
return true;
}
bool FEPlotNodeShellDisplacement::Save(FEMesh& m, FEDataStream& a)
{
FEModel* fem = GetFEModel();
const int dof_SX = fem->GetDOFIndex("sx");
const int dof_SY = fem->GetDOFIndex("sy");
const int dof_SZ = fem->GetDOFIndex("sz");
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return node.get_vec3d(dof_SX, dof_SY, dof_SZ);
});
return true;
}
bool FEPlotNodalShellDirector::Save(FEMesh& m, FEDataStream& a)
{
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return (node.HasFlags(FENode::SHELL)) ? node.m_dt : vec3d(0,0,0);
});
return true;
}
//! Store the nodal incremental displacements
bool FEPlotNodeIncrementalDisplacement::Save(FEMesh& m, FEDataStream& a)
{
int N = m.Nodes();
if (m_rp.size() != N)
{
m_rp.resize(N);
for (int i = 0; i < N; ++i) m_rp[i] = m.Node(i).m_rt;
}
// loop over all nodes
for (int i = 0; i < N; ++i)
{
vec3d& rt = m.Node(i).m_rt;
a << rt - m_rp[i];
m_rp[i] = rt;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotNodeVelocity::Save(FEMesh& m, FEDataStream& a)
{
FEModel* fem = GetFEModel();
const int dof_VX = fem->GetDOFIndex("vx");
const int dof_VY = fem->GetDOFIndex("vy");
const int dof_VZ = fem->GetDOFIndex("vz");
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return node.get_vec3d(dof_VX, dof_VY, dof_VZ);
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotNodeAcceleration::Save(FEMesh& m, FEDataStream& a)
{
writeNodalValues<vec3d>(m, a, [](const FENode& node) {
return node.m_at;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store nodal reaction forces
bool FEPlotNodeReactionForces::Save(FEMesh& m, FEDataStream& a)
{
// NOTE: Currently, for nodes attached to rigid bodies the reaction forces
// will actually be the rigid reaction forces.
FEModel& fem = *GetFEModel();
int dofX = fem.GetDOFIndex("x");
int dofY = fem.GetDOFIndex("y");
int dofZ = fem.GetDOFIndex("z");
if ((dofX >= 0) && (dofY >= 0) && (dofZ >= 0))
{
writeNodalValues<vec3d>(m, a, [=](const FENode& node) {
return node.get_load3(dofX, dofY, dofZ);
});
return true;
}
else
return false;
}
//=============================================================================
// S U R F A C E D A T A
//=============================================================================
bool FEPlotContactGap::SetFilter(const char* szfilter)
{
if (szfilter) m_interfaceName = szfilter;
return (szfilter != nullptr);
}
// Plot contact gap
bool FEPlotContactGap::Save(FESurface& surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface();
bool write = false;
if (pci == nullptr) write = true;
else if (pci->IsActive())
{
if (m_interfaceName.empty() || (m_interfaceName == pci->GetName())) write = true;
}
if (write)
{
// NOTE: the sliding surface does not use material points, so we need this little hack.
FESlidingSurface* slidingSurface = dynamic_cast<FESlidingSurface*>(pcs);
if (slidingSurface)
{
for (int i = 0; i < slidingSurface->Elements(); ++i)
{
FEElement& el = slidingSurface->Element(i);
double g = 0.0;
for (int j = 0; j < el.Nodes(); ++j)
{
double gj = slidingSurface->m_data[el.m_lnode[j]].m_gap;
g += gj;
}
g /= el.Nodes();
a << g;
}
return true;
}
FETiedContactSurface* tiedSurface = dynamic_cast<FETiedContactSurface*>(pcs);
if (tiedSurface)
{
for (int i = 0; i < tiedSurface->Elements(); ++i)
{
FEElement& el = tiedSurface->Element(i);
double g = 0.0;
for (int j = 0; j < el.Nodes(); ++j)
{
double gj = tiedSurface->m_data[el.m_lnode[j]].m_gap;
g += gj;
}
g /= el.Nodes();
a << g;
}
return true;
}
FEStickySurface* stickySurface = dynamic_cast<FEStickySurface*>(pcs);
if (stickySurface)
{
for (int i = 0; i < stickySurface->Elements(); ++i)
{
FEElement& el = stickySurface->Element(i);
double g = 0.0;
for (int j = 0; j < el.Nodes(); ++j)
{
double gj = stickySurface->m_data[el.m_lnode[j]].scalar_gap;
g += gj;
}
g /= el.Nodes();
a << g;
}
return true;
}
writeAverageElementValue<double>(surf, a, [=](const FEMaterialPoint& mp) {
const FEContactMaterialPoint* pt = dynamic_cast<const FEContactMaterialPoint*>(&mp);
return (pt ? pt->m_gap : 0.0);
});
return true;
}
else return false;
}
//-----------------------------------------------------------------------------
// Plot vector gap
bool FEPlotVectorGap::Save(FESurface& surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
writeElementValue<vec3d>(surf, a, [=](int nface) {
vec3d gn;
pcs->GetVectorGap(nface, gn);
return gn;
});
return true;
}
return false;
}
bool FEPlotContactPressure::SetFilter(const char* szfilter)
{
if (szfilter) m_interfaceName = szfilter;
return (szfilter != nullptr);
}
// Plot contact pressure
bool FEPlotContactPressure::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface();
bool write = false;
if (pci == nullptr) write = true;
else if (pci->IsActive())
{
if (m_interfaceName.empty() || (m_interfaceName == pci->GetName())) write = true;
}
if (write)
{
// NOTE: the sliding surface does not use material points, so we need this little hack.
FESlidingSurface* slidingSurface = dynamic_cast<FESlidingSurface*>(pcs);
if (slidingSurface)
{
for (int i = 0; i < slidingSurface->Elements(); ++i)
{
FEElement& el = slidingSurface->Element(i);
double Lm = 0.0;
for (int j = 0; j < el.Nodes(); ++j)
{
double Lmj = slidingSurface->m_data[el.m_lnode[j]].m_Ln;
Lm += Lmj;
}
Lm /= el.Nodes();
a << Lm;
}
return true;
}
writeAverageElementValue<double>(surf, a, [](const FEMaterialPoint& mp) {
const FEContactMaterialPoint* pt = dynamic_cast<const FEContactMaterialPoint*>(&mp);
return (pt ? pt->m_Ln : 0.0);
});
return true;
}
return false;
}
bool FEPlotContactTraction::SetFilter(const char* szfilter)
{
if (szfilter) m_interfaceName = szfilter;
return (szfilter != nullptr);
}
// Plot contact traction
bool FEPlotContactTraction::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface();
bool write = false;
if (pci == nullptr) write = true;
else if (pci->IsActive())
{
if (m_interfaceName.empty() || (m_interfaceName == pci->GetName())) write = true;
}
if (write)
{
writeElementValue<vec3d>(surf, a, [=](int nface) {
vec3d tn;
pcs->GetContactTraction(nface, tn);
return tn;
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot nodal contact gap
bool FEPlotNodalContactGap::Save(FESurface& surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
// NOTE: the sliding surface does not use material points, so we need this little hack.
FESlidingSurface* ss = dynamic_cast<FESlidingSurface*>(pcs);
if (ss)
{
for (int i = 0; i < ss->Elements(); ++i)
{
FEElement& el = ss->Element(i);
for (int j = 0; j < el.Nodes(); ++j)
{
double gap = ss->m_data[el.m_lnode[j]].m_gap;
a << gap;
}
}
return true;
}
writeNodalProjectedElementValues<double>(surf, a, [](const FEMaterialPoint& mp) {
const FEContactMaterialPoint* pt = dynamic_cast<const FEContactMaterialPoint*>(&mp);
return (pt ? pt->m_gap : 0.0);
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot nodal vector gap
bool FEPlotNodalVectorGap::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
int NF = pcs->Elements();
vec3d gn[FEElement::MAX_NODES];
for (int j = 0; j < NF; ++j)
{
FESurfaceElement& el = pcs->Element(j);
pcs->GetNodalVectorGap(j, gn);
// store in archive
int ne = el.Nodes();
for (int k = 0; k < ne; ++k) a << gn[k];
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot nodal contact pressure
bool FEPlotNodalContactPressure::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
writeNodalProjectedElementValues<double>(surf, a, [](const FEMaterialPoint& mp) {
const FEContactMaterialPoint* pt = dynamic_cast<const FEContactMaterialPoint*>(&mp);
return (pt ? pt->m_Ln : 0.0);
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot nodal contact traction
bool FEPlotNodalContactTraction::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
int NF = pcs->Elements();
vec3d tn[FEElement::MAX_NODES];
for (int j = 0; j < NF; ++j)
{
FESurfaceElement& el = pcs->Element(j);
pcs->GetNodalContactTraction(j, tn);
// store in archive
int ne = el.Nodes();
for (int k = 0; k < ne; ++k) a << tn[k];
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot surface traction
bool FEPlotSurfaceTraction::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
writeElementValue<vec3d>(surf, a, [=](int nface) {
vec3d tn;
pcs->GetSurfaceTraction(nface, tn);
return tn;
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot nodal contact traction
bool FEPlotNodalSurfaceTraction::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
int NF = pcs->Elements();
vec3d tn[FEElement::MAX_NODES];
for (int j = 0; j < NF; ++j)
{
FESurfaceElement& el = pcs->Element(j);
pcs->GetNodalSurfaceTraction(j, tn);
// store in archive
int ne = el.Nodes();
for (int k = 0; k < ne; ++k) a << tn[k];
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot stick status
bool FEPlotStickStatus::Save(FESurface& surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
writeElementValue<double>(surf, a, [=](int nface) {
double gn;
pcs->GetStickStatus(nface, gn);
return gn;
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotContactForce::Save(FESurface &surf, FEDataStream &a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
vec3d fn = pcs->GetContactForce();
a << fn;
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot contact area
bool FEPlotContactArea::Save(FESurface &surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
double area = pcs->GetContactArea();
a << area;
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Plot contact penalty parameter
bool FEPlotContactPenalty::Save(FESurface& surf, FEDataStream& a)
{
FEContactSurface* pcs = dynamic_cast<FEContactSurface*>(&surf);
if (pcs == 0) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = pcs->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
FEFacetSlidingSurface* ps = dynamic_cast<FEFacetSlidingSurface*>(&surf);
if (ps)
{
writeAverageElementValue<double>(surf, a, [](const FEMaterialPoint& mp) {
const FEFacetSlidingSurface::Data* pt = dynamic_cast<const FEFacetSlidingSurface::Data*>(&mp);
return (pt ? pt->m_eps : 0);
});
return true;
}
FESlidingElasticSurface* pse = dynamic_cast<FESlidingElasticSurface*>(&surf);
if (pse)
{
writeAverageElementValue<double>(surf, a, [](const FEMaterialPoint& mp) {
const FESlidingElasticSurface::Data* pt = dynamic_cast<const FESlidingElasticSurface::Data*>(&mp);
return (pt ? pt->m_epsn : 0);
});
return true;
}
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotContactStatus::Save(FESurface& surf, FEDataStream& a)
{
FEFacetSlidingSurface* ps = dynamic_cast<FEFacetSlidingSurface*>(&surf);
if (ps == nullptr) return false;
// make sure the corresponding contact interface is active
// (in case the parent was not set, we'll proceed regardless)
FEContactInterface* pci = ps->GetContactInterface(); assert(pci);
if ((pci == 0) || pci->IsActive())
{
int NF = ps->Elements();
for (int i = 0; i < NF; ++i)
{
FESurfaceElement& el = ps->Element(i);
double nc = 0.0;
int nint = el.GaussPoints();
for (int j = 0; j < nint; ++j)
{
FEContactMaterialPoint* mp = dynamic_cast<FEContactMaterialPoint*>(el.GetMaterialPoint(j));
if (mp && mp->m_pme) nc++;
}
a << nc;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotMortarContactGap::Save(FESurface& S, FEDataStream& a)
{
FEMortarSlidingSurface* ps = dynamic_cast<FEMortarSlidingSurface*>(&S);
if (ps)
{
writeNodalValues<double>(S, a, [=](int i) {
vec3d vA = ps->m_nu[i];
vec3d gA = ps->m_gap[i];
return gA*vA;
});
return true;
}
else return false;
}
//-----------------------------------------------------------------------------
bool FEPlotEnclosedVolume::Save(FESurface &surf, FEDataStream &a)
{
FESurface* pcs = &surf;
if (pcs == 0) return false;
writeIntegratedElementValue<double>(surf, a, [=](const FEMaterialPoint& mp) {
FESurfaceElement& el = static_cast<FESurfaceElement&>(*mp.m_elem);
int n = mp.m_index;
vec3d xi = pcs->Local2Global(el, n);
vec3d g[2];
pcs->CoBaseVectors(el, n, g);
return xi*(g[0] ^ g[1]) / 3;
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotEnclosedVolumeChange::Save(FESurface &surf, FEDataStream &a)
{
FESurface* pcs = &surf;
if (pcs == 0) return false;
writeIntegratedElementValue<double>(surf, a, [=](const FEMaterialPoint& mp) {
FESurfaceElement& el = static_cast<FESurfaceElement&>(*mp.m_elem);
int n = mp.m_index;
vec3d xi = pcs->Local2Global(el, n);
vec3d g[2];
pcs->CoBaseVectors(el, n, g);
vec3d Xi = pcs->Local2Global0(el, n);
vec3d G[2];
pcs->CoBaseVectors0(el, n, G);
return (xi*(g[0] ^ g[1]) - Xi*(G[0] ^ G[1])) / 3;
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotSurfaceArea::Save(FESurface &surf, FEDataStream &a)
{
FESurface* pcs = &surf;
if (pcs == 0) return false;
writeIntegratedElementValue<double>(surf, a, [=](const FEMaterialPoint& mp) {
FESurfaceElement& el = static_cast<FESurfaceElement&>(*mp.m_elem);
int n = mp.m_index;
vec3d g[2];
pcs->CoBaseVectors(el, n, g);
return (g[0] ^ g[1]).norm();
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotFacetArea::Save(FESurface& surf, FEDataStream& a)
{
FESurface* pcs = &surf;
if (pcs == 0) return false;
writeElementValue<double>(surf, a, [=](int nface) {
double A = pcs->CurrentFaceArea(pcs->Element(nface));
return A;
});
return true;
}
//-----------------------------------------------------------------------------
// Plot scalar surface load
bool FEPlotScalarSurfaceLoad::Save(FESurface &surf, FEDataStream& a)
{
FEModel* fem = GetFEModel();
int nsl = fem->ModelLoads();
FESurfaceLoad* psl = nullptr;
for (int i = 0; i<nsl; ++i)
{
psl = dynamic_cast<FESurfaceLoad*>(fem->ModelLoad(i));
if (psl && (&psl->GetSurface() == &surf)) break;
}
if (psl == nullptr) return false;
if (psl->IsActive()) {
writeAverageElementValue<double>(surf, a, [=](const FEMaterialPoint& mp) {
const FESurfaceMaterialPoint* pt = dynamic_cast<const FESurfaceMaterialPoint*>(&mp);
return (pt ? psl->ScalarLoad(*const_cast<FESurfaceMaterialPoint*>(pt)) : 0.0);
});
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotNetSurfaceReactionForce::Save(FESurface& surf, FEDataStream& a)
{
// NOTE: Currently, for nodes attached to rigid bodies the reaction forces
// will actually be the rigid reaction forces.
FEModel& fem = *GetFEModel();
int dofX = fem.GetDOFIndex("x");
int dofY = fem.GetDOFIndex("y");
int dofZ = fem.GetDOFIndex("z");
if ((dofX < 0) || (dofY < 0) || (dofZ < 0)) return false;
vec3d F(0, 0, 0);
for (int i = 0; i < surf.Nodes(); ++i)
{
FENode& n = surf.Node(i);
vec3d Fi = n.get_load3(dofX, dofY, dofZ);
F += Fi;
}
a << F;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotNetSurfaceReactionMoment::Save(FESurface& surf, FEDataStream& a)
{
// NOTE: Currently, for nodes attached to rigid bodies the reaction forces
// will actually be the rigid reaction forces.
FEModel& fem = *GetFEModel();
int dofX = fem.GetDOFIndex("x");
int dofY = fem.GetDOFIndex("y");
int dofZ = fem.GetDOFIndex("z");
if ((dofX < 0) || (dofY < 0) || (dofZ < 0)) return false;
vec3d M(0, 0, 0);
for (int i = 0; i < surf.Nodes(); ++i)
{
FENode& n = surf.Node(i);
vec3d Fi = n.get_load3(dofX, dofY, dofZ);
vec3d r = n.m_rt;
vec3d Mi = r ^ Fi;
M += Mi;
}
a << M;
return true;
}
//=============================================================================
// D O M A I N D A T A
//=============================================================================
//-----------------------------------------------------------------------------
bool FEPlotElementVelocity::Save(FEDomain &dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<vec3d>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.m_v;
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotElementAcceleration::Save(FEDomain &dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<vec3d>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.m_a;
});
return true;
}
//=============================================================================
class FEStress
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
return (pt ? pt->m_s : mat3ds(0));
}
};
class FEStrain
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
FEElement* el = mp.m_elem;
FEShellElementNew* se = dynamic_cast<FEShellElementNew*>(el);
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (se) return (se->m_E[mp.m_index].norm() > 0) ? se->m_E[mp.m_index] : pt->Strain();
else return (pt ? pt->Strain() : mat3ds(0));
}
};
//-----------------------------------------------------------------------------
//! Store the average stresses for each element.
bool FEPlotElementStress::Save(FEDomain& dom, FEDataStream& a)
{
FEDomainParameter* var = nullptr;
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if (pme)
{
if (!pme->IsRigid())
var = pme->FindDomainParameter("stress");
}
else var = dom.GetMaterial()->FindDomainParameter("stress");
if (var == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, var);
return true;
}
//-----------------------------------------------------------------------------
//! Store the average stresses for each element.
bool FEPlotElementPK2Stress::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& ep = *mp.ExtractData< FEElasticMaterialPoint>();
mat3ds s = ep.m_s;
mat3ds S = ep.pull_back(s);
return S;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the average PK1 stress for each element.
bool FEPlotElementPK1Stress::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<mat3d>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& ep = *mp.ExtractData< FEElasticMaterialPoint>();
mat3d F = ep.m_F;
double J = F.det();
mat3ds s = ep.m_s; // Cauchy stress
mat3d P = (s * F.transinv()) * J;
return P;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the average element plastic yield stress
bool FEPlotElementPlasticYieldStress::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
FEReactivePlasticity* pmp = pme->ExtractProperty<FEReactivePlasticity>();
if (pmp == nullptr) return false;
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEReactivePlasticityMaterialPoint& pp = *mp.ExtractData<FEReactivePlasticityMaterialPoint>();
if (pp.m_Kv.size() > 0) return pp.m_Kv[0];
return 0.0;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the average element yield stress based on Drucker shear stress criterion
bool FEPlotElementDruckerShear::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
FEDamageCriterionDrucker* pmd = pme->ExtractProperty<FEDamageCriterionDrucker>();
if (pmd == nullptr) return false;
writeAverageElementValue<double>(dom, a, [&pmd](const FEMaterialPoint& mp) {
double c = pmd->m_c(mp);
const FEElasticMaterialPoint& ep = *mp.ExtractData< FEElasticMaterialPoint>();
mat3ds s = ep.m_s; // Cauchy stress
mat3ds sdev = s.dev();
double J2 = 0.5*(sdev*sdev).trace();
double J3 = sdev.det();
double k = pow(pow(J2,3) - c*pow(J3,2),1./6.);
return k;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the average element yield stress based on Prager-Drucker criterion
bool FEPlotElementPragerDruckerStress::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
FEDamageCriterionDruckerPrager* pmd = pme->ExtractProperty<FEDamageCriterionDruckerPrager>();
if (pmd == nullptr) return false;
writeAverageElementValue<double>(dom, a, [&pmd](const FEMaterialPoint& mp) {
double b = pmd->m_b(mp);
const FEElasticMaterialPoint& ep = *mp.ExtractData< FEElasticMaterialPoint>();
mat3ds s = ep.m_s; // Cauchy stress
double se = sqrt((pow(s.xx()-s.yy(),2) + pow(s.yy()-s.zz(),2) + pow(s.zz()-s.xx(),2)
+ 6*(pow(s.xy(),2) + pow(s.yz(),2) + pow(s.xz(),2)))/2);
double sm = s.tr()/3;
double Phi = se - b*sm;
return Phi;
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the average element yield stress based on Deshpande-Fleck criterion
bool FEPlotElementDeshpandeFleckStress::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
FEDamageCriterionDeshpandeFleck* pmd = pme->ExtractProperty<FEDamageCriterionDeshpandeFleck>();
if (pmd == nullptr) return false;
writeAverageElementValue<double>(dom, a, [&pmd](const FEMaterialPoint& mp) {
double beta = pmd->m_beta(mp);
const FEElasticMaterialPoint& ep = *mp.ExtractData< FEElasticMaterialPoint>();
mat3ds s = ep.m_s; // Cauchy stress
double se = sqrt((pow(s.xx()-s.yy(),2) + pow(s.yy()-s.zz(),2) + pow(s.zz()-s.xx(),2)
+ 6*(pow(s.xy(),2) + pow(s.yz(),2) + pow(s.xz(),2)))/2);
double sm = s.tr()/3;
double Phi = sqrt((se*se+pow(3*beta*sm,2))/(1+beta*beta));
return Phi;
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotSPRStresses::Save(FEDomain& dom, FEDataStream& a)
{
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
// get the domain
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeSPRElementValueMat3ds(sd, a, FEStress());
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotSPRLinearStresses::Save(FEDomain& dom, FEDataStream& a)
{
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
// get the domain
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeSPRElementValueMat3ds(sd, a, FEStress(), 1);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotNodalStresses::Save(FEDomain& dom, FEDataStream& a)
{
if (dynamic_cast<FESSIShellDomain*>(&dom)) return false; // new shell elements should be excluded
writeNodalProjectedElementValues<mat3ds>(dom, a, FEStress());
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellTopStress::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellElementValues<mat3ds>(dom, a, FEStress(), false);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellBottomStress::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellElementValues<mat3ds>(dom, a, FEStress(), true);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellTopNodalStresses::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellNodalProjectedElementValues<mat3ds>(dom, a, FEStress(), false);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellBottomNodalStresses::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellNodalProjectedElementValues<mat3ds>(dom, a, FEStress(), true);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotNodalStrains::Save(FEDomain& dom, FEDataStream& a)
{
if (dynamic_cast<FESSIShellDomain*>(&dom)) return false; // new shell elements should be excluded
writeNodalProjectedElementValues<mat3ds>(dom, a, FEStrain());
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellTopStrain::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellElementValues<mat3ds>(dom, a, FEStrain(), false);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellBottomStrain::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellElementValues<mat3ds>(dom, a, FEStrain(), true);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellTopNodalStrains::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellNodalProjectedElementValues<mat3ds>(dom, a, FEStrain(), false);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotShellBottomNodalStrains::Save(FEDomain& dom, FEDataStream& a)
{
if (!dynamic_cast<FESSIShellDomain*>(&dom)) return false; // only use with new shell elements
writeShellNodalProjectedElementValues<mat3ds>(dom, a, FEStrain(), true);
return true;
}
//=============================================================================
FEPlotElementMixtureStress::FEPlotElementMixtureStress(FEModel* pfem) : FEPlotDomainData(pfem, PLT_MAT3FS, FMT_ITEM)
{
m_mat = -1;
m_comp = -1;
SetUnits(UNIT_PRESSURE);
}
bool FEPlotElementMixtureStress::SetFilter(const char* szfilter)
{
if (strncmp(szfilter, "material", 8) == 0)
{
if (sscanf(szfilter, "material[%d].solid[%d]", &m_mat, &m_comp) != 2) return false;
}
else
{
if (sscanf(szfilter, "solid[%d]", &m_comp) != 1) return false;
}
return true;
}
bool FEPlotElementMixtureStress::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* pm = dom.GetMaterial();
if (m_mat != -1)
{
if (pm != GetFEModel()->GetMaterial(m_mat)) return false;
}
// make sure we start from the elastic component
FEElasticMaterial* pmat = pm->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
// make sure this is a mixture
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if ((pmm == nullptr) && (pum == nullptr)) return false;
// get the mixture component
if (m_comp < 0) return false;
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
mat3ds savg; savg.zero();
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
FEElasticMaterialPoint& ep = *mmp->GetPointData(m_comp)->ExtractData<FEElasticMaterialPoint>();
savg += ep.m_s;
}
}
savg /= (double)el.GaussPoints();
a << savg;
}
return true;
}
//=============================================================================
//! Store the uncoupled pressure for each element.
bool FEPlotElementUncoupledPressure::Save(FEDomain& dom, FEDataStream& a)
{
FEUncoupledMaterial* pmu = dom.GetMaterial()->ExtractProperty<FEUncoupledMaterial>();
if (pmu == 0) return false;
// write element data
writeAverageElementValue<double>(dom, a, [=](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return 0.0;
return -pt->m_p; // use negative sign to get positive pressure in compression
});
return true;
}
//-----------------------------------------------------------------------------
//! Store the norm of the average Cauchy stress for each element.
bool FEPlotElementsnorm::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<mat3ds, double>(dom, a, FEStress(), [](const mat3ds& s) { return sqrt(s.dotdot(s)); });
return true;
}
//-----------------------------------------------------------------------------
//! Store the average elasticity for each element.
class FEElementElasticity
{
public:
FEElementElasticity(FESolidMaterial* pm) : m_mat(pm) {}
tens4ds operator()(const FEMaterialPoint& mp)
{
return m_mat->Tangent(const_cast<FEMaterialPoint&>(mp));
}
private:
FESolidMaterial* m_mat;
};
bool FEPlotElementElasticity::Save(FEDomain& dom, FEDataStream& a)
{
FESolidMaterial* pme = dom.GetMaterial()->ExtractProperty<FESolidMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<tens4ds>(dom, a, FEElementElasticity(pme));
return true;
}
//-----------------------------------------------------------------------------
//! Store the average deviatoric elasticity for each element.
class FEElementDevElasticity
{
public:
FEElementDevElasticity(FEUncoupledMaterial* pm) : m_mat(pm) {}
tens4ds operator()(const FEMaterialPoint& mp)
{
return m_mat->DevTangent(const_cast<FEMaterialPoint&>(mp));
}
private:
FEUncoupledMaterial* m_mat;
};
bool FEPlotElementDevElasticity::Save(FEDomain& dom, FEDataStream& a)
{
FEUncoupledMaterial* pme = dom.GetMaterial()->ExtractProperty<FEUncoupledMaterial>();
if ((pme == 0) || pme->IsRigid()) return false;
writeAverageElementValue<tens4ds>(dom, a, FEElementDevElasticity(pme));
return true;
}
//-----------------------------------------------------------------------------
class FEStrainEnergy
{
public:
FEStrainEnergy(FEElasticMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->StrainEnergyDensity(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotStrainEnergyDensity::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEStrainEnergy W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEDevStrainEnergy
{
public:
FEDevStrainEnergy(FEUncoupledMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->DevStrainEnergyDensity(const_cast<FEMaterialPoint&>(mp));
}
private:
FEUncoupledMaterial* m_mat;
};
bool FEPlotDevStrainEnergyDensity::Save(FEDomain &dom, FEDataStream& a)
{
FEUncoupledMaterial* pmu = dom.GetMaterial()->ExtractProperty<FEUncoupledMaterial>();
if (pmu == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEDevStrainEnergy devW(pmu);
writeAverageElementValue<double>(dom, a, devW);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FESpecificStrainEnergy
{
public:
FESpecificStrainEnergy(FEElasticMaterial* pm, int comp) : m_mat(pm), m_comp(comp) {}
double operator()(const FEMaterialPoint& mp)
{
if (dynamic_cast<FERemodelingInterface*>(m_mat) == 0) return 0;
FEMaterialPoint& lmp = const_cast<FEMaterialPoint&>(mp);
FERemodelingMaterialPoint* rpt = lmp.ExtractData<FERemodelingMaterialPoint>();
if (rpt == nullptr) {
FEMaterialPoint* pt = lmp.ExtractData<FEElasticMixtureMaterialPoint>()->GetPointData(m_comp);
rpt = pt->ExtractData<FERemodelingMaterialPoint>();
}
return (((rpt != nullptr) && (rpt->m_rhor > 0)) ? rpt->m_sed / rpt->m_rhor : 0.0);
}
private:
FEElasticMaterial* m_mat;
int m_comp;
};
bool FEPlotSpecificStrainEnergy::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESpecificStrainEnergy w(pme, -1);
writeAverageElementValue<double>(dom, a, w);
return true;
}
return false;
}
//=============================================================================
FEPlotMixtureStrainEnergyDensity::FEPlotMixtureStrainEnergyDensity(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_mat = -1;
m_comp = -1;
SetUnits(UNIT_PRESSURE);
}
bool FEPlotMixtureStrainEnergyDensity::SetFilter(const char* szfilter)
{
if (strncmp(szfilter, "material", 8) == 0)
{
if (sscanf(szfilter, "material[%d].solid[%d]", &m_mat, &m_comp) != 2) return false;
}
else
{
if (sscanf(szfilter, "solid[%d]", &m_comp) != 1) return false;
}
return true;
}
bool FEPlotMixtureStrainEnergyDensity::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* pm = dom.GetMaterial();
if (m_mat != -1)
{
if (pm != GetFEModel()->GetMaterial(m_mat)) return false;
}
// make sure we start from the elastic component
FEElasticMaterial* pmat = pm->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
// make sure this is a mixture
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if ((pmm == nullptr) && (pum == nullptr)) return false;
// get the mixture component
if (m_comp < 0) return false;
FEElasticMaterial* pme = nullptr;
if (pmm) pme = pmm->GetMaterial(m_comp);
else if (pum) pme = pum->GetMaterial(m_comp);
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEStrainEnergy W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//=============================================================================
FEPlotMixtureDevStrainEnergyDensity::FEPlotMixtureDevStrainEnergyDensity(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_mat = -1;
m_comp = -1;
SetUnits(UNIT_PRESSURE);
}
bool FEPlotMixtureDevStrainEnergyDensity::SetFilter(const char* szfilter)
{
if (strncmp(szfilter, "material", 8) == 0)
{
if (sscanf(szfilter, "material[%d].solid[%d]", &m_mat, &m_comp) != 2) return false;
}
else
{
if (sscanf(szfilter, "solid[%d]", &m_comp) != 1) return false;
}
return true;
}
bool FEPlotMixtureDevStrainEnergyDensity::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* pm = dom.GetMaterial();
if (m_mat != -1)
{
if (pm != GetFEModel()->GetMaterial(m_mat)) return false;
}
// make sure we start from the elastic component
FEElasticMaterial* pmat = pm->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
// make sure this is a mixture
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if (pum == nullptr) return false;
// get the mixture component
if (m_comp < 0) return false;
FEElasticMaterial* pme = pum->GetMaterial(m_comp);
FEUncoupledMaterial* pmu = pme->ExtractProperty<FEUncoupledMaterial>();
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEDevStrainEnergy devW(pmu);
writeAverageElementValue<double>(dom, a, devW);
return true;
}
return false;
}
//=============================================================================
FEPlotMixtureSpecificStrainEnergy::FEPlotMixtureSpecificStrainEnergy(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_mat = -1;
m_comp = -1;
SetUnits(UNIT_SPECIFIC_ENERGY);
}
bool FEPlotMixtureSpecificStrainEnergy::SetFilter(const char* szfilter)
{
if (strncmp(szfilter, "material", 8) == 0)
{
if (sscanf(szfilter, "material[%d].solid[%d]", &m_mat, &m_comp) != 2) return false;
}
else
{
if (sscanf(szfilter, "solid[%d]", &m_comp) != 1) return false;
}
return true;
}
bool FEPlotMixtureSpecificStrainEnergy::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* pm = dom.GetMaterial();
if (m_mat != -1)
{
if (pm != GetFEModel()->GetMaterial(m_mat)) return false;
}
// make sure we start from the elastic component
FEElasticMaterial* pmat = pm->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
// make sure this is a mixture
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if ((pmm == nullptr) && (pum == nullptr)) return false;
// get the mixture component
if (m_comp < 0) return false;
FEElasticMaterial* pme = nullptr;
if (pmm) pme = pmm->GetMaterial(m_comp);
else if (pum) pme = pum->GetMaterial(m_comp);
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESpecificStrainEnergy w(pme, m_comp);
writeAverageElementValue<double>(dom, a, w);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotKineticEnergyDensity::Save(FEDomain &dom, FEDataStream& a)
{
const int dof_VX = GetFEModel()->GetDOFIndex("vx");
const int dof_VY = GetFEModel()->GetDOFIndex("vy");
const int dof_VZ = GetFEModel()->GetDOFIndex("vz");
const int dof_VU = GetFEModel()->GetDOFIndex("vu");
const int dof_VV = GetFEModel()->GetDOFIndex("vv");
const int dof_VW = GetFEModel()->GetDOFIndex("vw");
FEMesh& mesh = *dom.GetMesh();
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i=0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double *H;
double* gw = el.GaussWeights();
// get nodal velocities
vec3d vt[FEElement::MAX_NODES];
vec3d vn[FEElement::MAX_NODES];
for (int j=0; j<el.Nodes(); ++j) {
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
{
H = el.H(j);
vn[j] = vec3d(0, 0, 0);
for (int k=0; k<el.Nodes(); ++k)
vn[j] += vt[k]*H[k];
}
// integrate kinetic energy
double ew = 0;
double V = 0;
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j];
V += detJ;
ew += vn[j]*vn[j]*(pme->Density(mp)/2*detJ);
}
a << ew/V;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i=0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
double ew = 0.0;
if ((dof_VU >= 0) && (dof_VV >= 0) && (dof_VW >= 0))
{
// get nodal velocities
vec3d vt[FEElement::MAX_NODES];
vec3d wt[FEElement::MAX_NODES];
vec3d vn[FEElement::MAX_NODES];
for (int j = 0; j < el.Nodes(); ++j) {
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
wt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VU, dof_VV, dof_VW);
}
// evaluate velocities at integration points
for (int j = 0; j < el.GaussPoints(); ++j)
vn[j] = bd->evaluate(el, vt, wt, j);
// integrate kinetic energy
double ew = 0;
double V = 0;
for (int j = 0; j < el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j) * gw[j];
V += detJ;
ew += vn[j] * vn[j] * (pme->Density(mp) / 2 * detJ);
}
// normalize by volume
ew /= V;
}
a << ew;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// TODO: Should I call the density for remodeling materials something else?
// Or maybe the FEElasticMaterialPoint should define a density parameter
// that will be updated by the materials to define the current density?
class FEDensity
{
public:
FEDensity(FEElasticMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
double J = ep.m_F.det();
return m_mat->Density(const_cast<FEMaterialPoint&>(mp)) / J;
}
private:
FEElasticMaterial* m_mat;
};
class FERemodelingDensity
{
public:
double operator()(const FEMaterialPoint& mp)
{
const FERemodelingMaterialPoint* pt = (mp.ExtractData<FERemodelingMaterialPoint>());
return (pt ? pt->m_rhor : 0.0);
}
};
bool FEPlotDensity::Save(FEDomain &dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
FEElasticMaterial* em = bd.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (em == 0) return false;
FERemodelingElasticMaterial* rm = dynamic_cast<FERemodelingElasticMaterial*>(em);
if (rm)
{
FERemodelingDensity dens;
writeAverageElementValue<double>(dom, a, dens);
return true;
}
else
{
FEDensity dens(em);
writeAverageElementValue<double>(dom, a, dens);
return true;
}
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FEElasticMaterial* em = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (em == 0) return false;
FEDensity dens(em);
writeAverageElementValue<double>(dom, a, dens);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotElementStrainEnergy::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<double>(bd, a, FEStrainEnergy(pme));
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
writeIntegratedElementValue(*bd, a, FEStrainEnergy(pme));
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// integrated element kinetic energy
class FEKineticEnergyDensity
{
public:
FEKineticEnergyDensity(FEElasticMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& ep = *(mp.ExtractData<FEElasticMaterialPoint>());
return 0.5*(ep.m_v*ep.m_v)*m_mat->Density(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotElementKineticEnergy::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<double>(bd, a, FEKineticEnergyDensity(pme));
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
writeIntegratedElementValue(*bd, a, FEKineticEnergyDensity(pme));
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotElementCenterOfMass::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i = 0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double* gw = el.GaussWeights();
// integrate zeroth and first mass moments
vec3d ew = vec3d(0, 0, 0);
double m = 0;
for (int j = 0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j];
ew += mp.m_rt*(pme->Density(mp)*detJ);
m += pme->Density(mp)*detJ;
}
a << ew / m;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i = 0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
// integrate zeroth and first mass moments
vec3d ew = vec3d(0, 0, 0);
double m = 0;
for (int j = 0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& pt = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j)*gw[j];
ew += pt.m_rt*(pme->Density(pt)*detJ);
m += pme->Density(pt)*detJ;
}
a << ew / m;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEElementLinearMomentum
{
public:
FEElementLinearMomentum(FEElasticMaterial* pm) : m_mat(pm) {}
vec3d operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& pt = *(mp.ExtractData<FEElasticMaterialPoint>());
return pt.m_v*m_mat->Density(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotElementLinearMomentum::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<vec3d>(bd, a, FEElementLinearMomentum(pme));
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
writeIntegratedElementValue(*bd, a, FEElementLinearMomentum(pme));
return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Integrated element angular momentum
class FEElementAngularMomentum
{
public:
FEElementAngularMomentum(FEElasticMaterial* pm) : m_mat(pm) {}
vec3d operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& pt = *(mp.ExtractData<FEElasticMaterialPoint>());
return (mp.m_rt ^ pt.m_v)*m_mat->Density(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotElementAngularMomentum::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<vec3d>(bd, a, FEElementAngularMomentum(pme));
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
writeIntegratedElementValue(*bd, a, FEElementAngularMomentum(pme));
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEElementStressPower
{
public:
double operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
return ep.m_s.dotdot(ep.m_L.sym())*ep.m_J;
}
};
bool FEPlotElementStressPower::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<double>(bd, a, FEElementStressPower());
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
writeIntegratedElementValue(*bd, a, FEElementStressPower());
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FECurrentElementStrainEnergy
{
public:
double operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
return ep.m_Wt;
}
};
bool FEPlotCurrentElementStrainEnergy::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
writeIntegratedElementValue<double>(bd, a, FECurrentElementStrainEnergy());
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
writeIntegratedElementValue(*bd, a, FECurrentElementStrainEnergy());
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotCurrentElementKineticEnergy::Save(FEDomain &dom, FEDataStream& a)
{
const int dof_VX = GetFEModel()->GetDOFIndex("vx");
const int dof_VY = GetFEModel()->GetDOFIndex("vy");
const int dof_VZ = GetFEModel()->GetDOFIndex("vz");
const int dof_VU = GetFEModel()->GetDOFIndex("vu");
const int dof_VV = GetFEModel()->GetDOFIndex("vv");
const int dof_VW = GetFEModel()->GetDOFIndex("vw");
FEMesh& mesh = *dom.GetMesh();
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
const int NELN = FEElement::MAX_NODES;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i=0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d vt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j)
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
vn[j] = el.Evaluate(vt, j);
// integrate kinetic energy
double ew = 0;
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j]* pme->Density(mp)/2;
ew += vn[j]*vn[j]*detJ;
}
a << ew;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i=0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d vt[NELN], wt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
wt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VU, dof_VV, dof_VW);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
vn[j] = bd->evaluate(el, vt, wt, j);
// integrate kinetic energy
double ew = 0;
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j)*gw[j]* pme->Density(mp)/2;
ew += vn[j]*vn[j]*detJ;
}
a << ew;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotCurrentElementCenterOfMass::Save(FEDomain &dom, FEDataStream& a)
{
FEMesh& mesh = *dom.GetMesh();
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
const int NELN = FEElement::MAX_NODES;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i=0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double* gw = el.GaussWeights();
// get nodal positions and velocities
vec3d rt[NELN], rn[NELN];
for (int j=0; j<el.Nodes(); ++j)
rt[j] = mesh.Node(el.m_node[j]).m_rt;
// evaluate positions at integration points
for (int j=0; j<el.GaussPoints(); ++j)
rn[j] = el.Evaluate(rt, j);
// integrate zeroth and first mass moment
double ez = 0;
vec3d ef = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j]* pme->Density(mp);
ez += detJ;
ef += rn[j]*detJ;
}
a << ef/ez;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i=0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d rt[NELN], st[NELN], rn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
rt[j] = mesh.Node(el.m_node[j]).m_rt;
st[j] = mesh.Node(el.m_node[j]).st();
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
rn[j] = bd->evaluate(el, rt, st, j);
// integrate zeroth and first mass moment
double ez = 0;
vec3d ef = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j)*gw[j]* pme->Density(mp);
ez += detJ;
ef += rn[j]*detJ;
}
a << ef/ez;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotCurrentElementLinearMomentum::Save(FEDomain &dom, FEDataStream& a)
{
const int dof_VX = GetFEModel()->GetDOFIndex("vx");
const int dof_VY = GetFEModel()->GetDOFIndex("vy");
const int dof_VZ = GetFEModel()->GetDOFIndex("vz");
const int dof_VU = GetFEModel()->GetDOFIndex("vu");
const int dof_VV = GetFEModel()->GetDOFIndex("vv");
const int dof_VW = GetFEModel()->GetDOFIndex("vw");
FEMesh& mesh = *dom.GetMesh();
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
const int NELN = FEElement::MAX_NODES;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i=0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d vt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
vn[j] = el.Evaluate(vt, j);
// integrate linear momentum
vec3d ew = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j];
ew += vn[j]*(pme->Density(mp)*detJ);
}
a << ew;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i=0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d vt[NELN], wt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
wt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VU, dof_VV, dof_VW);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j)
vn[j] = bd->evaluate(el, vt, wt, j);
// integrate linear momentum
vec3d ew = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j)*gw[j];
ew += vn[j]*(pme->Density(mp)*detJ);
}
a << ew;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotCurrentElementAngularMomentum::Save(FEDomain &dom, FEDataStream& a)
{
const int dof_VX = GetFEModel()->GetDOFIndex("vx");
const int dof_VY = GetFEModel()->GetDOFIndex("vy");
const int dof_VZ = GetFEModel()->GetDOFIndex("vz");
const int dof_SVX = GetFEModel()->GetDOFIndex("svx");
const int dof_SVY = GetFEModel()->GetDOFIndex("svy");
const int dof_SVZ = GetFEModel()->GetDOFIndex("svz");
FEMesh& mesh = *dom.GetMesh();
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
const int NELN = FEElement::MAX_NODES;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& bd = static_cast<FESolidDomain&>(dom);
for (int i=0; i<bd.Elements(); ++i)
{
FESolidElement& el = bd.Element(i);
double* gw = el.GaussWeights();
// get nodal positions and velocities
vec3d rt[NELN], rn[NELN];
vec3d vt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
rt[j] = mesh.Node(el.m_node[j]).m_rt;
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j) {
rn[j] = el.Evaluate(rt, j);
vn[j] = el.Evaluate(vt, j);
}
// integrate angular momentum
vec3d ew = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd.detJ0(el, j)*gw[j];
ew += (rn[j] ^ vn[j])*(pme->Density(mp)*detJ);
}
a << ew;
}
return true;
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
if (bd == 0) return false;
for (int i=0; i<bd->Elements(); ++i)
{
FEShellElement& el = bd->Element(i);
double* gw = el.GaussWeights();
// get nodal velocities
vec3d rt[NELN], st[NELN], rn[NELN];
vec3d vt[NELN], wt[NELN], vn[NELN];
for (int j=0; j<el.Nodes(); ++j) {
rt[j] = mesh.Node(el.m_node[j]).m_rt;
st[j] = mesh.Node(el.m_node[j]).st();
vt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_VX, dof_VY, dof_VZ);
wt[j] = mesh.Node(el.m_node[j]).get_vec3d(dof_SVX, dof_SVY, dof_SVZ);
}
// evaluate velocities at integration points
for (int j=0; j<el.GaussPoints(); ++j) {
rn[j] = bd->evaluate(el, rt, st, j);
vn[j] = bd->evaluate(el, vt, wt, j);
}
// integrate angular momentum
vec3d ew = vec3d(0,0,0);
for (int j=0; j<el.GaussPoints(); ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
double detJ = bd->detJ0(el, j)*gw[j];
ew += (rn[j] ^ vn[j])*(pme->Density(mp)*detJ);
}
a << ew;
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotRelativeVolume::Save(FEDomain &dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
return (pt ? pt->m_J : 0.0);
});
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom); assert(sd);
// a filter to get J from a strain tensor
auto getJfromE = [](const mat3ds& E) {
mat3ds C = mat3dd(1) + E * 2;
return sqrt(C.det());
};
FEShellDomainNew* newsd = dynamic_cast<FEShellDomainNew*>(sd);
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(newsd);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(newsd);
if (easd || ansd) {
writeAverageElementValue<mat3ds, double>(dom, a, [](FEElement& el, int ip) {
FEShellElementNew& se = static_cast<FEShellElementNew&>(el);
return se.m_E[ip];
}, getJfromE);
}
else {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
return (pt ? pt->m_J : 0.0);
});
}
return true;
}
else return false;
return true;
}
bool FEPlotSPRRelativeVolume::Save(FEDomain& dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FESolidDomain& solidDomain = dynamic_cast<FESolidDomain&>(dom);
writeSPRElementValue(solidDomain, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
return (pt ? pt->m_J : 0.0);
});
return true;
}
return false;
}
bool FEPlotShellRelativeVolume::Save(FEDomain& dom, FEDataStream& a)
{
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom);
if (sd == nullptr) return false;
// a filter to get J from a strain tensor
auto getJfromE = [](const mat3ds& E) {
mat3ds C = mat3dd(1) + E * 2;
return sqrt(C.det());
};
FEShellDomainNew* newsd = dynamic_cast<FEShellDomainNew*>(sd);
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(newsd);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(newsd);
if (easd || ansd) {
writeAverageElementValue<mat3ds, double>(dom, a, [](FEElement& el, int ip) {
FEShellElementNew& se = static_cast<FEShellElementNew&>(el);
return se.m_E[ip];
}, getJfromE);
}
else {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
return (pt ? pt->m_J : 0.0);
});
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotFiberStretch::SetFilter(const char* szfilter)
{
m_matComp = szfilter;
return true;
}
bool FEPlotFiberStretch::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (m_matComp.empty() == false)
{
pme = dynamic_cast<FEElasticMaterial*>(pme->GetProperty(m_matComp.c_str()));
if (pme == nullptr) return false;
}
// get the fiber property
FEVec3dValuator* vec = dynamic_cast<FEVec3dValuator*>(pme->GetProperty("fiber"));
if (vec == 0) return false;
if (dom.Class() != FE_DOMAIN_SOLID) return false;
writeAverageElementValue<double>(dom, a, [&](const FEMaterialPoint& mp) -> double {
const FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d Q = pme->GetLocalCS(mp);
vec3d a0 = vec->unitVector(mp);
vec3d ar = Q * a0;
mat3d F = ep.m_F;
vec3d a = F*ar;
return a.norm();
});
return true;
}
//-----------------------------------------------------------------------------
class FEFiberVector
{
public:
FEFiberVector(FEMaterial* pm, FEVec3dValuator& vec) : m_pm(pm), m_vec(vec) {}
vec3d operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<const FEElasticMaterialPoint>();
if (pt)
{
mat3d Q = m_pm->GetLocalCS(mp);
mat3d F = pt->m_F;
vec3d a0 = m_vec.unitVector(mp);
vec3d ar = Q * a0;
vec3d a = F * ar; a.unit();
return a;
}
else
return m_vec(mp);
}
private:
FEMaterial* m_pm;
FEVec3dValuator& m_vec;
};
FEPlotFiberVector::FEPlotFiberVector(FEModel* pfem) : FEPlotDomainData(pfem, PLT_VEC3F, FMT_ITEM)
{
}
bool FEPlotFiberVector::SetFilter(const char* szfilter)
{
m_matComp = szfilter;
return true;
}
bool FEPlotFiberVector::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (m_matComp.empty() == false)
{
pme = dynamic_cast<FEElasticMaterial*>(pme->GetProperty(m_matComp.c_str()));
if (pme == nullptr) return false;
}
// get the fiber property
FEVec3dValuator* vec = dynamic_cast<FEVec3dValuator*>(pme->GetProperty("fiber"));
if (vec == 0) return false;
writeAverageElementValue<vec3d, vec3d>(dom, a, FEFiberVector(pme, *vec), [](const vec3d& r) -> vec3d { vec3d n(r); n.unit(); return n; });
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotMaterialAxes::SetFilter(const char* szfilter)
{
m_matComp = szfilter;
return true;
}
bool FEPlotMaterialAxes::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (m_matComp.empty() == false)
{
pme = dynamic_cast<FEElasticMaterial*>(pme->GetProperty(m_matComp.c_str()));
if (pme == nullptr) return false;
}
int BE = dom.Elements();
for (int i = 0; i<BE; ++i)
{
FEElement& el = dom.ElementRef(i);
// I cannot average the material axes since the average may not be orthogonal
// Until I find a better option, I'll just export the first integration point.
FEMaterialPoint& mp = *el.GetMaterialPoint(0);
mat3d Q = pme->GetLocalCS(mp);
a << Q;
}
return true;
}
//-----------------------------------------------------------------------------
// TODO: The factor Jm13 is not used. This doesn't look correct
class FEDevFiberStretch
{
public:
FEDevFiberStretch(FEElasticMaterial* mat) : m_mat(mat) {}
public:
double operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d Q = m_mat->GetLocalCS(mp);
// get the material fiber axis
vec3d r0 = Q.col(0);
// apply deformation
vec3d r = pt.m_F*r0;
// calculate the deviatoric fiber stretch
double lam = r.norm();
return lam;
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotDevFiberStretch::SetFilter(const char* szfilter)
{
m_matComp = szfilter;
return true;
}
bool FEPlotDevFiberStretch::Save(FEDomain &dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (m_matComp.empty() == false)
{
pme = dynamic_cast<FEElasticMaterial*>(pme->GetProperty(m_matComp.c_str()));
if (pme == nullptr) return false;
}
if (dom.Class() != FE_DOMAIN_SOLID) return false;
FEDevFiberStretch lam(pme);
writeAverageElementValue<double>(dom, a, lam);
return true;
}
//=============================================================================
// Principal components of stress
class FEPrincStresses
{
public:
mat3dd operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
const mat3ds& s = ep.m_s;
double l[3];
s.exact_eigen(l);
return mat3dd(l[0], l[1], l[2]);
}
};
bool FEPlotSPRPrincStresses::Save(FEDomain& dom, FEDataStream& a)
{
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
// get the domain
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeSPRElementValueMat3dd(sd, a, FEPrincStresses());
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotDeformationGradient::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3d>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.m_F;
});
return true;
}
//=============================================================================
//! Store the average Lagrangian strain
class FELagrangeStrain
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d C = pt->RightCauchyGreen();
mat3ds E = ((C - mat3dd(1.0))*0.5).sym();
return E;
}
};
//-----------------------------------------------------------------------------
bool FEPlotLagrangeStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.Strain();
});
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom); assert(sd);
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(&dom);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(&dom);
if (easd || ansd)
{
writeAverageElementValue<mat3ds>(dom, a, [](FEElement& el, int ip) {
FEShellElementNew& se = static_cast<FEShellElementNew&>(el);
return se.m_E[ip];
});
}
else
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.Strain();
});
}
}
else return false;
return true;
}
bool FEPlotShellStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom);
if (sd == nullptr) return false;
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(&dom);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(&dom);
if (easd || ansd)
{
writeAverageElementValue<mat3ds>(dom, a, [](FEElement& el, int ip) {
FEShellElementNew& se = static_cast<FEShellElementNew&>(el);
return se.m_E[ip];
});
}
else
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
return pt.Strain();
});
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotInfStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// displacement tensor
mat3d U = pt.m_F - mat3dd(1.0);
// evaluate small strain tensor eij = 0.5*(Uij + Uji)
mat3ds e = U.sym();
return e;
});
}
else return false;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotSPRLagrangeStrain::Save(FEDomain& dom, FEDataStream& a)
{
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeSPRElementValueMat3ds(sd, a, FELagrangeStrain());
return true;
}
bool FEPlotSPRInfStrain::Save(FEDomain& dom, FEDataStream& a)
{
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeSPRElementValueMat3ds(sd, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// displacement tensor
mat3d U = pt.m_F - mat3dd(1.0);
// evaluate small strain tensor eij = 0.5*(Uij + Uji)
mat3ds e = U.sym();
return e;
});
return true;
}
//=============================================================================
//! Store the average Almansi tensor
class FEAlmansiStrain
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->AlmansiStrain();
}
};
//-----------------------------------------------------------------------------
bool FEPlotAlmansiStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FEAlmansiStrain());
return true;
}
//=============================================================================
//! Store the average right Cauchy Green tensor
class FERightCauchyGreen
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->RightCauchyGreen();
}
};
//-----------------------------------------------------------------------------
bool FEPlotRightCauchyGreen::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FERightCauchyGreen());
return true;
}
//=============================================================================
//! Store the average left Cauchy Green tensor
class FELeftCauchyGreen
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->LeftCauchyGreen();
}
};
//-----------------------------------------------------------------------------
bool FEPlotLeftCauchyGreen::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FELeftCauchyGreen());
return true;
}
//=============================================================================
//! Store the average right stretch
class FERightStretch
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->RightStretch();
}
};
//-----------------------------------------------------------------------------
bool FEPlotRightStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FERightStretch());
return true;
}
//=============================================================================
//! Store the average right stretch
class FELeftStretch
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->LeftStretch();
}
};
//-----------------------------------------------------------------------------
bool FEPlotLeftStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FELeftStretch());
return true;
}
//=============================================================================
//! Store the average right Hencky
class FERightHencky
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->RightHencky();
}
};
//-----------------------------------------------------------------------------
bool FEPlotRightHencky::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FERightHencky());
return true;
}
//=============================================================================
//! Store the average left Hencky
class FELeftHencky
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->LeftHencky();
}
};
//-----------------------------------------------------------------------------
bool FEPlotLeftHencky::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FELeftHencky());
return true;
}
//=============================================================================
//! Store the average rate of deformation
class FERateOfDeformation
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pt = mp.ExtractData<FEElasticMaterialPoint>();
if (pt == 0) return mat3ds(0, 0, 0, 0, 0, 0);
return pt->RateOfDeformation();
}
};
//-----------------------------------------------------------------------------
bool FEPlotRateOfDeformation::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FERateOfDeformation());
return true;
}
//-----------------------------------------------------------------------------
//! Store shell thicknesses
bool FEPlotShellThickness::Save(FEDomain &dom, FEDataStream &a)
{
if (dom.Class() == FE_DOMAIN_SHELL)
{
FEShellDomain& sd = static_cast<FEShellDomain&>(dom);
int NS = sd.Elements();
for (int i=0; i<NS; ++i)
{
FEShellElement& e = sd.Element(i);
int n = e.Nodes();
for (int j=0; j<n; ++j) a << e.m_ht[j];
}
return true;
}
return false;
}
//-----------------------------------------------------------------------------
//! Store shell directors
bool FEPlotShellDirector::Save(FEDomain &dom, FEDataStream &a)
{
const int dof_X = GetFEModel()->GetDOFIndex("x");
const int dof_Y = GetFEModel()->GetDOFIndex("y");
const int dof_Z = GetFEModel()->GetDOFIndex("z");
const int dof_SX = GetFEModel()->GetDOFIndex("sx");
const int dof_SY = GetFEModel()->GetDOFIndex("sy");
const int dof_SZ = GetFEModel()->GetDOFIndex("sz");
if (dom.Class() == FE_DOMAIN_SHELL)
{
if (dynamic_cast<FEElasticShellDomainOld*>(&dom))
{
FEShellDomainOld& sd = static_cast<FEShellDomainOld&>(dom);
int NS = sd.Elements();
FEMesh& mesh = *sd.GetMesh();
for (int i = 0; i<NS; ++i)
{
FEShellElementOld& e = sd.ShellElement(i);
int n = e.Nodes();
for (int j = 0; j<n; ++j)
{
FENode& nj = mesh.Node(e.m_node[j]);
vec3d D = e.m_D0[j] + nj.get_vec3d(dof_SX, dof_SY, dof_SZ);
a << D;
}
}
return true;
}
else if (dynamic_cast<FESSIShellDomain*>(&dom))
{
FESSIShellDomain* bd = dynamic_cast<FESSIShellDomain*>(&dom);
int NS = bd->Elements();
FEMesh& mesh = *bd->GetMesh();
for (int i=0; i<NS; ++i)
{
FEShellElement& e = bd->Element(i);
int n = e.Nodes();
for (int j=0; j<n; ++j)
{
FENode& nj = mesh.Node(e.m_node[j]);
vec3d D;
if (bd->m_bnodalnormals) {
D = nj.m_d0;
}
else {
D = e.m_d0[j];
}
D += nj.get_vec3d(dof_X, dof_Y, dof_Z) - nj.get_vec3d(dof_SX, dof_SY, dof_SZ);
a << D;
}
}
return true;
}
}
return false;
}
//=============================================================================
FEPlotDamage::FEPlotDamage(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotDamage::SetFilter(const char* szfilter)
{
int nread = sscanf(szfilter, "solid[%d]", &m_comp);
return (nread == 1);
}
//-----------------------------------------------------------------------------
bool FEPlotDamage::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& pt) {
const FEReactiveMaterialPoint* ppd = pt.ExtractData<FEReactiveMaterialPoint>();
FEElasticMixtureMaterialPoint* pem = const_cast<FEElasticMixtureMaterialPoint*>(pt.ExtractData<FEElasticMixtureMaterialPoint>());
FEMultigenerationMaterialPoint* pmg = const_cast<FEMultigenerationMaterialPoint*>(pt.ExtractData<FEMultigenerationMaterialPoint>());
double D = 0.0;
if (ppd) D += (float)ppd->BrokenBonds();
else if (pem) {
for (int k = 0; k < pem->Components(); ++k)
{
const FEReactiveMaterialPoint* ppd = pem->GetPointData(k)->ExtractData<FEReactiveMaterialPoint>();
if (ppd) D += (float)ppd->BrokenBonds();
}
}
else if (pmg) {
for (int k = 0; k < pmg->Components(); ++k)
{
FEReactiveMaterialPoint* ppd = pmg->GetPointData(k)->ExtractData<FEReactiveMaterialPoint>();
FEElasticMixtureMaterialPoint* pem = pmg->GetPointData(k)->ExtractData<FEElasticMixtureMaterialPoint>();
if (ppd) D += (float)ppd->BrokenBonds();
else if (pem)
{
for (int l = 0; l < pem->Components(); ++l)
{
FEReactiveMaterialPoint* ppd = pem->GetPointData(l)->ExtractData<FEReactiveMaterialPoint>();
if (ppd) D += (float)ppd->BrokenBonds();
}
}
}
}
return D;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
double D = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
FEReactiveMaterialPoint* dp = mmp->GetPointData(m_comp)->ExtractData<FEReactiveMaterialPoint>();
if (dp) D += dp->BrokenBonds();
}
}
D /= (float)el.GaussPoints();
a << D;
}
return true;
}
}
//=============================================================================
FEPlotIntactBondFraction::FEPlotIntactBondFraction(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotIntactBondFraction::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotIntactBondFraction::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& pt) {
FEMaterialPoint& mp = const_cast<FEMaterialPoint&>(pt);
double D = 0.0;
FEReactiveMaterialPoint* prm = mp.ExtractData<FEReactiveMaterialPoint>();
FEReactiveViscoelasticMaterialPoint* pve = mp.ExtractData<FEReactiveViscoelasticMaterialPoint>();
if (prm) D = (float) prm->IntactBonds();
else if (pve) {
const FEReactiveMaterialPoint* pr = pve->GetPointData(0)->ExtractData< FEReactiveMaterialPoint>();
if (pr) D = (float) pr->IntactBonds();
}
return D;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
float D = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
FEReactiveMaterialPoint* prm = mmp->GetPointData(m_comp)->ExtractData<FEReactiveMaterialPoint>();
FEReactiveViscoelasticMaterialPoint* pve = mmp->GetPointData(m_comp)->ExtractData<FEReactiveViscoelasticMaterialPoint>();
if (prm) D += (float) prm->IntactBonds();
else if (pve) {
FEReactiveMaterialPoint* pr = pve->GetPointData(0)->ExtractData<FEReactiveMaterialPoint>();
if (pr) D += (float) pr->IntactBonds();
}
}
}
D /= (float)el.GaussPoints();
a << D;
}
return true;
}
}
//=============================================================================
FEPlotFatigueBondFraction::FEPlotFatigueBondFraction(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotFatigueBondFraction::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotFatigueBondFraction::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& pt) {
FEMaterialPoint& mp = const_cast<FEMaterialPoint&>(pt);
float wf = 0.0;
FEReactiveMaterialPoint* prm = mp.ExtractData<FEReactiveMaterialPoint>();
FEReactiveViscoelasticMaterialPoint* pve = mp.ExtractData<FEReactiveViscoelasticMaterialPoint>();
if (prm) wf = (float) prm->FatigueBonds();
else if (pve) {
FEReactiveMaterialPoint* pr = pve->GetPointData(0)->ExtractData<FEReactiveMaterialPoint>();
if (pr) wf = (float) pr->FatigueBonds();
}
return wf;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
float wf = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
FEReactiveMaterialPoint* ppr = mmp->GetPointData(m_comp)->ExtractData<FEReactiveMaterialPoint>();
FEReactiveViscoelasticMaterialPoint* pve = mmp->GetPointData(m_comp)->ExtractData<FEReactiveViscoelasticMaterialPoint>();
if (ppr) wf += (float) ppr->FatigueBonds();
else if (pve) {
FEReactiveMaterialPoint* pr = pve->GetPointData(0)->ExtractData<FEReactiveMaterialPoint>();
if (pr) wf += (float) pr->FatigueBonds();
}
}
}
wf /= (float)el.GaussPoints();
a << wf;
}
return true;
}
}
//=============================================================================
FEPlotYieldedBondFraction::FEPlotYieldedBondFraction(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotYieldedBondFraction::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotYieldedBondFraction::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
float wy = 0.0;
const FEReactiveMaterialPoint* prp = mp.ExtractData<FEReactiveMaterialPoint>();
if (prp) wy = (float) prp->YieldedBonds();
return wy;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
float wy = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
const FEReactiveMaterialPoint* prp = mmp->GetPointData(m_comp)->ExtractData<FEReactiveMaterialPoint>();
if (prp) wy += (float) prp->YieldedBonds();
}
}
wy /= (float)el.GaussPoints();
a << wy;
}
return true;
}
}
//=============================================================================
FEPlotReactivePlasticityHeatSupply::FEPlotReactivePlasticityHeatSupply(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotReactivePlasticityHeatSupply::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotReactivePlasticityHeatSupply::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
float Rhat = 0.0;
const FEReactivePlasticityMaterialPoint* prp = mp.ExtractData<FEReactivePlasticityMaterialPoint>();
const FEReactivePlasticDamageMaterialPoint* ppp = mp.ExtractData<FEReactivePlasticDamageMaterialPoint>();
if (prp) Rhat = (float) prp->m_Rhat;
else if (ppp) Rhat = (float) ppp->m_Rhat;
return Rhat;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
float Rhat = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
const FEReactivePlasticityMaterialPoint* prp = mmp->GetPointData(m_comp)->ExtractData<FEReactivePlasticityMaterialPoint>();
const FEReactivePlasticDamageMaterialPoint* ppp = mmp->GetPointData(m_comp)->ExtractData<FEReactivePlasticDamageMaterialPoint>();
if (prp) Rhat += (float) prp->m_Rhat;
else if (ppp) Rhat += (float) ppp->m_Rhat;
}
}
Rhat /= (float)el.GaussPoints();
a << Rhat;
}
return true;
}
}
//=============================================================================
FEPlotOctahedralPlasticStrain::FEPlotOctahedralPlasticStrain(FEModel* pfem) : FEPlotDomainData(pfem, PLT_FLOAT, FMT_ITEM)
{
m_comp = -1;
}
//-----------------------------------------------------------------------------
bool FEPlotOctahedralPlasticStrain::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotOctahedralPlasticStrain::Save(FEDomain &dom, FEDataStream& a)
{
if (m_comp == -1) {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
float gp = 0.0;
const FEReactivePlasticityMaterialPoint* prp = mp.ExtractData<FEReactivePlasticityMaterialPoint>();
const FEReactivePlasticDamageMaterialPoint* ppp = mp.ExtractData<FEReactivePlasticDamageMaterialPoint>();
if (prp && prp->m_gp.size()) gp = (float) prp->m_gp[0];
else if (ppp && ppp->m_gp.size()) gp = (float) ppp->m_gp[0];
return gp;
});
return true;
}
else {
for (int i = 0; i < dom.Elements(); ++i)
{
FEElement& el = dom.ElementRef(i);
float gp = 0.0;
for (int n = 0; n < el.GaussPoints(); ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMixtureMaterialPoint* mmp = mp.ExtractData< FEElasticMixtureMaterialPoint>();
if (mmp && (m_comp < mmp->Components()))
{
const FEReactivePlasticityMaterialPoint* prp = mmp->GetPointData(m_comp)->ExtractData<FEReactivePlasticityMaterialPoint>();
const FEReactivePlasticDamageMaterialPoint* ppp = mmp->GetPointData(m_comp)->ExtractData<FEReactivePlasticDamageMaterialPoint>();
if (prp && prp->m_gp.size()) gp += (float) prp->m_gp[0];
else if (ppp && ppp->m_gp.size()) gp += (float) ppp->m_gp[0];
}
}
gp /= (float)el.GaussPoints();
a << gp;
}
return true;
}
}
//-----------------------------------------------------------------------------
bool FEPlotMixtureVolumeFraction::Save(FEDomain &dom, FEDataStream &a)
{
// extract the mixture material
FEMaterial* pmat = dom.GetMaterial();
FEElasticMixture* pm = dynamic_cast<FEElasticMixture*>(pmat);
if (pm == 0) return false;
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
return pt.m_w[0];
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotUT4NodalStresses::Save(FEDomain& dom, FEDataStream& a)
{
// make sure this is a UT4 domain
FEUT4Domain* pd = dynamic_cast<FEUT4Domain*>(&dom);
if (pd == 0) return false;
// write the nodal values
writeNodalValues<mat3ds>(dom, a, [=](int i) {
FEUT4Domain::UT4NODE& n = pd->UT4Node(i);
return n.si;
});
return true;
}
//==============================================================================
// R I G I D B O D Y D A T A
//==============================================================================
//-----------------------------------------------------------------------------
bool FEPlotRigidDisplacement::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store the rigid body position
// TODO: why do we not store displacement?
a << rb.m_rt;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidVelocity::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store the rigid velocity
a << rb.m_vt;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidAcceleration::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store rigid body acceleration
a << rb.m_at;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidRotation::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
vec3d q = rb.GetRotation().GetRotationVector();
// store rotation vector
a << q;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidAngularVelocity::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store rigid angular velocity
a << rb.m_wt;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidAngularAcceleration::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store angular acceleration
a << rb.m_alt;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidKineticEnergy::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
vec3d v = rb.m_vt;
double m = rb.m_mass;
vec3d w = rb.m_wt;
mat3d Rt = rb.GetRotation().RotationMatrix();
mat3ds Jt = (Rt*rb.m_moi*Rt.transpose()).sym();
double ke = ((v*v)*m + w*(Jt*w))/2;
// store kinetic energy
a << ke;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidLinearMomentum::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store linear momentum (mass x velocity)
a << rb.m_vt*rb.m_mass;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidAngularMomentum::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// store angular momentum (mass moment of inertia x angular velocity)
mat3d Rt = rb.GetRotation().RotationMatrix();
mat3ds Jt = (Rt*rb.m_moi*Rt.transpose()).sym();
a << Jt*rb.m_wt;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidEuler::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// get the Euler angles
double E[3];
quat2euler(rb.GetRotation(), E);
// store Euler
a << E[0] << E[1] << E[2];
return true;
}
//-----------------------------------------------------------------------------
// TODO: I think this already gets stored somewhere
bool FEPlotRigidRotationVector::Save(FEDomain& dom, FEDataStream& a)
{
// get the rigid material
FEMaterial* pm = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pm);
if (prm == 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(prm->GetRigidBodyID());
// get the rotation vector and angle
vec3d r = rb.GetRotation().GetRotationVector();
// store rotation vector
a << r;
return true;
}
//=============================================================================
bool FEPlotRigidReactionForce::Save(FEDomain& dom, FEDataStream& a)
{
// get the material
FEMaterial* pmat = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pmat);
if (prm == 0) return false;
// get the rigid body ID
int nrid = prm->GetRigidBodyID();
if (nrid < 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(nrid);
a << rb.m_Fr;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRigidReactionTorque::Save(FEDomain& dom, FEDataStream& a)
{
// get the material
FEMaterial* pmat = dom.GetMaterial();
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(pmat);
if (prm == 0) return false;
// get the rigid body ID
int nrid = prm->GetRigidBodyID();
if (nrid < 0) return false;
// get the rigid body
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(nrid);
a << rb.m_Mr;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotStressError::Save(FEDomain& dom, FEDataStream& a)
{
writeRelativeError(dom, a, [](FEMaterialPoint& mp) {
FEElasticMaterialPoint* ep = mp.ExtractData<FEElasticMaterialPoint>();
mat3ds& s = ep->m_s;
double v = s.effective_norm();
return v;
});
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotFiberTargetStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* mat = dom.GetMaterial();
FEPrestrainMaterial * pmat = dynamic_cast<FEPrestrainMaterial*>(mat);
if (pmat == nullptr) return false;
// get the elastic component
FEProperty* prop = mat->FindProperty("elastic");
if (prop == nullptr) return false;
FEElasticMaterial* pme = dynamic_cast<FEElasticMaterial*>(prop->get(0));
if (pme == 0) return false;
// get the fiber property
FEVec3dValuator* vec = dynamic_cast<FEVec3dValuator*>(pme->GetProperty("fiber"));
if (vec == 0) return false;
// we're good so store the in-situ stretch
int NE = dom.Elements();
for (int i = 0; i<NE; ++i)
{
FEElement& e = dom.ElementRef(i);
int nint = e.GaussPoints();
double lam = 0.0;
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *e.GetMaterialPoint(j)->GetPointData(0);
FEPrestrainMaterialPoint& pp = *mp.ExtractData<FEPrestrainMaterialPoint>();
mat3d Fp = pp.initialPrestrain();
mat3d Q = mat->GetLocalCS(mp);
vec3d a0 = vec->unitVector(mp);
vec3d ar = Q * a0;
vec3d a = Fp*ar;
double lamp = a.norm();
lam += lamp;
}
lam /= (double)nint;
a << lam;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotPreStrainStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* mat = dom.GetMaterial();
FEPrestrainMaterial* pmat = dynamic_cast<FEPrestrainMaterial*>(mat);
if (pmat == 0) return false;
// get the elastic component
FEProperty* prop = mat->FindProperty("elastic");
if (prop == nullptr) return false;
FEElasticMaterial* pme = dynamic_cast<FEElasticMaterial*>(prop->get(0));
if (pme== 0) return false;
// get the fiber property
FEVec3dValuator* vec = dynamic_cast<FEVec3dValuator*>(pme->GetProperty("fiber"));
if (vec == 0) return false;
int NE = dom.Elements();
for (int i = 0; i<NE; ++i)
{
FEElement& e = dom.ElementRef(i);
int nint = e.GaussPoints();
double lam = 0.0;
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *e.GetMaterialPoint(j)->GetPointData(0);
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
FEPrestrainMaterialPoint& pp = *mp.ExtractData<FEPrestrainMaterialPoint>();
mat3d& F = pt.m_F;
mat3d Fp = pp.prestrain();
mat3d Ft = F*Fp;
mat3d Q = mat->GetLocalCS(mp);
vec3d a0 = vec->unitVector(mp);
vec3d ar = Q * a0;
vec3d a = Ft*ar;
double lambda = a.norm();
lam += lambda;
}
lam /= (double)nint;
a << lam;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotPreStrainStretchError::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* mat = dom.GetMaterial();
FEPrestrainMaterial* pmat = dynamic_cast<FEPrestrainMaterial*>(mat);
if (pmat == 0) return false;
// get the elastic component
FEProperty* prop = mat->FindProperty("elastic");
if (prop == nullptr) return false;
FEElasticMaterial* pme = dynamic_cast<FEElasticMaterial*>(prop->get(0));
if (pme == 0) return false;
// get the fiber property
FEVec3dValuator* vec = dynamic_cast<FEVec3dValuator*>(pme->GetProperty("fiber"));
if (vec == 0) return false;
int NE = dom.Elements();
for (int i = 0; i<NE; ++i)
{
FEElement& e = dom.ElementRef(i);
int nint = e.GaussPoints();
double err = 0.0;
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *e.GetMaterialPoint(j)->GetPointData(0);
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
FEPrestrainMaterialPoint& pp = *mp.ExtractData<FEPrestrainMaterialPoint>();
// initial fiber vector
mat3d Q = mat->GetLocalCS(mp);
vec3d a0 = vec->unitVector(mp);
vec3d ar = Q * a0;
// target stretch
mat3d Fp = pp.initialPrestrain();
vec3d a = Fp*ar;
double lam_trg = a.norm();
// current stretch
mat3d& F = pt.m_F;
Fp = pp.prestrain();
mat3d Ft = F*Fp;
a = Ft*ar;
double lam_cur = a.norm();
err += fabs(lam_cur / lam_trg - 1.0);
}
err /= (double)nint;
a << err;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotPreStrainCorrection::Save(FEDomain& dom, FEDataStream& a)
{
FEMaterial* mat = dom.GetMaterial();
FEElasticMaterial* solidMat = mat->ExtractProperty<FEElasticMaterial>();
FEPrestrainMaterial* pmat = dynamic_cast<FEPrestrainMaterial*>(solidMat);
if (pmat == 0) return false;
int NE = dom.Elements();
for (int i = 0; i<NE; ++i)
{
FEElement& e = dom.ElementRef(i);
int nint = e.GaussPoints();
mat3d Fc; Fc.zero();
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *e.GetMaterialPoint(j)->GetPointData(0);
FEPrestrainMaterialPoint& pt = *mp.ExtractData<FEPrestrainMaterialPoint>();
Fc += pt.PrestrainCorrection();
}
Fc *= 1.0 / (double)nint;
a << Fc;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotSPRPreStrainCorrection::Save(FEDomain& dom, FEDataStream& a)
{
const int LUT[9][2] = { { 0,0 },{ 0,1 },{ 0,2 },{ 1,0 },{ 1,1 },{ 1,2 },{ 2,0 },{ 2,1 },{ 2,2 } };
FEPrestrainMaterial* pmat = dynamic_cast<FEPrestrainMaterial*>(dom.GetMaterial());
if (pmat == 0) return false;
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
// get the domain
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
int NN = sd.Nodes();
int NE = sd.Elements();
// build the element data array
vector< vector<double> > ED;
ED.resize(NE);
for (int i = 0; i<NE; ++i)
{
FESolidElement& e = sd.Element(i);
int nint = e.GaussPoints();
ED[i].assign(nint, 0.0);
}
// this array will store the results
FESPRProjection map(sd);
vector<double> val[9];
// loop over stress components
for (int n = 0; n<9; ++n)
{
// fill the ED array
for (int i = 0; i<NE; ++i)
{
FESolidElement& el = sd.Element(i);
int nint = el.GaussPoints();
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j)->GetPointData(0);
FEPrestrainMaterialPoint& pt = *mp.ExtractData<FEPrestrainMaterialPoint>();
const mat3d& F = pt.PrestrainCorrection();
ED[i][j] = F(LUT[n][0], LUT[n][1]);
}
}
// project to nodes
map.Project(ED, val[n]);
}
// copy results to archive
for (int i = 0; i<NN; ++i)
{
a << val[0][i];
a << val[1][i];
a << val[2][i];
a << val[3][i];
a << val[4][i];
a << val[5][i];
a << val[6][i];
a << val[7][i];
a << val[8][i];
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotPreStrainCompatibility::Save(FEDomain& dom, FEDataStream& a)
{
const int LUT[9][2] = { { 0,0 },{ 0,1 },{ 0,2 },{ 1,0 },{ 1,1 },{ 1,2 },{ 2,0 },{ 2,1 },{ 2,2 } };
// make sure this is a pre-strain material
FEPrestrainMaterial* pmat = dynamic_cast<FEPrestrainMaterial*>(dom.GetMaterial());
if (pmat == 0) return false;
// For now, this is only available for solid domains
if (dom.Class() != FE_DOMAIN_SOLID) return false;
// get the domain
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
int NE = sd.Elements();
// STEP 1 - first we do an SPR recovery of the pre-strain gradient
// build the element data array
vector< vector<double> > ED;
ED.resize(NE);
for (int i = 0; i<NE; ++i)
{
FESolidElement& e = sd.Element(i);
int nint = e.GaussPoints();
ED[i].assign(nint, 0.0);
}
// this array will store the results
FESPRProjection map(sd);
vector<double> val[9];
// create a global-to-local node list
FEMesh& mesh = *dom.GetMesh();
vector<int> g2l; g2l.assign(mesh.Nodes(), -1);
int nn = 0;
for (int i = 0; i<NE; ++i)
{
FESolidElement& el = sd.Element(i);
int neln = el.Nodes();
for (int j = 0; j<neln; ++j)
{
if (g2l[el.m_node[j]] == -1) g2l[el.m_node[j]] = nn++;
}
}
// loop over tensor components
for (int n = 0; n<9; ++n)
{
// fill the ED array
for (int i = 0; i<NE; ++i)
{
FESolidElement& el = sd.Element(i);
int nint = el.GaussPoints();
for (int j = 0; j<nint; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j)->GetPointData(0);
FEPrestrainMaterialPoint& pt = *mp.ExtractData<FEPrestrainMaterialPoint>();
mat3d Fp = pt.prestrain();
ED[i][j] = Fp(LUT[n][0], LUT[n][1]);
}
}
// project to nodes
map.Project(ED, val[n]);
}
// STEP 2 - now we calculate the gradient of the nodal values at the integration points
vector<double> vn(FEElement::MAX_NODES);
for (int i = 0; i<NE; ++i)
{
FESolidElement& el = sd.Element(i);
int neln = el.Nodes();
int nint = el.GaussPoints();
vector<mat3d> gF[3];
gF[0].assign(nint, mat3dd(0));
gF[1].assign(nint, mat3dd(0));
gF[2].assign(nint, mat3dd(0));
for (int n = 0; n<9; ++n)
{
// get the nodal values
for (int m = 0; m<neln; ++m) vn[m] = val[n][g2l[el.m_node[m]]];
// calculate the gradient at the integration points
for (int j = 0; j<nint; ++j)
{
vec3d g = sd.gradient(el, vn, j);
gF[0][j](LUT[n][0], LUT[n][1]) = g.x;
gF[1][j](LUT[n][0], LUT[n][1]) = g.y;
gF[2][j](LUT[n][0], LUT[n][1]) = g.z;
}
}
double c = 0.0;
for (int j = 0; j<nint; ++j)
{
mat3d C;
C(0, 0) = gF[1][j](0, 2) - gF[2][j](0, 1);
C(0, 1) = gF[1][j](1, 2) - gF[2][j](1, 1);
C(0, 2) = gF[1][j](2, 2) - gF[2][j](2, 1);
C(1, 0) = gF[2][j](0, 0) - gF[0][j](0, 2);
C(1, 1) = gF[2][j](1, 0) - gF[0][j](1, 2);
C(1, 2) = gF[2][j](2, 0) - gF[0][j](2, 2);
C(2, 0) = gF[0][j](0, 1) - gF[1][j](0, 0);
C(2, 1) = gF[0][j](1, 1) - gF[1][j](1, 0);
C(2, 2) = gF[0][j](2, 1) - gF[1][j](2, 0);
c += sqrt(C.dotdot(C));
}
c /= (double)nint;
// store the compatibility
a << c;
}
return true;
}
bool FEPlotDiscreteElementStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteDomain* pdiscreteDomain = dynamic_cast<FEDiscreteDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteDomain& discreteDomain = *pdiscreteDomain;
FEMesh& mesh = *dom.GetMesh();
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
vec3d ra0 = mesh.Node(el.m_node[0]).m_r0;
vec3d ra1 = mesh.Node(el.m_node[0]).m_rt;
vec3d rb0 = mesh.Node(el.m_node[1]).m_r0;
vec3d rb1 = mesh.Node(el.m_node[1]).m_rt;
double L0 = (rb0 - ra0).norm();
double Lt = (rb1 - ra1).norm();
double l = Lt / L0;
a << l;
}
return true;
}
bool FEPlotDiscreteElementElongation::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteDomain* pdiscreteDomain = dynamic_cast<FEDiscreteDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteDomain& discreteDomain = *pdiscreteDomain;
FEMesh& mesh = *dom.GetMesh();
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
vec3d ra0 = mesh.Node(el.m_node[0]).m_r0;
vec3d ra1 = mesh.Node(el.m_node[0]).m_rt;
vec3d rb0 = mesh.Node(el.m_node[1]).m_r0;
vec3d rb1 = mesh.Node(el.m_node[1]).m_rt;
double L0 = (rb0 - ra0).norm();
double Lt = (rb1 - ra1).norm();
double l = Lt - L0;
a << l;
}
return true;
}
bool FEPlotDiscreteElementPercentElongation::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteDomain* pdiscreteDomain = dynamic_cast<FEDiscreteDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteDomain& discreteDomain = *pdiscreteDomain;
FEMesh& mesh = *dom.GetMesh();
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
vec3d ra0 = mesh.Node(el.m_node[0]).m_r0;
vec3d ra1 = mesh.Node(el.m_node[0]).m_rt;
vec3d rb0 = mesh.Node(el.m_node[1]).m_r0;
vec3d rb1 = mesh.Node(el.m_node[1]).m_rt;
double L0 = (rb0 - ra0).norm();
double Lt = (rb1 - ra1).norm();
double l = (Lt - L0)/L0;
a << l;
}
return true;
}
bool FEPlotDiscreteElementDirection::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteDomain* pdiscreteDomain = dynamic_cast<FEDiscreteDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteDomain& discreteDomain = *pdiscreteDomain;
FEMesh& mesh = *dom.GetMesh();
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
vec3d ra = mesh.Node(el.m_node[0]).m_rt;
vec3d rb = mesh.Node(el.m_node[1]).m_rt;
vec3d e = (rb - ra); e.unit();
a << e;
}
return true;
}
bool FEPlotDiscreteElementLength::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteDomain* pdiscreteDomain = dynamic_cast<FEDiscreteDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteDomain& discreteDomain = *pdiscreteDomain;
FEMesh& mesh = *dom.GetMesh();
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
vec3d ra = mesh.Node(el.m_node[0]).m_rt;
vec3d rb = mesh.Node(el.m_node[1]).m_rt;
double L = (rb - ra).Length();
a << L;
}
return true;
}
bool FEPlotDiscreteElementForce::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteElasticDomain* pdiscreteDomain = dynamic_cast<FEDiscreteElasticDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteElasticDomain& discreteDomain = *pdiscreteDomain;
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
// get the (one) material point data
FEMaterialPoint& mp = *el.GetMaterialPoint(0);
FEDiscreteElasticMaterialPoint& dmp = *mp.ExtractData<FEDiscreteElasticMaterialPoint>();
// write the force
a << dmp.m_Ft;
}
return true;
}
bool FEPlotDiscreteElementSignedForce::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteElasticDomain* pdiscreteDomain = dynamic_cast<FEDiscreteElasticDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteElasticDomain& discreteDomain = *pdiscreteDomain;
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
// get the (one) material point data
FEMaterialPoint& mp = *el.GetMaterialPoint(0);
FEDiscreteElasticMaterialPoint& dmp = *mp.ExtractData<FEDiscreteElasticMaterialPoint>();
vec3d ra1 = dom.Node(el.m_lnode[0]).m_rt;
vec3d rb1 = dom.Node(el.m_lnode[1]).m_rt;
vec3d e = rb1 - ra1; e.unit();
vec3d F = dmp.m_Ft;
double Fm = F * e;
// write the force
a << Fm;
}
return true;
}
bool FEPlotDiscreteElementStrainEnergy::Save(FEDomain& dom, FEDataStream& a)
{
FEDiscreteElasticDomain* pdiscreteDomain = dynamic_cast<FEDiscreteElasticDomain*>(&dom);
if (pdiscreteDomain == nullptr) return false;
FEDiscreteElasticDomain& discreteDomain = *pdiscreteDomain;
FEDiscreteElasticMaterial* discreteMaterial = dynamic_cast<FEDiscreteElasticMaterial*>(discreteDomain.GetMaterial());
int NE = discreteDomain.Elements();
for (int i = 0; i < NE; ++i)
{
FEDiscreteElement& el = discreteDomain.Element(i);
// get the (one) material point data
FEMaterialPoint& mp = *el.GetMaterialPoint(0);
FEDiscreteElasticMaterialPoint& dmp = *mp.ExtractData<FEDiscreteElasticMaterialPoint>();
// write the strain energy
a << discreteMaterial->StrainEnergy(dmp);
}
return true;
}
//=================================================================================================
FEPlotContinuousDamage_::FEPlotContinuousDamage_(FEModel* fem, int n) : FEPlotDomainData(fem, PLT_FLOAT, FMT_ITEM)
{
m_propIndex = 0;
m_comp = n;
}
bool FEPlotContinuousDamage_::SetFilter(const char* sz)
{
m_prop = sz;
return true;
}
bool FEPlotContinuousDamage_::Save(FEDomain& dom, FEDataStream& a)
{
// get the material
FEMaterial* domMat = dom.GetMaterial();
if (domMat == nullptr) return false;
// get the fiber damage component
FEDamageElasticFiber* mat = nullptr;
if (m_prop.empty()) mat = dynamic_cast<FEDamageElasticFiber*>(domMat);
else
{
ParamString ps(m_prop.c_str());
m_propIndex = ps.Index();
mat = dynamic_cast<FEDamageElasticFiber*>(domMat->GetProperty(ps));
}
if (mat == nullptr) return false;
int NE = dom.Elements();
for (int i = 0; i < NE; ++i)
{
FEElement& el = dom.ElementRef(i);
double D = 0.0;
int nint = el.GaussPoints();
for (int j = 0; j < nint; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
FEMaterialPoint* pt = mp.GetPointData(m_propIndex);
double Dj = mat->Damage(*pt, m_comp);
D += Dj;
}
D /= (double)nint;
a << D;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRVEgenerations::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
bool FEPlotRVEgenerations::Save(FEDomain& dom, FEDataStream& a)
{
int N = dom.Elements();
FEElasticMaterial* pmat = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
FEReactiveViscoelasticMaterial* rvmat = nullptr;
FEUncoupledReactiveViscoelasticMaterial* rumat = nullptr;
if (m_comp > -1) {
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if (pmm) rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmm->GetMaterial(m_comp));
if (pum) rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pum->GetMaterial(m_comp));
}
else {
rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmat);
rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pmat);
}
if (rvmat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rvmat->RVEGenerations(*el.GetMaterialPoint(j));
a << bmf/nint;
}
}
else if (rumat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rumat->RVEGenerations(*el.GetMaterialPoint(j));
a << bmf/nint;
}
}
else {
return false;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRVEbonds::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
bool FEPlotRVEbonds::Save(FEDomain& dom, FEDataStream& a)
{
int N = dom.Elements();
FEElasticMaterial* pmat = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
FEReactiveViscoelasticMaterial* rvmat = nullptr;
FEUncoupledReactiveViscoelasticMaterial* rumat = nullptr;
if (m_comp > -1) {
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if (pmm) rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmm->GetMaterial(m_comp));
if (pum) rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pum->GetMaterial(m_comp));
}
else {
rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmat);
rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pmat);
}
if (rvmat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rvmat->ReformingBondMassFraction(*rvmat->GetBondMaterialPoint(*el.GetMaterialPoint(j)));
a << bmf/nint;
}
}
else if (rumat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rumat->ReformingBondMassFraction(*rumat->GetBondMaterialPoint(*el.GetMaterialPoint(j)));
a << bmf/nint;
}
}
else {
return false;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRVErecruitment::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
bool FEPlotRVErecruitment::Save(FEDomain& dom, FEDataStream& a)
{
int N = dom.Elements();
FEElasticMaterial* pmat = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
FEReactiveViscoelasticMaterial* rvmat = nullptr;
FEUncoupledReactiveViscoelasticMaterial* rumat = nullptr;
if (m_comp > -1) {
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if (pmm) rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmm->GetMaterial(m_comp));
if (pum) rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pum->GetMaterial(m_comp));
}
else {
rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmat);
rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pmat);
}
if (rvmat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j) {
FEMaterialPoint& mp = *rvmat->GetBondMaterialPoint(*el.GetMaterialPoint(j));
FEReactiveVEMaterialPoint& pt = *mp.ExtractData<FEReactiveVEMaterialPoint>();
if (!pt.m_wv.empty()) bmf += pt.m_wv.back();
else bmf += 1.0;
}
a << bmf/nint;
}
}
else if (rumat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j) {
FEMaterialPoint& mp = *rvmat->GetBondMaterialPoint(*el.GetMaterialPoint(j));
FEReactiveVEMaterialPoint & pt = *mp.ExtractData<FEReactiveVEMaterialPoint>();
if (!pt.m_wv.empty()) bmf += pt.m_wv.back();
else bmf += 1.0;
}
a << bmf/nint;
}
}
else {
return false;
}
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotRVEstrain::SetFilter(const char* szfilter)
{
sscanf(szfilter, "solid[%d]", &m_comp);
return true;
}
bool FEPlotRVEstrain::Save(FEDomain& dom, FEDataStream& a)
{
int N = dom.Elements();
FEElasticMaterial* pmat = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pmat == nullptr) return false;
FEReactiveViscoelasticMaterial* rvmat = nullptr;
FEUncoupledReactiveViscoelasticMaterial* rumat = nullptr;
if (m_comp > -1) {
FEElasticMixture* pmm = dynamic_cast<FEElasticMixture*>(pmat);
FEUncoupledElasticMixture* pum = dynamic_cast<FEUncoupledElasticMixture*>(pmat);
if (pmm) rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmm->GetMaterial(m_comp));
if (pum) rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pum->GetMaterial(m_comp));
}
else {
rvmat = dynamic_cast<FEReactiveViscoelasticMaterial*>(pmat);
rumat = dynamic_cast<FEUncoupledReactiveViscoelasticMaterial*>(pmat);
}
if (rvmat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rvmat->ScalarStrain(*rvmat->GetBondMaterialPoint(*el.GetMaterialPoint(j)));
a << bmf/nint;
}
}
else if (rumat) {
for (int iel=0; iel<N; ++iel)
{
FEElement& el = dom.ElementRef(iel);
int nint = el.GaussPoints();
double bmf = 0;
for (int j=0; j<nint; ++j)
bmf += rumat->ScalarStrain(*rumat->GetBondMaterialPoint(*el.GetMaterialPoint(j)));
a << bmf/nint;
}
}
else {
return false;
}
return true;
}
//-----------------------------------------------------------------------------
class FEStrongBondSED
{
public:
FEStrongBondSED(FEElasticMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->StrongBondSED(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotStrongBondSED::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEStrongBondSED W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEWeakBondSED
{
public:
FEWeakBondSED(FEElasticMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->WeakBondSED(const_cast<FEMaterialPoint&>(mp));
}
private:
FEElasticMaterial* m_mat;
};
bool FEPlotWeakBondSED::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEWeakBondSED W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEStrongBondDevSED
{
public:
FEStrongBondDevSED(FEUncoupledMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->StrongBondDevSED(const_cast<FEMaterialPoint&>(mp));
}
private:
FEUncoupledMaterial* m_mat;
};
bool FEPlotStrongBondDevSED::Save(FEDomain& dom, FEDataStream& a)
{
FEUncoupledMaterial* pme = dom.GetMaterial()->ExtractProperty<FEUncoupledMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEStrongBondDevSED W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
class FEWeakBondDevSED
{
public:
FEWeakBondDevSED(FEUncoupledMaterial* pm) : m_mat(pm) {}
double operator()(const FEMaterialPoint& mp)
{
return m_mat->WeakBondDevSED(const_cast<FEMaterialPoint&>(mp));
}
private:
FEUncoupledMaterial* m_mat;
};
bool FEPlotWeakBondDevSED::Save(FEDomain& dom, FEDataStream& a)
{
FEUncoupledMaterial* pme = dom.GetMaterial()->ExtractProperty<FEUncoupledMaterial>();
if (pme == 0) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEWeakBondDevSED W(pme);
writeAverageElementValue<double>(dom, a, W);
return true;
}
return false;
}
//-----------------------------------------------------------------------------
bool FEPlotTrussStretch::Save(FEDomain& dom, FEDataStream& a)
{
FETrussDomain* td = dynamic_cast<FETrussDomain*>(&dom);
if (td == nullptr) return false;
for (int i = 0; i < td->Elements(); ++i)
{
FETrussElement& el = td->Element(i);
a << el.m_lam;
}
return true;
}
//=============================================================================
//! Store the average growth Lagrangian strain
class FEGrowthLagrangeStrain
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
mat3d C = Fg.transpose()*Fg;
mat3ds E = ((C - mat3dd(1.0))*0.5).sym();
return E;
}
};
//-----------------------------------------------------------------------------
bool FEPlotGrowthLagrangeStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.Strain();
});
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom); assert(sd);
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(&dom);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(&dom);
if (easd || ansd)
{
return false;
}
else
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.Strain();
});
}
}
else return false;
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotGrowthInfStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<mat3ds>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
// displacement tensor
mat3d U = Fg - mat3dd(1.0);
// evaluate small strain tensor eij = 0.5*(Uij + Uji)
mat3ds e = U.sym();
return e;
});
}
else return false;
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamStress::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d t(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
t += mp.m_t;
}
t /= (double)nint;
a << t;
}
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamReferenceStress::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d T(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
quatd Ri = mp.m_Rt.Conjugate();
T += Ri*mp.m_t;
}
T /= (double)nint;
a << T;
}
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamStressCouple::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d m(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
m += mp.m_m;
}
m /= (double)nint;
a << m;
}
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamReferenceStressCouple::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d M(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
quatd Ri = mp.m_Rt.Conjugate();
M += Ri*mp.m_m;
}
M /= (double)nint;
a << M;
}
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamStrain::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d t(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
t += mp.m_Rt * mp.m_Gamma;
}
t /= (double)nint;
a << t;
}
return true;
}
//-------------------------------------------------------------------------------
bool FEPlotBeamCurvature::Save(FEDomain& dom, FEDataStream& a)
{
FEElasticBeamDomain* beam = dynamic_cast<FEElasticBeamDomain*>(&dom);
if (beam == nullptr) return false;
for (int i = 0; i < beam->Elements(); ++i)
{
FEBeamElement& el = beam->Element(i);
vec3d t(0, 0, 0);
int nint = el.GaussPoints();
for (int n = 0; n < nint; ++n)
{
// get the material point
FEElasticBeamMaterialPoint& mp = *(el.GetMaterialPoint(n)->ExtractData<FEElasticBeamMaterialPoint>());
t += mp.m_Rt*mp.m_Kappa;
}
t /= (double)nint;
a << t;
}
return true;
}
//=============================================================================
//! Store the average right stretch
class FEGrowthRightStretch
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.RightStretch();
}
};
//-----------------------------------------------------------------------------
bool FEPlotGrowthRightStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FEGrowthRightStretch());
return true;
}
//=============================================================================
//! Store the average right stretch
class FEGrowthLeftStretch
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.LeftStretch();
}
};
//-----------------------------------------------------------------------------
bool FEPlotGrowthLeftStretch::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FEGrowthLeftStretch());
return true;
}
//=============================================================================
//! Store the average growth right Hencky
class FEGrowthRightHencky
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.RightHencky();
}
};
//-----------------------------------------------------------------------------
bool FEPlotGrowthRightHencky::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FEGrowthRightHencky());
return true;
}
//=============================================================================
//! Store the average left Hencky
class FEGrowthLeftHencky
{
public:
mat3ds operator()(const FEMaterialPoint& mp)
{
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return mat3ds(0, 0, 0, 0, 0, 0);
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
if (kp == 0) return mat3ds(0, 0, 0, 0, 0, 0);
mat3d Fg = kp->m_Fg;
FEElasticMaterialPoint pe2;
pe2.m_F = Fg;
return pe2.LeftHencky();
}
};
//-----------------------------------------------------------------------------
bool FEPlotGrowthLeftHencky::Save(FEDomain& dom, FEDataStream& a)
{
FEKinematicGrowth* pme = dom.GetMaterial()->ExtractProperty<FEKinematicGrowth>();
if (pme == nullptr) return false;
writeAverageElementValue<mat3ds>(dom, a, FEGrowthLeftHencky());
return true;
}
//-----------------------------------------------------------------------------
bool FEPlotGrowthRelativeVolume::Save(FEDomain &dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return 0.0;
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
return (kp ? kp->m_Fg.det() : 0.0);
});
}
else if (dom.Class() == FE_DOMAIN_SHELL)
{
// TODO: implement relative volume calculation for kinematic growth material in EAS and ANS shells
FEShellDomain* sd = dynamic_cast<FEShellDomain*>(&dom); assert(sd);
FEShellDomainNew* newsd = dynamic_cast<FEShellDomainNew*>(sd);
FEElasticEASShellDomain* easd = dynamic_cast<FEElasticEASShellDomain*>(newsd);
FEElasticANSShellDomain* ansd = dynamic_cast<FEElasticANSShellDomain*>(newsd);
if (easd || ansd) {
return false;
}
else {
writeAverageElementValue<double>(dom, a, [](const FEMaterialPoint& mp) {
const FEElasticMaterialPoint* pe = mp.ExtractData<FEElasticMaterialPoint>();
if (pe == nullptr) return 0.0;
const FEKinematicMaterialPoint* kp = pe->ExtractData<FEKinematicMaterialPoint>();
return (kp ? kp->m_Fg.det() : 0.0);
});
}
return true;
}
else return false;
return true;
}
bool FEPlotIdealGasPressure::Init()
{
FEModel* fem = GetFEModel();
if (fem == nullptr) return false;
for (int i = 0; i < fem->ModelLoads(); ++i)
{
m_load = dynamic_cast<FEIdealGasPressure*>(fem->ModelLoad(i));
if (m_load) return true;
}
return (m_load != nullptr);
}
bool FEPlotIdealGasPressure::Save(FESurface& surf, FEDataStream& a)
{
if (m_binit == false)
{
if (!Init()) return false;
m_binit = true;
}
if (m_load == nullptr) return false;
if (m_load->GetSurface().GetFacetSet() == surf.GetFacetSet())
{
a << m_load->GetCurrentPressure();
return true;
}
else return false;
}
bool FEPlotBodyForce::Save(FEDomain& dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEModel* fem = GetFEModel();
FESolidDomain& sd = static_cast<FESolidDomain&>(dom);
writeAverageElementValue<vec3d>(dom, a, [&](const FEMaterialPoint& mp) {
int NBL = fem->ModelLoads();
vec3d bf(0, 0, 0);
for (int j = 0; j < NBL; ++j)
{
FEBodyForce* pbf = dynamic_cast<FEBodyForce*>(fem->ModelLoad(j));
FEMaterialPoint& pt = const_cast<FEMaterialPoint&>(mp);
if (pbf && pbf->IsActive()) bf += pbf->force(pt);
}
// NOTE: We flip the sign because FEBio applies the negative of the body force.
// see FEElasticSolidDomain::BodyForce
return -bf;
});
return true;
}
return false;
}
bool FEPlotEdgeContactGap::Save(FEEdge& edge, FEDataStream& a)
{
FEEdgeToSurfaceSlidingContactEdge* pe = dynamic_cast<FEEdgeToSurfaceSlidingContactEdge*>(&edge);
if (pe == nullptr) return false;
for (int i = 0; i < pe->Nodes(); ++i)
{
FEE2SSlidingContactPoint& pt = pe->m_points[i];
a << pt.m_gap;
}
return true;
}
bool FEPlotTotalLinearMomentum::Save(FEDomain& dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
vec3d L(0,0,0);
FESolidDomain& solidDomain = dynamic_cast<FESolidDomain&>(dom);
for (int i = 0; i < solidDomain.Elements(); ++i)
{
FESolidElement& el = solidDomain.Element(i);
int nint = el.GaussPoints();
double* w = el.GaussWeights();
for (int n = 0; n < nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
vec3d& v = pt.m_v;
double J0 = solidDomain.detJ0(el, n);
L.x += v.x * J0 * w[n];
L.y += v.y * J0 * w[n];
L.z += v.z * J0 * w[n];
}
}
a << L;
return true;
}
return false;
}
bool FEPlotTotalAngularMomentum::Save(FEDomain& dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
vec3d J(0, 0, 0);
FESolidDomain& solidDomain = dynamic_cast<FESolidDomain&>(dom);
for (int i = 0; i < solidDomain.Elements(); ++i)
{
FESolidElement& el = solidDomain.Element(i);
int nint = el.GaussPoints();
double* w = el.GaussWeights();
for (int n = 0; n < nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
vec3d& r = mp.m_rt;
vec3d& v = pt.m_v;
vec3d j = r ^ v;
double J0 = solidDomain.detJ0(el, n);
J.x += j.x * J0 * w[n];
J.y += j.y * J0 * w[n];
J.z += j.z * J0 * w[n];
}
}
a << J;
return true;
}
return false;
}
bool FEPlotTotalEnergy::Save(FEDomain& dom, FEDataStream& a)
{
if (dom.Class() == FE_DOMAIN_SOLID)
{
FEElasticMaterial* pme = dom.GetMaterial()->ExtractProperty<FEElasticMaterial>();
if (pme == 0) return false;
double E = 0.0;
FESolidDomain& solidDomain = dynamic_cast<FESolidDomain&>(dom);
for (int i = 0; i < solidDomain.Elements(); ++i)
{
FESolidElement& el = solidDomain.Element(i);
int nint = el.GaussPoints();
double* w = el.GaussWeights();
for (int n = 0; n < nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// strain energy
double W = pme->StrainEnergyDensity(mp);
// kinetic energy
double D = pme->Density(mp);
vec3d& v = pt.m_v;
double K = 0.5 * (v * v) * D;
double J0 = solidDomain.detJ0(el, n);
E += (K + W) * J0 * w[n];
}
}
a << E;
return true;
}
return false;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEMembraneMaterial.h | .h | 3,064 | 104 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEMaterial.h>
#include <FECore/DumpStream.h>
#include "febiomech_api.h"
//-----------------------------------------------------------------------------
class FEMembraneMaterialPoint : public FEMaterialPointData
{
public:
FEMembraneMaterialPoint()
{
s[0] = s[1] = s[2] = 0;
}
FEMaterialPointData* Copy()
{
return new FEMembraneMaterialPoint(*this);
}
void Serialize(DumpStream& ar)
{
FEMaterialPointData::Serialize(ar);
ar & g & s;
}
public:
// calculate membrane strain
void strain(double e[3]);
public:
double g[6]; // deformation gradient
double s[3]; // in-plane PK2 stress
};
//-----------------------------------------------------------------------------
class FEBIOMECH_API FEMembraneMaterial : public FEMaterial
{
public:
FEMembraneMaterial(FEModel* pfem) : FEMaterial(pfem) {}
virtual ~FEMembraneMaterial() {}
//! create material point data
FEMaterialPointData* CreateMaterialPointData() { return new FEMembraneMaterialPoint; }
public:
//! calculate in-plane membrane stress
virtual void Stress(FEMaterialPoint& mp, double s[3]) = 0;
//! calculate in-plane membrane tangent
virtual void Tangent(FEMaterialPoint& mp, double D[3][3]) = 0;
FECORE_BASE_CLASS(FEMembraneMaterial)
};
//-----------------------------------------------------------------------------
// class for triangular membranes
class FEElasticMembrane : public FEMembraneMaterial
{
public:
//! constructor
FEElasticMembrane(FEModel* pfem) : FEMembraneMaterial(pfem) {}
public:
//! calculate in-plane membrane stress
void Stress(FEMaterialPoint& mp, double s[3]) override;
//! calculate in-plane membrane tangent
void Tangent(FEMaterialPoint& mp, double D[3][3]) override;
public:
double m_E;
double m_v;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEFiberIntegrationTriangle.cpp | .cpp | 15,204 | 508 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFiberIntegrationTriangle.h"
#include "triangle_sphere.h"
#ifndef SQR
#define SQR(x) ((x)*(x))
#endif
class FEFiberIntegrationTriangle::Iterator : public FEFiberIntegrationSchemeIterator
{
public:
Iterator(int nint, const double* cth, const double* cph, const double* sth, const double* sph, const double* wn)
{
m_nint = nint;
m_cth = cth;
m_cph = cph;
m_sth = sth;
m_sph = sph;
m_wn = wn;
n = -1;
Next();
}
bool IsValid()
{
return (n < m_nint);
}
// move to the next integration point
bool Next()
{
n++;
if (n < m_nint)
{
m_fiber.x = m_cth[n] * m_sph[n];
m_fiber.y = m_sth[n] * m_sph[n];
m_fiber.z = m_cph[n];
m_weight = m_wn[n];
return true;
}
else return false;
}
private:
int n;
int m_nint;
const double* m_cth;
const double* m_cph;
const double* m_sth;
const double* m_sph;
const double* m_wn;
};
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEFiberIntegrationTriangle, FEFiberIntegrationScheme)
ADD_PARAMETER(m_nre, "resolution")->setEnums(" 20\0 34\0 60\0 74\0 196\0 210\0 396\0 410\0 596\0 610\0 796\0 810\0 996\0 1010\0 1196\0 1210\0 1396\0 1410\0 1596\0 1610\0 1796\0");
END_FECORE_CLASS();
FEFiberIntegrationTriangle::FEFiberIntegrationTriangle(FEModel* pfem) : FEFiberIntegrationScheme(pfem)
{
m_nres = 0;
m_nre = -1;
}
FEFiberIntegrationTriangle::~FEFiberIntegrationTriangle()
{
}
//-----------------------------------------------------------------------------
bool FEFiberIntegrationTriangle::Init()
{
int list[21] = {NST20, NST34, NST60, NST74, NST196, NST210, NST396, NST410, NST596, NST610, NST796, NST810, NST996, NST1010, NST1196, NST1210, NST1396, NST1410, NST1596, NST1610, NST1796};
// this is needed to maintain backward compatibility
if (m_nre > 21) m_nres = m_nre;
else m_nres = list[m_nre];
// initialize integration rule data
InitIntegrationRule();
// also initialize the parent class
return FEFiberIntegrationScheme::Init();
}
//-----------------------------------------------------------------------------
void FEFiberIntegrationTriangle::Serialize(DumpStream& ar)
{
FEFiberIntegrationScheme::Serialize(ar);
if (ar.IsSaving() == false)
{
InitIntegrationRule();
}
}
//-----------------------------------------------------------------------------
void FEFiberIntegrationTriangle::InitIntegrationRule()
{
switch (m_nres) {
case 20:
m_nint=NST20;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA20[n]);
m_sth[n] = sin(THETA20[n]);
m_cph[n] = cos(PHI20[n]);
m_sph[n] = sin(PHI20[n]);
m_w[n] = AREA20[n];
}
break;
case 34:
m_nint=NST34;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA34[n]);
m_sth[n] = sin(THETA34[n]);
m_cph[n] = cos(PHI34[n]);
m_sph[n] = sin(PHI34[n]);
m_w[n] = AREA34[n];
}
break;
case 60:
m_nint=NST60;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA60[n]);
m_sth[n] = sin(THETA60[n]);
m_cph[n] = cos(PHI60[n]);
m_sph[n] = sin(PHI60[n]);
m_w[n] = AREA60[n];
}
break;
case 74:
m_nint=NST74;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA74[n]);
m_sth[n] = sin(THETA74[n]);
m_cph[n] = cos(PHI74[n]);
m_sph[n] = sin(PHI74[n]);
m_w[n] = AREA74[n];
}
break;
case 196:
m_nint=NST196;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA196[n]);
m_sth[n] = sin(THETA196[n]);
m_cph[n] = cos(PHI196[n]);
m_sph[n] = sin(PHI196[n]);
m_w[n] = AREA196[n];
}
break;
case 210:
m_nint=NST210;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA210[n]);
m_sth[n] = sin(THETA210[n]);
m_cph[n] = cos(PHI210[n]);
m_sph[n] = sin(PHI210[n]);
m_w[n] = AREA210[n];
}
break;
case 396:
m_nint=NST396;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA396[n]);
m_sth[n] = sin(THETA396[n]);
m_cph[n] = cos(PHI396[n]);
m_sph[n] = sin(PHI396[n]);
m_w[n] = AREA396[n];
}
break;
case 410:
m_nint=NST410;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA410[n]);
m_sth[n] = sin(THETA410[n]);
m_cph[n] = cos(PHI410[n]);
m_sph[n] = sin(PHI410[n]);
m_w[n] = AREA410[n];
}
break;
case 596:
m_nint=NST596;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA596[n]);
m_sth[n] = sin(THETA596[n]);
m_cph[n] = cos(PHI596[n]);
m_sph[n] = sin(PHI596[n]);
m_w[n] = AREA596[n];
}
break;
case 610:
m_nint=NST610;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA610[n]);
m_sth[n] = sin(THETA610[n]);
m_cph[n] = cos(PHI610[n]);
m_sph[n] = sin(PHI610[n]);
m_w[n] = AREA610[n];
}
break;
case 796:
m_nint=NST796;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA796[n]);
m_sth[n] = sin(THETA796[n]);
m_cph[n] = cos(PHI796[n]);
m_sph[n] = sin(PHI796[n]);
m_w[n] = AREA796[n];
}
break;
case 810:
m_nint=NST810;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA810[n]);
m_sth[n] = sin(THETA810[n]);
m_cph[n] = cos(PHI810[n]);
m_sph[n] = sin(PHI810[n]);
m_w[n] = AREA810[n];
}
break;
case 996:
m_nint=NST996;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA996[n]);
m_sth[n] = sin(THETA996[n]);
m_cph[n] = cos(PHI996[n]);
m_sph[n] = sin(PHI996[n]);
m_w[n] = AREA996[n];
}
break;
case 1010:
m_nint=NST1010;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1010[n]);
m_sth[n] = sin(THETA1010[n]);
m_cph[n] = cos(PHI1010[n]);
m_sph[n] = sin(PHI1010[n]);
m_w[n] = AREA1010[n];
}
break;
case 1196:
m_nint=NST1196;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1196[n]);
m_sth[n] = sin(THETA1196[n]);
m_cph[n] = cos(PHI1196[n]);
m_sph[n] = sin(PHI1196[n]);
m_w[n] = AREA1196[n];
}
break;
case 1210:
m_nint=NST1210;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1210[n]);
m_sth[n] = sin(THETA1210[n]);
m_cph[n] = cos(PHI1210[n]);
m_sph[n] = sin(PHI1210[n]);
m_w[n] = AREA1210[n];
}
break;
case 1396:
m_nint=NST1396;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1396[n]);
m_sth[n] = sin(THETA1396[n]);
m_cph[n] = cos(PHI1396[n]);
m_sph[n] = sin(PHI1396[n]);
m_w[n] = AREA1396[n];
}
break;
case 1410:
m_nint=NST1410;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1410[n]);
m_sth[n] = sin(THETA1410[n]);
m_cph[n] = cos(PHI1410[n]);
m_sph[n] = sin(PHI1410[n]);
m_w[n] = AREA1410[n];
}
break;
case 1596:
m_nint=NST1596;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1596[n]);
m_sth[n] = sin(THETA1596[n]);
m_cph[n] = cos(PHI1596[n]);
m_sph[n] = sin(PHI1596[n]);
m_w[n] = AREA1596[n];
}
break;
case 1610:
m_nint=NST1610;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1610[n]);
m_sth[n] = sin(THETA1610[n]);
m_cph[n] = cos(PHI1610[n]);
m_sph[n] = sin(PHI1610[n]);
m_w[n] = AREA1610[n];
}
break;
case 1796:
m_nint=NST1796;
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(THETA1796[n]);
m_sth[n] = sin(THETA1796[n]);
m_cph[n] = cos(PHI1796[n]);
m_sph[n] = sin(PHI1796[n]);
m_w[n] = AREA1796[n];
}
break;
}
}
//-----------------------------------------------------------------------------
FEFiberIntegrationSchemeIterator* FEFiberIntegrationTriangle::GetIterator(FEMaterialPoint* mp)
{
return new Iterator(m_nint, &m_cth[0], &m_cph[0], &m_sth[0], &m_sph[0], &m_w[0]);
}
/*
//-----------------------------------------------------------------------------
mat3ds FEFiberIntegrationTriangle::Stress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
mat3d QT = Q.transpose();
// loop over all integration points
double R;
vec3d n0e, n0a;
mat3ds s;
s.zero();
for (int n=0; n<m_nint; ++n)
{
// set the global fiber direction in reference configuration
n0e.x = m_cth[n]*m_sph[n];
n0e.y = m_sth[n]*m_sph[n];
n0e.z = m_cph[n];
m_pFmat->SetFiberDirection(mp, n0e);
// get the local material fiber direction in reference configuration
n0a = QT*n0e;
// evaluate the fiber density
R = m_pFDD->FiberDensity(n0a);
// evaluate this fiber's contribution to the stress
s += m_pFmat->Stress(mp)*(R*m_w[n]);
}
return s;
}
//-----------------------------------------------------------------------------
tens4ds FEFiberIntegrationTriangle::Tangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
mat3d QT = Q.transpose();
// loop over all integration points
double R;
vec3d n0e, n0a;
tens4ds c;
c.zero();
for (int n=0; n<m_nint; ++n)
{
// set the global fiber direction in reference configuration
n0e.x = m_cth[n]*m_sph[n];
n0e.y = m_sth[n]*m_sph[n];
n0e.z = m_cph[n];
m_pFmat->SetFiberDirection(mp, n0e);
// get the local material fiber direction in reference configuration
n0a = QT*n0e;
// evaluate the fiber density
R = m_pFDD->FiberDensity(n0a);
// evaluate this fiber's contribution to the tangent
c += m_pFmat->Tangent(mp)*(R*m_w[n]);
}
return c;
}
//-----------------------------------------------------------------------------
double FEFiberIntegrationTriangle::StrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
mat3d QT = Q.transpose();
// loop over all integration points
double R;
vec3d n0e, n0a;
double sed = 0.0;
for (int n=0; n<m_nint; ++n)
{
// set the global fiber direction in reference configuration
n0e.x = m_cth[n]*m_sph[n];
n0e.y = m_sth[n]*m_sph[n];
n0e.z = m_cph[n];
m_pFmat->SetFiberDirection(mp, n0e);
// get the local material fiber direction in reference configuration
n0a = QT*n0e;
// evaluate the fiber density
R = m_pFDD->FiberDensity(n0a);
// evaluate this fiber's contribution to the stress
sed += m_pFmat->StrainEnergyDensity(mp)*(R*m_w[n]);
}
return sed;
}
//-----------------------------------------------------------------------------
double FEFiberIntegrationTriangle::IntegratedFiberDensity()
{
// initialize integrated fiber density distribution
double IFD = 1;
// loop over all integration points
double R;
vec3d n0a;
double C = 0;
for (int n=0; n<m_nint; ++n)
{
// set the global fiber direction in reference configuration
n0a.x = m_cth[n]*m_sph[n];
n0a.y = m_sth[n]*m_sph[n];
n0a.z = m_cph[n];
// evaluate the fiber density
R = m_pFDD->FiberDensity(n0a);
// integrate the fiber density
C += R*m_w[n];
}
IFD = C;
return IFD;
}
*/
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEUncoupledElasticMixture.cpp | .cpp | 9,900 | 292 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEUncoupledElasticMixture.h"
#include <FECore/FECoreKernel.h>
#include <FECore/log.h>
// define the material parameters
BEGIN_FECORE_CLASS(FEUncoupledElasticMixture, FEUncoupledMaterial)
ADD_PROPERTY(m_pMat, "solid");
ADD_PROPERTY(m_Q, "mat_axis")->SetFlags(FEProperty::Optional);
END_FECORE_CLASS();
//////////////////////////////////////////////////////////////////////
// Mixture of uncoupled elastic solids
//////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
FEUncoupledElasticMixture::FEUncoupledElasticMixture(FEModel* pfem) : FEUncoupledMaterial(pfem)
{
}
//-----------------------------------------------------------------------------
FEMaterialPointData* FEUncoupledElasticMixture::CreateMaterialPointData()
{
FEElasticMixtureMaterialPoint* pt = new FEElasticMixtureMaterialPoint();
int NMAT = Materials();
for (int i=0; i<NMAT; ++i) pt->AddMaterialPoint(new FEMaterialPoint(m_pMat[i]->CreateMaterialPointData()));
return pt;
}
//-----------------------------------------------------------------------------
void FEUncoupledElasticMixture::AddMaterial(FEElasticMaterial* pm)
{
m_pMat.push_back(dynamic_cast<FEUncoupledMaterial*>(pm));
}
//-----------------------------------------------------------------------------
//! data initialization
bool FEUncoupledElasticMixture::Init()
{
// check if any of the solid materials are elastic mixtures -- none allowed,
// otherwise FEBio does not know which FEElasticMixtureMaterialPoint to access
int nmix = 0;
for (int i=0; i<Materials(); ++i) {
if (dynamic_cast<FEElasticMixture*>(m_pMat[i])) nmix++;
if (dynamic_cast<FEUncoupledElasticMixture*>(m_pMat[i])) nmix++;
}
if (nmix > 0) {
feLogError("Solids in uncoupled solid mixture material cannot be solid mixtures");
return false;
}
return FEElasticMaterial::Init();
}
//-----------------------------------------------------------------------------
mat3ds FEUncoupledElasticMixture::DevStress(FEMaterialPoint& mp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
vector<double>& w = pt.m_w;
assert(w.size() == m_pMat.size());
// get the elastic material point
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate stress
mat3ds s; s.zero();
for (int i=0; i < (int)m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
// copy the elastic material point data to the components
FEElasticMaterialPoint& epi = *mpi.ExtractData<FEElasticMaterialPoint>();
epi.m_F = ep.m_F;
epi.m_J = ep.m_J;
epi.m_v = ep.m_v;
epi.m_a = ep.m_a;
epi.m_L = ep.m_L;
FEUncoupledMaterial* uMat = dynamic_cast<FEUncoupledMaterial*>(m_pMat[i]);
if (uMat)
s += epi.m_s = uMat->DevStress(mpi)*w[i];
else
s += epi.m_s = m_pMat[i]->Stress(mpi)*w[i];
}
return s;
}
//-----------------------------------------------------------------------------
tens4ds FEUncoupledElasticMixture::DevTangent(FEMaterialPoint& mp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
vector<double>& w = pt.m_w;
assert(w.size() == m_pMat.size());
// get the elastic material point
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate elasticity tensor
tens4ds c(0.);
for (int i=0; i < (int)m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
// copy the elastic material point data to the components
FEElasticMaterialPoint& epi = *mpi.ExtractData<FEElasticMaterialPoint>();
epi.m_F = ep.m_F;
epi.m_J = ep.m_J;
epi.m_v = ep.m_v;
epi.m_a = ep.m_a;
epi.m_L = ep.m_L;
FEUncoupledMaterial* uMat = dynamic_cast<FEUncoupledMaterial*>(m_pMat[i]);
if (uMat)
c += uMat->DevTangent(mpi)*w[i];
else
c += m_pMat[i]->Tangent(mpi)*w[i];
}
return c;
}
//-----------------------------------------------------------------------------
double FEUncoupledElasticMixture::DevStrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
vector<double>& w = pt.m_w;
assert(w.size() == m_pMat.size());
// get the elastic material point
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate strain energy density
double sed = 0.0;
for (int i=0; i < (int)m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
// copy the elastic material point data to the components
FEElasticMaterialPoint& epi = *mpi.ExtractData<FEElasticMaterialPoint>();
epi.m_F = ep.m_F;
epi.m_J = ep.m_J;
epi.m_v = ep.m_v;
epi.m_a = ep.m_a;
epi.m_L = ep.m_L;
FEUncoupledMaterial* uMat = dynamic_cast<FEUncoupledMaterial*>(m_pMat[i]);
if (uMat)
sed += uMat->DevStrainEnergyDensity(mpi)*w[i];
else
sed += m_pMat[i]->StrainEnergyDensity(mpi)*w[i];
}
return sed;
}
//-----------------------------------------------------------------------------
double FEUncoupledElasticMixture::StrongBondDevSED(FEMaterialPoint& mp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
vector<double>& w = pt.m_w;
assert(w.size() == m_pMat.size());
// get the elastic material point
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate strain energy density
double sed = 0.0;
for (int i=0; i < (int)m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
// copy the elastic material point data to the components
FEElasticMaterialPoint& epi = *mpi.ExtractData<FEElasticMaterialPoint>();
epi.m_F = ep.m_F;
epi.m_J = ep.m_J;
epi.m_v = ep.m_v;
epi.m_a = ep.m_a;
epi.m_L = ep.m_L;
FEUncoupledMaterial* uMat = dynamic_cast<FEUncoupledMaterial*>(m_pMat[i]);
if (uMat)
sed += uMat->StrongBondDevSED(mpi)*w[i];
else
sed += m_pMat[i]->StrongBondSED(mpi)*w[i];
}
return sed;
}
//-----------------------------------------------------------------------------
double FEUncoupledElasticMixture::WeakBondDevSED(FEMaterialPoint& mp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
vector<double>& w = pt.m_w;
assert(w.size() == m_pMat.size());
// get the elastic material point
FEElasticMaterialPoint& ep = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate strain energy density
double sed = 0.0;
for (int i=0; i < (int)m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
// copy the elastic material point data to the components
FEElasticMaterialPoint& epi = *mpi.ExtractData<FEElasticMaterialPoint>();
epi.m_F = ep.m_F;
epi.m_J = ep.m_J;
epi.m_v = ep.m_v;
epi.m_a = ep.m_a;
epi.m_L = ep.m_L;
FEUncoupledMaterial* uMat = dynamic_cast<FEUncoupledMaterial*>(m_pMat[i]);
if (uMat)
sed += uMat->WeakBondDevSED(*pt.GetPointData(i))*w[i];
else
sed += m_pMat[i]->WeakBondSED(*pt.GetPointData(i))*w[i];
}
return sed;
}
//-----------------------------------------------------------------------------
//! specialized material points
void FEUncoupledElasticMixture::UpdateSpecializedMaterialPoints(FEMaterialPoint& mp, const FETimeInfo& tp)
{
FEElasticMixtureMaterialPoint& pt = *mp.ExtractData<FEElasticMixtureMaterialPoint>();
for (int i=0; i < (int) m_pMat.size(); ++i)
{
FEMaterialPoint& mpi = *pt.GetPointData(i);
mpi.m_elem = mp.m_elem;
mpi.m_index = mp.m_index;
mpi.m_rt = mp.m_rt;
mpi.m_r0 = mp.m_r0;
FEMaterial* pmj = GetMaterial(i);
pmj->UpdateSpecializedMaterialPoints(mpi, tp);
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEEFDNeoHookean.h | .h | 3,065 | 102 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FECore/FEMaterial.h"
#include "FENeoHookean.h"
#include "FEEllipsoidalFiberDistribution.h"
class FEEFDNeoHookean : public FEElasticMaterial
{
public:
FEEFDNeoHookean(FEModel* pfem);
public:
double m_E; //!< Young's modulus
double m_v; //!< Poisson's ratio
double m_ksi[3]; //!< ksi
double m_beta[3]; //!< beta
public:
//! calculate stress at material point
virtual mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
virtual tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
virtual double StrainEnergyDensity(FEMaterialPoint& pt) override;
//! data initialization
bool Init() override;
//! serialization
void Serialize(DumpStream& ar) override;
public:
FEEllipsoidalFiberDistribution m_EFD;
FENeoHookean m_NH;
// declare the parameter list
DECLARE_FECORE_CLASS();
};
//----------------------------------------------------------------
// "old" version using full-sphere integration
class FEEFDNeoHookeanOld : public FEElasticMaterial
{
public:
FEEFDNeoHookeanOld(FEModel* pfem) : FEElasticMaterial(pfem), m_EFD(pfem), m_NH(pfem) {}
public:
//! calculate stress at material point
virtual mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
virtual tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
virtual double StrainEnergyDensity(FEMaterialPoint& pt) override;
//! data initialization and checking
bool Init() override;
//! serialization
void Serialize(DumpStream& ar) override;
public:
FEEllipsoidalFiberDistributionOld m_EFD;
FENeoHookean m_NH;
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEIdealGasPressure.h | .h | 2,272 | 69 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESurfaceLoad.h>
#include <FECore/FEModelParam.h>
//-----------------------------------------------------------------------------
//! The pressure surface is a surface domain that sustains pressure boundary
//! conditions
//!
class FEIdealGasPressure : public FESurfaceLoad
{
public:
//! constructor
FEIdealGasPressure(FEModel* pfem);
//! initialization
bool Init() override;
void Activate() override;
void Update() override;
public:
double GetCurrentPressure() const { return m_currentPressure; }
public:
//! calculate residual
void LoadVector(FEGlobalVector& R) override;
//! calculate stiffness
void StiffnessMatrix(FELinearSystem& LS) override;
protected:
double m_initialPressure; //!< initial pressure value
bool m_bsymm; //!< use symmetric formulation
bool m_bshellb; //!< flag for prescribing pressure on shell bottom
private:
double m_initialVolume;
double m_currentVolume;
double m_currentPressure;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEEFDVerondaWestmann.cpp | .cpp | 3,140 | 84 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEEFDVerondaWestmann.h"
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEEFDVerondaWestmann, FEUncoupledMaterial)
ADD_PARAMETER(m_VW.m_c1, "c1")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_VW.m_c2, "c2");
ADD_PARAMETER(m_EFD.m_beta, 3, "beta");
ADD_PARAMETER(m_EFD.m_ksi , 3, "ksi" )->setUnits(UNIT_PRESSURE);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEEFDVerondaWestmann::FEEFDVerondaWestmann(FEModel* pfem) : FEUncoupledMaterial(pfem), m_VW(pfem), m_EFD(pfem)
{
m_VW.SetParent(this);
m_EFD.SetParent(this);
}
//-----------------------------------------------------------------------------
bool FEEFDVerondaWestmann::Init()
{
if (FEUncoupledMaterial::Init() == false) return false;
if (m_VW.Init() == false) return false;
if (m_EFD.Init() == false) return false;
return true;
}
//-----------------------------------------------------------------------------
void FEEFDVerondaWestmann::Serialize(DumpStream& ar)
{
FEUncoupledMaterial::Serialize(ar);
m_VW.Serialize(ar);
m_EFD.Serialize(ar);
}
//-----------------------------------------------------------------------------
mat3ds FEEFDVerondaWestmann::DevStress(FEMaterialPoint& pt)
{
return m_VW.DevStress(pt) + m_EFD.DevStress(pt);
}
//-----------------------------------------------------------------------------
tens4ds FEEFDVerondaWestmann::DevTangent(FEMaterialPoint& pt)
{
return m_VW.DevTangent(pt) + m_EFD.DevTangent(pt);
}
//-----------------------------------------------------------------------------
//! calculate deviatoric strain energy density
double FEEFDVerondaWestmann::DevStrainEnergyDensity(FEMaterialPoint& pt)
{
return m_VW.DevStrainEnergyDensity(pt) + m_EFD.DevStrainEnergyDensity(pt);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEFungOrthoCompressible.h | .h | 2,161 | 61 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEElasticMaterial.h"
class FEFungOrthoCompressible : public FEElasticMaterial
{
public:
double E1, E2, E3; // Young's moduli
double v12, v23, v31; // Poisson's ratio
double G12, G23, G31; // Shear moduli
double lam[3][3]; // first Lame coefficients
double mu[3]; // second Lame coefficients
double m_c; // c coefficient
double m_k; // bulk modulus
public:
FEFungOrthoCompressible(FEModel* pfem) : FEElasticMaterial(pfem) {}
//! calculate stress at material point
mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
double StrainEnergyDensity(FEMaterialPoint& pt) override;
//! data initialization
bool Validate() override;
// declare parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FENodeToNodeConstraint.h | .h | 2,243 | 63 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FENLConstraint.h>
class FENodeToNodeConstraint : public FENLConstraint
{
public:
FENodeToNodeConstraint(FEModel* fem);
// allocate equations
int InitEquations(int neq) override;
// The LoadVector function evaluates the "forces" that contribute to the residual of the system
void LoadVector(FEGlobalVector& R, const FETimeInfo& tp) override;
// Evaluates the contriubtion to the stiffness matrix
void StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) override;
// Build the matrix profile
void BuildMatrixProfile(FEGlobalMatrix& M) override;
protected:
void UnpackLM(vector<int>& lm);
void Serialize(DumpStream& ar) override;
void PrepStep();
void Update(const std::vector<double>& Ui, const std::vector<double>& ui) override;
void UpdateIncrements(std::vector<double>& Ui, const std::vector<double>& ui) override;
private:
int m_a, m_b;
vec3d m_Lm, m_Lp;
vector<int> m_LM;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEDonnanEquilibrium.cpp | .cpp | 7,468 | 234 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEDonnanEquilibrium.h"
#include <FECore/FEModel.h>
#include <FECore/log.h>
FEMaterialPointData* FEDonnanEquilibriumMaterialPoint::Copy()
{
FEDonnanEquilibriumMaterialPoint* pt = new FEDonnanEquilibriumMaterialPoint(*this);
if (m_pNext) pt->m_pNext = m_pNext->Copy();
return pt;
}
void FEDonnanEquilibriumMaterialPoint::Init()
{
FEMaterialPointData::Init();
// intialize data to zero
m_cF = 0;
m_osm = 0;
m_p = 0;
m_bpi = 0;
}
void FEDonnanEquilibriumMaterialPoint::Serialize(DumpStream& ar)
{
FEMaterialPointData::Serialize(ar);
ar & m_cFr & m_cF & m_osm & m_p & m_bpi;
}
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDonnanEquilibrium, FEElasticMaterial)
ADD_PARAMETER(m_phiwr, FE_RANGE_LEFT_OPEN(0.0, 1.0), "phiw0");
ADD_PARAMETER(m_phisr, "phis0");
ADD_PARAMETER(m_cFr , "cF0")->setUnits(UNIT_CONCENTRATION);
ADD_PARAMETER(m_bosm , FE_RANGE_GREATER_OR_EQUAL(0.0), "bosm")->setUnits(UNIT_CONCENTRATION);
ADD_PARAMETER(m_Phi , FE_RANGE_GREATER_OR_EQUAL(0.0), "Phi");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEDonnanEquilibrium::FEDonnanEquilibrium(FEModel* pfem) : FEElasticMaterial(pfem)
{
m_Rgas = 0; m_Tabs = 0; m_cFr = 0; m_phiwr = -1; m_phisr = -1;
m_bnew = false; m_binit = false; m_Phi = 1;
}
//-----------------------------------------------------------------------------
// FEDonnanEquilibrium
bool FEDonnanEquilibrium::Init()
{
if (!m_binit) {
if (m_phisr >= 0) {
m_bnew = true;
m_phiwr = 1 - m_phisr; // use value at t=0 to initialize
}
m_binit = true;
}
m_Rgas = GetFEModel()->GetGlobalConstant("R");
m_Tabs = GetFEModel()->GetGlobalConstant("T");
if (m_Rgas <= 0) { feLogError("A positive universal gas constant R must be defined in Globals section"); return false; }
if (m_Tabs <= 0) { feLogError("A positive absolute temperature T must be defined in Globals section"); return false; }
return FEElasticMaterial::Init();
}
void FEDonnanEquilibrium::Serialize(DumpStream& ar)
{
FEElasticMaterial::Serialize(ar);
ar & m_Rgas & m_Tabs & m_binit & m_bnew & m_phiwr;
}
//-----------------------------------------------------------------------------
mat3ds FEDonnanEquilibrium::Stress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
// calculate fixed charge density in current configuration
double cF;
if (m_bnew)
cF = m_phiwr*m_cFr(mp)/(J-m_phisr);
else
cF = m_phiwr*m_cFr(mp)/(J-1+m_phiwr);
// calculate osmotic pressure
double p = m_Rgas*m_Tabs*m_Phi*(sqrt(cF*cF+m_bosm*m_bosm) - m_bosm);
// calculate T = -p*I
mat3dd I(1.0); // identity tensor
mat3ds s = -p*I;
return s;
}
//-----------------------------------------------------------------------------
tens4ds FEDonnanEquilibrium::Tangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
// calculate fixed charge density in current configuration
double cF;
if (m_bnew)
cF = m_phiwr*m_cFr(mp)/(J-m_phisr);
else
cF = m_phiwr*m_cFr(mp)/(J-1+m_phiwr);
// calculate osmotic pressure
double tosm = sqrt(cF*cF+m_bosm*m_bosm); // tissue osmolarity
double p = m_Rgas*m_Tabs*m_Phi*(tosm - m_bosm); // osmotic pressure
// calculate derivative of osmotic pressure w.r.t. J
double bpi;
if (m_bnew)
bpi = m_Rgas*m_Tabs*m_Phi*J*cF*cF/(J-m_phisr)/tosm;
else
bpi = m_Rgas*m_Tabs*m_Phi*J*cF*cF/(J-1+m_phiwr)/tosm;
mat3dd I(1.0); // Identity
tens4ds IxI = dyad1s(I);
tens4ds I4 = dyad4s(I);
// calculate tangent osmotic modulus
tens4ds c = bpi*IxI + p*(2.0*I4 - IxI);
return c;
}
//-----------------------------------------------------------------------------
double FEDonnanEquilibrium::FixedChargeDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
// calculate fixed charge density in current configuration
double cF;
if (m_bnew)
cF = m_phiwr*m_cFr(mp)/(J-m_phisr);
else
cF = m_phiwr*m_cFr(mp)/(J-1+m_phiwr);
return cF;
}
//-----------------------------------------------------------------------------
double FEDonnanEquilibrium::OsmoticPressure(FEMaterialPoint& mp)
{
double cF = FixedChargeDensity(mp);
// calculate osmotic pressure
double p = m_Rgas*m_Tabs*m_Phi*(sqrt(cF*cF+m_bosm*m_bosm) - m_bosm);
return p;
}
//-----------------------------------------------------------------------------
double FEDonnanEquilibrium::OsmoticPressureTangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
double cF = FixedChargeDensity(mp);
double tosm = Osmolarity(mp);
// calculate derivative of osmotic pressure w.r.t. J
double bpi;
if (m_bnew)
bpi = m_Rgas*m_Tabs*m_Phi*J*cF*cF/(J-m_phisr)/tosm;
else
bpi = m_Rgas*m_Tabs*m_Phi*J*cF*cF/(J-1+m_phiwr)/tosm;
return bpi;
}
//-----------------------------------------------------------------------------
double FEDonnanEquilibrium::Osmolarity(FEMaterialPoint& mp)
{
double cF = FixedChargeDensity(mp);
double tosm = sqrt(cF*cF+m_bosm*m_bosm); // tissue osmolarity
return tosm;
}
//-----------------------------------------------------------------------------
// update Donnan equilibrium material point at each iteration
void FEDonnanEquilibrium::UpdateSpecializedMaterialPoints(FEMaterialPoint& pt, const FETimeInfo& tp)
{
// get the Donnan equilibrium material point data
FEDonnanEquilibriumMaterialPoint& pd = *pt.ExtractData<FEDonnanEquilibriumMaterialPoint>();
pd.m_cFr = m_cFr(pt);
pd.m_cF = FixedChargeDensity(pt);
pd.m_osm = Osmolarity(pt);
pd.m_p = OsmoticPressure(pt);
pd.m_bpi = OsmoticPressureTangent(pt);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEConstPrestrain.h | .h | 2,025 | 61 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEPreStrainElastic.h"
//-----------------------------------------------------------------------------
// A constant, full-tensor pre-strain gradient
class FEConstPrestrainGradient : public FEPrestrainGradient
{
public:
class MaterialPointData : public FEMaterialPointData
{
public:
MaterialPointData();
void Init(bool bflag);
FEMaterialPointData* Copy();
void Serialize(DumpStream& ar);
public:
mat3d Fp;
};
public:
FEConstPrestrainGradient(FEModel* pfem);
FEMaterialPointData* CreateMaterialPointData() override;
mat3d Prestrain(FEMaterialPoint& mp) override;
void Initialize(const mat3d& F, FEMaterialPoint& mp) override;
protected:
double m_ramp;
FEParamMat3d m_Fp;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEDamageCDF.cpp | .cpp | 12,081 | 389 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEDamageCDF.h"
#include "FEDamageCriterion.h"
#include "FEDamageMaterialPoint.h"
#include <FECore/log.h>
#include <FECore/gamma.h>
#include <math.h>
#ifndef M_PI
#define M_PI 3.141592653589793238462643
#endif
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDF, FEMaterialProperty)
ADD_PARAMETER(m_Dmax , FE_RANGE_CLOSED(0.0, 1.0), "Dmax");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
double FEDamageCDF::Damage(FEMaterialPoint& mp) {
// get the damage material point data
FEDamageMaterialPoint& dp = *mp.ExtractData<FEDamageMaterialPoint>();
// get the damage criterion (assuming dp.m_Etrial is up-to-date)
double Es = max(dp.m_Etrial, dp.m_Emax);
dp.m_D = cdf(mp,Es)*m_Dmax;
return dp.m_D;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFSimo, FEDamageCDF)
ADD_PARAMETER(m_alpha, FE_RANGE_GREATER(0.0), "a");
ADD_PARAMETER(m_beta , FE_RANGE_CLOSED(0.0, 1.0), "b");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFSimo::FEDamageCDFSimo(FEModel* pfem) : FEDamageCDF(pfem)
{
}
//-----------------------------------------------------------------------------
// Simo damage cumulative distribution function
// Simo, CMAME 60 (1987), 153-173
// Simo damage cumulative distribution function
double FEDamageCDFSimo::cdf(FEMaterialPoint& mp, const double X)
{
double alpha = m_alpha(mp);
double beta = m_beta(mp);
if (alpha == 0) {
return 0;
}
double cdf = 0;
// this CDF only admits positive values
if (X >= 0) {
if (X > 1e-12) cdf = 1 - beta - (1.0 - beta)*(1.0 - exp(-X/alpha))*alpha/X;
else cdf = 0.5*(1.0 - beta)/alpha*X;
}
return cdf;
}
// Simo damage probability density function
double FEDamageCDFSimo::pdf(FEMaterialPoint& mp, const double X)
{
double alpha = m_alpha(mp);
double beta = m_beta(mp);
if (alpha == 0) {
return 0;
}
double pdf = 0;
// this CDF only admits positive values
if (X >= 0) {
if (X > 1e-12) pdf = (1.0 - beta)*(alpha - (alpha + X)*exp(-X/alpha))/(X*X);
else pdf = (1.0 - beta)/alpha*(0.5 - X/3/alpha);
}
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFLogNormal, FEDamageCDF)
ADD_PARAMETER(m_mu , FE_RANGE_GREATER(0.0), "mu");
ADD_PARAMETER(m_sigma, FE_RANGE_GREATER(0.0), "sigma");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFLogNormal::FEDamageCDFLogNormal(FEModel* pfem) : FEDamageCDF(pfem)
{
m_mu = 1;
m_sigma = 1;
m_Dmax = 1;
}
//-----------------------------------------------------------------------------
// Lognormal damage cumulative distribution function
double FEDamageCDFLogNormal::cdf(FEMaterialPoint& mp, const double X)
{
double cdf = 0;
double mu = m_mu(mp);
double sigma = m_sigma(mp);
// this CDF only admits positive values
if (X >= 0)
cdf = 0.5*erfc(-log(X/mu)/sigma/sqrt(2.));
return cdf;
}
// Lognormal damage probability density function
double FEDamageCDFLogNormal::pdf(FEMaterialPoint& mp, const double X)
{
double pdf = 0;
double mu = m_mu(mp);
double sigma = m_sigma(mp);
// this CDF only admits positive values
if (X > 1e-12) pdf = exp(-pow(log(X/mu)/sigma,2)/2)/(sqrt(2*M_PI)*X*sigma);
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFWeibull, FEDamageCDF)
ADD_PARAMETER(m_alpha, FE_RANGE_GREATER_OR_EQUAL(0.0), "alpha");
ADD_PARAMETER(m_mu , FE_RANGE_GREATER_OR_EQUAL(0.0), "mu");
ADD_PARAMETER(m_ploc, "ploc");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFWeibull::FEDamageCDFWeibull(FEModel* pfem) : FEDamageCDF(pfem)
{
m_alpha = 1;
m_mu = 1;
m_ploc = 0;
}
//-----------------------------------------------------------------------------
// Weibull damage cumulative distribution function
double FEDamageCDFWeibull::cdf(FEMaterialPoint& mp, const double X)
{
double cdf = 0;
double alpha = m_alpha(mp);
double mu = m_mu(mp);
double ploc = m_ploc(mp);
// this CDF only admits positive values
if (X > ploc)
cdf = 1 - exp(-pow((X-ploc)/mu,alpha));
return cdf;
}
// Weibull damage probability density function
double FEDamageCDFWeibull::pdf(FEMaterialPoint& mp, const double X)
{
double pdf = 0;
double alpha = m_alpha(mp);
double mu = m_mu(mp);
double ploc = m_ploc(mp);
// this CDF only admits positive values
if ((alpha > 1) && (X > ploc))
pdf = exp(-pow((X-ploc)/mu,alpha))*alpha*pow(X-ploc, alpha-1)/pow(mu, alpha);
else if ((alpha == 1) && (X > ploc))
pdf = exp(-(X-ploc)/mu)/mu;
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFStep, FEDamageCDF)
ADD_PARAMETER(m_mu , FE_RANGE_GREATER_OR_EQUAL(0.0), "mu");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFStep::FEDamageCDFStep(FEModel* pfem) : FEDamageCDF(pfem)
{
m_mu = 1;
}
//-----------------------------------------------------------------------------
// Step cumulative distribution function (sudden fracture)
// Step damage cumulative distribution function
double FEDamageCDFStep::cdf(FEMaterialPoint& mp, const double X)
{
double cdf = 0;
double mu = m_mu(mp);
// this CDF only admits positive values
if (X > mu)
cdf = 1.0;
return cdf;
}
// Step damage probability density function
double FEDamageCDFStep::pdf(FEMaterialPoint& mp, const double X)
{
double pdf = 0;
double mu = m_mu(mp);
// this PDF only admits positive values
if (X == mu) pdf = 1.0;
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFPQP, FEDamageCDF)
ADD_PARAMETER(m_mumin, FE_RANGE_GREATER_OR_EQUAL(0.0), "mumin");
ADD_PARAMETER(m_mumax, "mumax");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFPQP::FEDamageCDFPQP(FEModel* pfem) : FEDamageCDF(pfem)
{
m_mumin = 0;
m_mumax = 1;
}
//-----------------------------------------------------------------------------
//! Initialization.
bool FEDamageCDFPQP::Validate()
{
return FEDamageCDF::Validate();
}
//-----------------------------------------------------------------------------
// Piecewise S-shaped quintic polynomial damage cumulative distribution function
double FEDamageCDFPQP::cdf(FEMaterialPoint& mp, const double X)
{
double cdf = 0;
double mumin = m_mumin(mp);
double mumax = m_mumax(mp);
if (X <= mumin) cdf = 0;
else if (X >= mumax) cdf = 1;
else
{
double x = (X - mumin)/(mumax - mumin);
cdf = pow(x,3)*(10 - 15*x + 6*x*x);
}
return cdf;
}
// Piecewise S-shaped quintic polynomial damage probability density function
double FEDamageCDFPQP::pdf(FEMaterialPoint& mp, const double X)
{
double pdf = 0;
double mumin = m_mumin(mp);
double mumax = m_mumax(mp);
if (X <= mumin) pdf = 0;
else if (X >= mumax) pdf = 0;
else
{
double x = (X - mumin)/(mumax - mumin);
pdf = pow(x*(x-1),2)*30;
}
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFGamma, FEDamageCDF)
ADD_PARAMETER(m_alpha, FE_RANGE_GREATER(0) , "alpha");
ADD_PARAMETER(m_mu , FE_RANGE_GREATER_OR_EQUAL(0.0), "mu" );
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFGamma::FEDamageCDFGamma(FEModel* pfem) : FEDamageCDF(pfem)
{
m_alpha = 2;
m_mu = 4;
}
//-----------------------------------------------------------------------------
// Gamma damage cumulative distribution function
double FEDamageCDFGamma::cdf(FEMaterialPoint& mp, const double X)
{
double cdf = 0;
double alpha = m_alpha(mp);
double mu = m_mu(mp);
// this CDF only admits positive values
double scale = gamma_inc_Q(alpha,0);
if (X > 0)
cdf = gamma_inc_P(alpha,X/mu)/scale;
return cdf;
}
// Gamma damage probability density function
double FEDamageCDFGamma::pdf(FEMaterialPoint& mp, const double X)
{
double pdf = 0;
double alpha = m_alpha(mp);
double mu = m_mu(mp);
// this CDF only admits positive values
if (X > 0)
pdf = pow(X/mu, alpha-1)*exp(-X/mu)/mu*gammainv(alpha);
return pdf;
}
///////////////////////////////////////////////////////////////////////////////
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageCDFUser, FEDamageCDF)
ADD_PROPERTY(m_cdf, "cdf");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FEDamageCDFUser::FEDamageCDFUser(FEModel* pfem) : FEDamageCDF(pfem)
{
m_cdf = nullptr;
}
//-----------------------------------------------------------------------------
// User-defined loadcurve for damage cumulative distribution function
double FEDamageCDFUser::cdf(FEMaterialPoint& mp, const double X)
{
return m_cdf->value(X);
}
// Derivative of user-defined loadcurve damage probability density function
double FEDamageCDFUser::pdf(FEMaterialPoint& mp, const double X)
{
return m_cdf->derive(X);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FESolidModule.cpp | .cpp | 3,311 | 74 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "FESolidModule.h"
#include <FECore/DOFS.h>
#include <FECore/FEModel.h>
#include "FEBioMech.h"
FESolidModule::FESolidModule() {}
void FESolidModule::InitModel(FEModel* fem)
{
// Allocate degrees of freedom
DOFS& dofs = fem->GetDOFS();
int varD = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::DISPLACEMENT), VAR_VEC3);
dofs.SetDOFName(varD, 0, "x");
dofs.SetDOFName(varD, 1, "y");
dofs.SetDOFName(varD, 2, "z");
int varQ = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::ROTATION), VAR_VEC3);
dofs.SetDOFName(varQ, 0, "u");
dofs.SetDOFName(varQ, 1, "v");
dofs.SetDOFName(varQ, 2, "w");
int varQR = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::RIGID_ROTATION), VAR_VEC3);
dofs.SetDOFName(varQR, 0, "Ru");
dofs.SetDOFName(varQR, 1, "Rv");
dofs.SetDOFName(varQR, 2, "Rw");
int varV = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::VELOCITY), VAR_VEC3);
dofs.SetDOFName(varV, 0, "vx");
dofs.SetDOFName(varV, 1, "vy");
dofs.SetDOFName(varV, 2, "vz");
int varSU = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::SHELL_DISPLACEMENT), VAR_VEC3);
dofs.SetDOFName(varSU, 0, "sx");
dofs.SetDOFName(varSU, 1, "sy");
dofs.SetDOFName(varSU, 2, "sz");
int varSV = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::SHELL_VELOCITY), VAR_VEC3);
dofs.SetDOFName(varSV, 0, "svx");
dofs.SetDOFName(varSV, 1, "svy");
dofs.SetDOFName(varSV, 2, "svz");
int varSA = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::SHELL_ACCELERATION), VAR_VEC3);
dofs.SetDOFName(varSA, 0, "sax");
dofs.SetDOFName(varSA, 1, "say");
dofs.SetDOFName(varSA, 2, "saz");
int varBW = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::BEAM_ANGULAR_VELOCITY), VAR_VEC3);
dofs.SetDOFName(varBW, 0, "bwx");
dofs.SetDOFName(varBW, 1, "bwy");
dofs.SetDOFName(varBW, 2, "bwz");
int varBA = dofs.AddVariable(FEBioMech::GetVariableName(FEBioMech::BEAM_ANGULAR_ACCELERATION), VAR_VEC3);
dofs.SetDOFName(varBA, 0, "bax");
dofs.SetDOFName(varBA, 1, "bay");
dofs.SetDOFName(varBA, 2, "baz");
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FERigidAngularDamper.cpp | .cpp | 7,195 | 243 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidAngularDamper.h"
#include "FERigidBody.h"
#include "FECore/log.h"
#include "FECore/FEAnalysis.h"
#include "FECore/FEMaterial.h"
#include <FECore/FELinearSystem.h>
//-----------------------------------------------------------------------------
BEGIN_FECORE_CLASS(FERigidAngularDamper, FERigidConnector);
ADD_PARAMETER(m_c, "c");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FERigidAngularDamper::FERigidAngularDamper(FEModel* pfem) : FERigidConnector(pfem)
{
m_nID = m_ncount++;
}
//-----------------------------------------------------------------------------
//! TODO: This function is called twice: once in the Init and once in the Solve
//! phase. Is that necessary?
bool FERigidAngularDamper::Init()
{
// base class first
if (FERigidConnector::Init() == false) return false;
// reset force
m_F = vec3d(0,0,0);
return true;
}
//-----------------------------------------------------------------------------
void FERigidAngularDamper::Serialize(DumpStream& ar)
{
FERigidConnector::Serialize(ar);
ar & m_c;
}
//-----------------------------------------------------------------------------
//! \todo Why is this class not using the FESolver for assembly?
void FERigidAngularDamper::LoadVector(FEGlobalVector& R, const FETimeInfo& tp)
{
vector<double> fa(6);
vector<double> fb(6);
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
double alpha = tp.alphaf;
// body A
vec3d wa = RBa.m_wt*alpha + RBa.m_wp*(1-alpha);
// body b
vec3d wb = RBb.m_wt*alpha + RBb.m_wp*(1-alpha);
m_M = (wb - wa)*m_c;
fa[0] = 0;
fa[1] = 0;
fa[2] = 0;
fa[3] = m_M.x;
fa[4] = m_M.y;
fa[5] = m_M.z;
fb[0] = 0;
fb[1] = 0;
fb[2] = 0;
fb[3] = -m_M.x;
fb[4] = -m_M.y;
fb[5] = -m_M.z;
for (int i=0; i<6; ++i) if (RBa.m_LM[i] >= 0) R[RBa.m_LM[i]] += fa[i];
for (int i=0; i<6; ++i) if (RBb.m_LM[i] >= 0) R[RBb.m_LM[i]] += fb[i];
RBa.m_Fr -= vec3d(fa[0],fa[1],fa[2]);
RBa.m_Mr -= vec3d(fa[3],fa[4],fa[5]);
RBb.m_Fr -= vec3d(fb[0],fb[1],fb[2]);
RBb.m_Mr -= vec3d(fb[3],fb[4],fb[5]);
}
//-----------------------------------------------------------------------------
//! \todo Why is this class not using the FESolver for assembly?
void FERigidAngularDamper::StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp)
{
double alpha = tp.alphaf;
double beta = tp.beta;
double gamma = tp.gamma;
// get time increment
double dt = tp.timeIncrement;
int j;
vector<int> LM(12);
FEElementMatrix ke;
ke.resize(12, 12);
ke.zero();
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
mat3dd I(1);
// body A
vec3d wa = RBa.m_wt*alpha + RBa.m_wp*(1-alpha);
quatd qai = RBa.GetRotation()*RBa.m_qp.Inverse(); qai.MakeUnit();
vec3d cai = qai.GetVector()*(2*tan(qai.GetAngle()/2));
mat3d Ta = I + skew(cai)/2 + dyad(cai)/4;
// body b
vec3d wb = RBb.m_wt*alpha + RBb.m_wp*(1-alpha);
quatd qbi = RBb.GetRotation()*RBb.m_qp.Inverse(); qbi.MakeUnit();
vec3d cbi = qbi.GetVector()*(2*tan(qbi.GetAngle()/2));
mat3d Tb = I + skew(cbi)/2 + dyad(cbi)/4;
m_M = (wb - wa)*m_c;
mat3d Ba = Ta.transpose()*(gamma/beta/dt);
mat3d Bb = Tb.transpose()*(gamma/beta/dt);
mat3d K;
K.zero();
// (2,2)
K = Ba*(alpha*m_c);
ke[3][3] = K[0][0]; ke[3][4] = K[0][1]; ke[3][5] = K[0][2];
ke[4][3] = K[1][0]; ke[4][4] = K[1][1]; ke[4][5] = K[1][2];
ke[5][3] = K[2][0]; ke[5][4] = K[2][1]; ke[5][5] = K[2][2];
// (2,4)
K = Bb*(-alpha*m_c);
ke[3][9] = K[0][0]; ke[3][10] = K[0][1]; ke[3][11] = K[0][2];
ke[4][9] = K[1][0]; ke[4][10] = K[1][1]; ke[4][11] = K[1][2];
ke[5][9] = K[2][0]; ke[5][10] = K[2][1]; ke[5][11] = K[2][2];
// (4,2)
K = Ba*(-alpha*m_c);
ke[9 ][3] = K[0][0]; ke[ 9][4] = K[0][1]; ke[ 9][5] = K[0][2];
ke[10][3] = K[1][0]; ke[10][4] = K[1][1]; ke[10][5] = K[1][2];
ke[11][3] = K[2][0]; ke[11][4] = K[2][1]; ke[11][5] = K[2][2];
// (4,4)
K = Bb*(alpha*m_c);
ke[9 ][9] = K[0][0]; ke[ 9][10] = K[0][1]; ke[ 9][11] = K[0][2];
ke[10][9] = K[1][0]; ke[10][10] = K[1][1]; ke[10][11] = K[1][2];
ke[11][9] = K[2][0]; ke[11][10] = K[2][1]; ke[11][11] = K[2][2];
for (j=0; j<6; ++j)
{
LM[j ] = RBa.m_LM[j];
LM[j+6] = RBb.m_LM[j];
}
ke.SetIndices(LM);
LS.Assemble(ke);
}
//-----------------------------------------------------------------------------
bool FERigidAngularDamper::Augment(int naug, const FETimeInfo& tp)
{
return true;
}
//-----------------------------------------------------------------------------
void FERigidAngularDamper::Update()
{
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
const FETimeInfo& tp = GetTimeInfo();
double alpha = tp.alphaf;
// body A
vec3d wa = RBa.m_wt*alpha + RBa.m_wp*(1-alpha);
// body b
vec3d wb = RBb.m_wt*alpha + RBb.m_wp*(1-alpha);
m_M = (wb - wa)*m_c;
}
//-----------------------------------------------------------------------------
void FERigidAngularDamper::Reset()
{
m_F = vec3d(0,0,0);
m_M = vec3d(0,0,0);
}
//-----------------------------------------------------------------------------
vec3d FERigidAngularDamper::RelativeTranslation(const bool global)
{
return vec3d(0,0,0);
}
//-----------------------------------------------------------------------------
vec3d FERigidAngularDamper::RelativeRotation(const bool global)
{
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
// get relative rotation
quatd Q = RBb.GetRotation()*RBa.GetRotation().Inverse(); Q.MakeUnit();
// relative rotation vector
vec3d q = Q.GetRotationVector();
return q;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FENewtonianViscousSolid.h | .h | 2,090 | 57 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEElasticMaterial.h"
class FENewtonianViscousSolid : public FEElasticMaterial
{
public:
FENewtonianViscousSolid(FEModel* pfem);
public:
double m_kappa; //!< bulk viscosity
double m_mu; //!< shear viscosity
bool m_secant_tangent; //!< flag for using secant tangent calculation
public:
//! calculate stress at material point
mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
double StrainEnergyDensity(FEMaterialPoint& pt) override;
bool UseSecantTangent() override { return m_secant_tangent; }
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/RigidBC.h | .h | 5,761 | 239 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEBoundaryCondition.h>
#include <FECore/FEInitialCondition.h>
#include "febiomech_api.h"
class FERigidBody;
//-----------------------------------------------------------------------------
class FEBIOMECH_API FERigidBC : public FEBoundaryCondition
{
FECORE_BASE_CLASS(FERigidBC)
public:
FERigidBC(FEModel* fem);
bool Init() override;
virtual void InitTimeStep();
void Serialize(DumpStream& ar) override;
FERigidBody& GetRigidBody();
void CopyFrom(FEBoundaryCondition* pbc) override;
void SetRigidMaterial(int rigidMat);
private:
int m_rb; // rigid body ID
protected:
int m_rigidMat; // rigid material ID
bool m_binit;
};
//-----------------------------------------------------------------------------
class FEBIOMECH_API FERigidIC : public FEInitialCondition
{
FECORE_BASE_CLASS(FERigidIC)
public:
FERigidIC(FEModel* fem);
bool Init() override;
void Activate() override;
void Serialize(DumpStream& ar) override;
FERigidBody& GetRigidBody();
private:
int m_rigidMat; // rigid material ID
int m_rb; // rigid body ID
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! fixed rigid body constraint
class FEBIOMECH_API FERigidFixedBC : public FERigidBC
{
public:
FERigidFixedBC(FEModel* pfem);
};
//-----------------------------------------------------------------------------
//! fixed rigid body constraint
class FEBIOMECH_API FERigidFixedBCNew : public FERigidFixedBC
{
public:
FERigidFixedBCNew(FEModel* pfem);
void Activate() override;
void Deactivate() override;
public:
bool m_dof[6]; //!< constrained dof list
private:
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! fixed rigid body constraint
class FEBIOMECH_API FERigidFixedBCOld : public FERigidFixedBC
{
public:
FERigidFixedBCOld(FEModel* pfem);
bool Init() override;
void Activate() override;
void Deactivate() override;
public:
vector<int> m_dofs; //!< constrained dof list
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! rigid body displacement
class FEBIOMECH_API FERigidPrescribedBC : public FERigidBC
{
public:
FERigidPrescribedBC(FEModel* pfem);
bool Init() override;
double Value();
void InitTimeStep() override;
void Serialize(DumpStream& ar) override;
void Activate() override;
void Deactivate() override;
void SetBC(int bc) { m_dof = bc; }
int GetBC() const { return m_dof; }
void SetRelativeFlag(bool b) { m_brel = b; }
bool GetRelativeFlag() const { return m_brel; }
void SetValue(double v) { m_val = v; }
protected:
int m_dof; //!< displacement direction
double m_val; //!< displacement value
double m_ref; //!< reference value for relative displacement
bool m_brel; //!< relative displacement flag
bool m_binit; //!init flag
};
//-----------------------------------------------------------------------------
//! prescribed rigid body rotation
class FEBIOMECH_API FERigidDisplacement : public FERigidPrescribedBC
{
public:
FERigidDisplacement(FEModel* pfem);
bool Init() override;
private:
int m_bc;
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! prescribed rigid body rotation
class FEBIOMECH_API FERigidRotation : public FERigidPrescribedBC
{
public:
FERigidRotation(FEModel* pfem);
bool Init() override;
private:
int m_bc;
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! Obsolete rigid prescribed bc class. Used only for backward compatibility.
class FEBIOMECH_API FERigidPrescribedOld : public FERigidPrescribedBC
{
public:
FERigidPrescribedOld(FEModel* pfem);
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! rigid body initial velocity
class FEBIOMECH_API FERigidBodyVelocity : public FERigidIC
{
public:
FERigidBodyVelocity(FEModel* pfem);
void Activate() override;
public:
vec3d m_vel; //!< initial velocity
DECLARE_FECORE_CLASS();
};
//-----------------------------------------------------------------------------
//! rigid body initial angular velocity
class FEBIOMECH_API FERigidBodyAngularVelocity : public FERigidIC
{
public:
FERigidBodyAngularVelocity(FEModel* pfem);
void Activate() override;
public:
vec3d m_w; //!< value
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEPointBodyForce.h | .h | 2,232 | 61 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEBodyForce.h"
#include <FECore/FESolidElement.h>
//-----------------------------------------------------------------------------
class FEBIOMECH_API FEPointBodyForce : public FEBodyForce
{
public:
FEPointBodyForce(FEModel* pfem);
vec3d force(FEMaterialPoint& mp) override;
double divforce(FEMaterialPoint& mp) override;
mat3d stiffness(FEMaterialPoint& mp) override;
void Serialize(DumpStream& ar) override;
bool Init() override;
void Update() override;
public:
double m_a, m_b; //!< coefficients of exponential decay of body force
vec3d m_rc; //!< center point of body force
int m_inode; //!< node number of center of body force, or -1 if not a node
bool m_brigid; //!< flag if center point is located within a rigid body
FESolidElement* m_pel; //!< element in which point m_r0 lies
double m_rs[3]; //!< isoparametric coordinates
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FERelativeVolumeCriterion.cpp | .cpp | 1,841 | 49 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERelativeVolumeCriterion.h"
#include "FEElasticMaterial.h"
BEGIN_FECORE_CLASS(FERelativeVolumeCriterion, FEMeshAdaptorCriterion)
END_FECORE_CLASS();
FERelativeVolumeCriterion::FERelativeVolumeCriterion(FEModel* fem) : FEMeshAdaptorCriterion(fem)
{
}
bool FERelativeVolumeCriterion::GetMaterialPointValue(FEMaterialPoint& mp, double& value)
{
FEElasticMaterialPoint* ep = mp.ExtractData<FEElasticMaterialPoint>();
if (ep == nullptr) return false;
// evaluate the relative volume at this point
value = ep->m_J;
return true;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FETorsionalSpring.cpp | .cpp | 2,502 | 92 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FETorsionalSpring.h"
BEGIN_FECORE_CLASS(FETorsionalSpring, FEDiscreteElasticMaterial)
ADD_PARAMETER(m_r, "r");
END_FECORE_CLASS();
FETorsionalSpring::FETorsionalSpring(FEModel* fem) : FEDiscreteElasticMaterial(fem)
{
m_r = 0.0;
}
// evaluate the force at a discrete element
vec3d FETorsionalSpring::Force(FEDiscreteMaterialPoint& mp)
{
vec3d e0 = mp.m_dr0; e0.unit();
vec3d et = mp.m_drt;
double l = et.unit();
double w = e0 * et;
mat3ds exe = dyad(et);
mat3dd I(1.0);
mat3ds P = (I - exe) / l;
vec3d t = P * e0;
double F = -m_r*w;
return t*F;
}
// evaluate the stiffness at a discrete element (= dF / dr)
mat3d FETorsionalSpring::Stiffness(FEDiscreteMaterialPoint& mp)
{
vec3d e0 = mp.m_dr0; e0.unit();
vec3d et = mp.m_drt;
double l = et.unit();
double w = e0 * et;
mat3ds exe = dyad(et);
mat3dd I(1.0);
mat3ds P = (I - exe) / l;
vec3d t = P * e0;
mat3ds Q = dyads(e0, et) + I*w - exe*(3.0*w);
mat3ds T = dyad(t);
return T*(m_r) + Q*(m_r*w);
}
double FETorsionalSpring::StrainEnergy(FEDiscreteMaterialPoint& mp)
{
vec3d e0 = mp.m_dr0; e0.unit();
vec3d et = mp.m_drt;
double l = et.unit();
double w = e0 * et;
double E = m_r*(1-w*w)/2;
return E;
} | C++ |
3D | febiosoftware/FEBio | FEBioMech/FECellGrowth.cpp | .cpp | 3,631 | 110 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FECellGrowth.h"
#include <FECore/log.h>
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FECellGrowth, FEElasticMaterial)
ADD_PARAMETER(m_phir, FE_RANGE_GREATER(0.0), "phir");
ADD_PARAMETER(m_cr , FE_RANGE_GREATER(0.0), "cr")->setUnits(UNIT_CONCENTRATION);
ADD_PARAMETER(m_ce , FE_RANGE_GREATER(0.0), "ce")->setUnits(UNIT_CONCENTRATION);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FECellGrowth::FECellGrowth(FEModel* pfem) : FEElasticMaterial(pfem)
{
m_Rgas = 0;
m_Tabs = 0;
m_phir = 0;
m_cr = 0;
m_ce = 0;
}
//-----------------------------------------------------------------------------
bool FECellGrowth::Init()
{
if (FEElasticMaterial::Init() == false) return false;
m_Rgas = GetGlobalConstant("R");
m_Tabs = GetGlobalConstant("T");
if (m_Rgas <= 0) { feLogError("A positive universal gas constant R must be defined in Globals section"); return false; }
if (m_Tabs <= 0) { feLogError("A positive absolute temperature T must be defined in Globals section"); return false; }
return true;
}
//-----------------------------------------------------------------------------
mat3ds FECellGrowth::Stress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
// calculate intracellular osmolarity relative to mixture volume in reference configuration
double c = m_cr/(J-m_phir);
// calculate osmotic pressure
double p = m_Rgas*m_Tabs*(c - m_ce);
// calculate T = -p*I
mat3dd I(1.0); // identity tensor
mat3ds s = -p*I;
return s;
}
//-----------------------------------------------------------------------------
tens4ds FECellGrowth::Tangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// jacobian
double J = pt.m_J;
// calculate intracellular osmolarity relative to mixture volume in reference configuration
double c = m_cr/(J-m_phir);
// calculate osmotic pressure
double p = m_Rgas*m_Tabs*(c - m_ce);
mat3dd I(1.0); // Identity
tens4ds I1 = dyad1s(I);
tens4ds I4 = dyad4s(I);
// calculate tangent osmotic modulus
tens4ds C = I4*(2*p) - I1*(p-m_Rgas*m_Tabs*c*J/(J-m_phir));
return C;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEFacet2FacetSliding.h | .h | 5,358 | 173 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEContactInterface.h"
#include "FEContactSurface.h"
//-----------------------------------------------------------------------------
//! Contact surface for facet-to-facet sliding interfaces
class FEFacetSlidingSurface : public FEContactSurface
{
public:
//! Integration point data
class Data : public FEContactMaterialPoint
{
public:
Data();
void Serialize(DumpStream& ar);
void Init() override;
public:
double m_Lm; //!< Lagrange multipliers
double m_eps; //!< penalty value at integration point
vec3d m_nu; //!< secondary surface normal at integration points
vec2d m_rs; //!< natural coordinates of projection of integration point
};
public:
//! constructor
FEFacetSlidingSurface(FEModel* pfem);
//! initialization
bool Init() override;
//! evaluate net contact force
vec3d GetContactForce() override;
//! evaluate net contact area
double GetContactArea() override;
//! create material point data
FEMaterialPoint* CreateMaterialPoint() override;
//! serialization
void Serialize(DumpStream& ar) override;
public:
void GetContactTraction(int nface, vec3d& pt) override;
void GetNodalContactPressure(int nface, double* pn) override;
void GetNodalContactTraction(int nface, vec3d* tn) override;
public:
vector<vec3d> m_Fn; //!< equivalent nodal forces
};
//-----------------------------------------------------------------------------
//! Sliding interface with facet to facet integration
//! This class is similar to the sliding interface except that it uses
//! a Gaussian quadrature rule in stead of a nodal integration rule
//! as its base class does.
//
class FEFacet2FacetSliding : public FEContactInterface
{
public:
//! constructor
FEFacet2FacetSliding(FEModel* pfem);
//! initialization routine
bool Init() override;
//! interface activation
void Activate() override;
//! calculate contact pressures for file output
void UpdateContactPressures();
//! serialize data to archive
void Serialize(DumpStream& ar) override;
//! get primary and secondary surfaces
FESurface* GetPrimarySurface() override { return &m_ss; }
FESurface* GetSecondarySurface() override { return &m_ms; }
//! return integration rule class
bool UseNodalIntegration() override { return false; }
//! build the matrix profile for use in the stiffness matrix
void BuildMatrixProfile(FEGlobalMatrix& K) override;
public:
//! calculate contact forces
void LoadVector(FEGlobalVector& R, const FETimeInfo& tp) override;
//! calculate contact stiffness
void StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) override;
//! calculate Lagrangian augmentations
bool Augment(int naug, const FETimeInfo& tp) override;
//! update
void Update() override;
protected:
//! project primary surface onto secondary
void ProjectSurface(FEFacetSlidingSurface& ss, FEFacetSlidingSurface& ms, bool bsegup, bool bmove = false);
//! calculate auto-penalty
void UpdateAutoPenalty();
void CalcAutoPenalty(FEFacetSlidingSurface& s);
public:
double m_epsn; //!< normal penalty factor
double m_knmult; //!< normal stiffness multiplier
double m_stol; //!< search tolerance
bool m_btwo_pass; //!< two-pass flag
bool m_bautopen; //!< auto-penalty flag
bool m_bupdtpen; //!< update penalty at each time step
double m_srad; //!< search radius (% of model size)
int m_nsegup; //!< segment update parameter
bool m_breloc; //!< node relocation on initialization
bool m_bsmaug; //!< smooth augmentation
double m_atol; //!< aug lag tolerance
double m_gtol; //!< gap tolerance
int m_naugmin; //!< min nr of augmentations
int m_naugmax; //!< max nr of augmentations
double m_mu; //!< friction coefficient (not implemented yet)
double m_epsf; //!< penalty scale factor for friction (not implementer yet)
double m_dxtol; //!< penalty insertion distance
FEFacetSlidingSurface m_ss; //!< primary surface
FEFacetSlidingSurface m_ms; //!< secondary surface
private:
bool m_bfirst;
double m_normg0;
public:
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FERigidFollowerMoment.cpp | .cpp | 4,513 | 129 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidFollowerMoment.h"
#include "FERigidBody.h"
#include "FECore/FEAnalysis.h"
#include "FECore/FEMaterial.h"
#include "FECore/FELoadCurve.h"
#include "FEMechModel.h"
#include "FERigidMaterial.h"
#include <FECore/FELinearSystem.h>
//=============================================================================
BEGIN_FECORE_CLASS(FERigidFollowerMoment, FERigidLoad);
ADD_PARAMETER(m_rid , "rb" )->setEnums("$(rigid_materials)");
ADD_PARAMETER(m_m , "moment" );
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FERigidFollowerMoment::FERigidFollowerMoment(FEModel* pfem) : FERigidLoad(pfem)
{
m_rid = -1;
m_m = vec3d(0,0,0);
}
//-----------------------------------------------------------------------------
//! do some sanity checks
bool FERigidFollowerMoment::Init()
{
// At this point the rigid ID's are still associated with the materials.
// We want to associate them with the rigid objects instead.
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_rid-1));
if (pm == 0) return false;
m_rid = pm->GetRigidBodyID(); if (m_rid < 0) return false;
// all is well in the world
return true;
}
//-----------------------------------------------------------------------------
void FERigidFollowerMoment::Serialize(DumpStream& ar)
{
FEModelLoad::Serialize(ar);
ar & m_rid;
ar & m_m;
}
//-----------------------------------------------------------------------------
//! Residual
void FERigidFollowerMoment::LoadVector(FEGlobalVector& R)
{
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& body = *fem.GetRigidBody(m_rid);
const FETimeInfo& tp = fem.GetTime();
double alpha = tp.alphaf;
// calculate the moment value
vec3d mt = body.GetRotation()*m_m;
vec3d mp = body.GetPreviousRotation()*m_m;
vec3d m = mt*alpha + mp*(1-alpha);
// apply force and moment to body
int n;
n = body.m_LM[3]; if (n >= 0) R[n] += m.x;
n = body.m_LM[4]; if (n >= 0) R[n] += m.y;
n = body.m_LM[5]; if (n >= 0) R[n] += m.z;
body.m_Mr += m;
}
//-----------------------------------------------------------------------------
//! Stiffness matrix
//! TODO: Only the stiffness contribution in the were the axial forces are applied
//! to the center of mass has been implemented.
void FERigidFollowerMoment::StiffnessMatrix(FELinearSystem& LS)
{
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& body = *fem.GetRigidBody(m_rid);
const FETimeInfo& tp = fem.GetTime();
double alpha = tp.alphaf;
// calculate the moment value
vec3d mt = body.GetRotation()*m_m;
// build the stiffness matrix components
mat3da mthat(mt);
mat3d Kqq = mthat*(-alpha);
// put it all together
FEElementMatrix K; K.resize(3, 3); K.zero();
K.sub(0,0, Kqq);
// get the equation numbers
vector<int> lm(3);
lm[ 0] = body.m_LM[3];
lm[ 1] = body.m_LM[4];
lm[ 2] = body.m_LM[5];
// assemble into global matrix
K.SetIndices(lm);
LS.Assemble(K);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEFiberExpPowUncoupled.cpp | .cpp | 6,194 | 204 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFiberExpPowUncoupled.h"
#include <FECore/log.h>
// define the material parameters
BEGIN_FECORE_CLASS(FEFiberExpPowUC, FEFiberMaterialUncoupled)
ADD_PARAMETER(m_alpha, FE_RANGE_GREATER_OR_EQUAL(0.0), "alpha");
ADD_PARAMETER(m_beta , FE_RANGE_GREATER_OR_EQUAL(2.0), "beta");
ADD_PARAMETER(m_ksi , FE_RANGE_GREATER_OR_EQUAL(0.0), "ksi" )->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_mu, FE_RANGE_GREATER_OR_EQUAL(0.0), "mu")->setUnits(UNIT_PRESSURE);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
// FEFiberExpPowUC
//-----------------------------------------------------------------------------
FEFiberExpPowUC::FEFiberExpPowUC(FEModel* pfem) : FEFiberMaterialUncoupled(pfem)
{
m_ksi = 0.0;
m_alpha = 0.0;
m_beta = 2.0;
m_mu = 0;
}
//-----------------------------------------------------------------------------
mat3ds FEFiberExpPowUC::DevFiberStress(FEMaterialPoint& mp, const vec3d& n0)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
double J = pt.m_J;
mat3d F = pt.m_F*pow(J,-1.0/3.0);
// loop over all integration points
const double eps = 0;
mat3ds C = pt.DevRightCauchyGreen();
mat3ds s;
// Calculate In = n0*C*n0
double In_1 = n0*(C*n0) - 1.0;
double ksi = m_ksi(mp);
// only take fibers in tension into consideration
if (In_1 >= eps)
{
// get the global spatial fiber direction in current configuration
vec3d nt = F*n0;
// calculate the outer product of nt
mat3ds N = dyad(nt);
// calculate strain energy derivative
double Wl = ksi*pow(In_1, m_beta-1.0)*exp(m_alpha*pow(In_1, m_beta));
// calculate the fiber stress
s = N*(2.0*Wl/J);
// add the contribution from shear
mat3ds BmI = pt.DevLeftCauchyGreen() - mat3dd(1);
s += (N*BmI).sym()*(m_mu / J);
}
else
{
s.zero();
}
return s.dev();
}
//-----------------------------------------------------------------------------
tens4ds FEFiberExpPowUC::DevFiberTangent(FEMaterialPoint& mp, const vec3d& n0)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
double J = pt.m_J;
mat3d F = pt.m_F*pow(J,-1.0/3.0);
// loop over all integration points
const double eps = 0;
mat3ds C = pt.DevRightCauchyGreen();
mat3ds s;
tens4ds c;
// Calculate In = n0*C*n0
double In_1 = n0*(C*n0) - 1.0;
double ksi = m_ksi(mp);
// only take fibers in tension into consideration
if (In_1 >= eps)
{
// get the global spatial fiber direction in current configuration
vec3d nt = F*n0;
// calculate the outer product of nt
mat3ds N = dyad(nt);
tens4ds NxN = dyad1s(N);
mat3dd I(1);
tens4ds IxI = dyad1s(I);
tens4ds I4 = dyad4s(I);
// calculate strain energy derivatives
double tmp = m_alpha*pow(In_1, m_beta);
double Wl = ksi*pow(In_1, m_beta-1.0)*exp(m_alpha*pow(In_1, m_beta));
double Wll = ksi*pow(In_1, m_beta-2.0)*((tmp+1)*m_beta-1.0)*exp(tmp);
// calculate the fiber stress
s = N*(2.0*Wl/J);
// add the contribution from shear
mat3ds B = pt.DevLeftCauchyGreen();
mat3ds BmI = B - I;
s += (N*BmI).sym()*(m_mu / J);
// calculate the fiber tangent
c = NxN*(4.0*Wll/J);
// add the contribution from shear
c += dyad4s(N, B)*(m_mu / J);
// This is the final value of the elasticity tensor
c += ((I4+IxI/3.0)*s.tr() - dyad1s(I,s))*(2./3.)
- (ddots(IxI, c)-IxI*(c.tr()/3.))/3.;
}
else
{
c.zero();
}
return c;
}
//-----------------------------------------------------------------------------
double FEFiberExpPowUC::DevFiberStrainEnergyDensity(FEMaterialPoint& mp, const vec3d& n0)
{
double sed = 0.0;
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// loop over all integration points
mat3ds C = pt.DevRightCauchyGreen();
mat3ds C2 = C.sqr();
// Calculate In = n0*C*n0
double In_1 = n0*(C*n0) - 1.0;
double ksi = m_ksi(mp);
// only take fibers in tension into consideration
const double eps = 0;
if (In_1 >= eps)
{
// calculate strain energy derivative
if (m_alpha > 0) {
sed = ksi/(m_alpha*m_beta)*(exp(m_alpha*pow(In_1, m_beta))-1);
}
else
sed = ksi/m_beta*pow(In_1, m_beta);
// add the contribution from shear
sed += m_mu*(n0*(C2*n0) - 2 * In_1 - 1) / 4.0;
}
return sed;
}
// define the material parameters
BEGIN_FECORE_CLASS(FEUncoupledFiberExpPow, FEElasticFiberMaterialUC)
ADD_PARAMETER(m_fib.m_alpha, FE_RANGE_GREATER_OR_EQUAL(0.0), "alpha");
ADD_PARAMETER(m_fib.m_beta , FE_RANGE_GREATER_OR_EQUAL(2.0), "beta");
ADD_PARAMETER(m_fib.m_ksi , FE_RANGE_GREATER_OR_EQUAL(0.0), "ksi" )->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_fib.m_mu, FE_RANGE_GREATER_OR_EQUAL(0.0), "mu")->setUnits(UNIT_PRESSURE);
END_FECORE_CLASS();
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FERigidForce.cpp | .cpp | 14,943 | 510 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidForce.h"
#include "FERigidBody.h"
#include "FECore/FEAnalysis.h"
#include "FECore/FEMaterial.h"
#include "FECore/FELoadCurve.h"
#include "FEMechModel.h"
#include "FERigidMaterial.h"
#include <FECore/FELinearSystem.h>
#include <FECore/log.h>
//=============================================================================
BEGIN_FECORE_CLASS(FERigidAxialForce, FERigidLoad);
ADD_PARAMETER(m_ida , "rbA" )->setEnums("$(rigid_materials)");
ADD_PARAMETER(m_idb , "rbB" )->setEnums("$(rigid_materials)");
ADD_PARAMETER(m_ra0 , "ra" );
ADD_PARAMETER(m_rb0 , "rb" );
ADD_PARAMETER(m_s , "force" )->setUnits(UNIT_FORCE);
ADD_PARAMETER(m_brelative, "relative");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FERigidAxialForce::FERigidAxialForce(FEModel* pfem) : FERigidLoad(pfem)
{
m_ida = m_idb = -1;
m_ra0 = m_rb0 = vec3d(0,0,0);
m_s = 0.0;
m_brelative = false;
}
//-----------------------------------------------------------------------------
//! do some sanity checks
bool FERigidAxialForce::Init()
{
// At this point the rigid ID's are still associated with the materials.
// We want to associate them with the rigid objects instead.
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_ida-1));
if (pm == 0) return false;
m_ida = pm->GetRigidBodyID(); if (m_ida < 0) return false;
pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_idb-1));
if (pm == 0) return false;
m_idb = pm->GetRigidBodyID(); if (m_idb < 0) return false;
// get the actual rigid bodies
FERigidBody& bodyA = *fem.GetRigidBody(m_ida);
FERigidBody& bodyB = *fem.GetRigidBody(m_idb);
// get the attachment position in global coordinates for body A
vec3d da0 = (m_brelative ? m_ra0 : m_ra0 - bodyA.m_r0);
vec3d da = bodyA.GetRotation()*da0;
vec3d a = da + bodyA.m_rt;
// get the attachment position in global coordinates for body B
vec3d db0 = (m_brelative ? m_rb0 : m_rb0 - bodyB.m_r0);
vec3d db = bodyB.GetRotation()*db0;
vec3d b = db + bodyB.m_rt;
// get the unit axial vector
// and make sure it is of finite length
vec3d N = b - a;
double L = N.unit();
if (L < 1e-17) return false;
// all is well in the world
return true;
}
//-----------------------------------------------------------------------------
void FERigidAxialForce::Serialize(DumpStream& ar)
{
FEModelLoad::Serialize(ar);
ar & m_ida & m_idb;
ar & m_ra0 & m_rb0;
ar & m_s & m_brelative;
}
//-----------------------------------------------------------------------------
//! Residual
void FERigidAxialForce::LoadVector(FEGlobalVector& R)
{
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& bodyA = *fem.GetRigidBody(m_ida);
FERigidBody& bodyB = *fem.GetRigidBody(m_idb);
// get the attachment position in global coordinates for body A
vec3d da0 = (m_brelative ? m_ra0 : m_ra0 - bodyA.m_r0);
vec3d da = bodyA.GetRotation()*da0;
vec3d a = da + bodyA.m_rt;
// get the attachment position in global coordinates for body B
vec3d db0 = (m_brelative ? m_rb0 : m_rb0 - bodyB.m_r0);
vec3d db = bodyB.GetRotation()*db0;
vec3d b = db + bodyB.m_rt;
// get the unit axial vector
vec3d N = b - a; N.unit();
// calculate the force value
double f = m_s;
// get the axial force and torques
vec3d F = N*f;
vec3d Ma = da^F;
vec3d Mb = db^F;
// apply force and torque to body A
int n;
n = bodyA.m_LM[0]; if (n >= 0) R[n] += F.x;
n = bodyA.m_LM[1]; if (n >= 0) R[n] += F.y;
n = bodyA.m_LM[2]; if (n >= 0) R[n] += F.z;
n = bodyA.m_LM[3]; if (n >= 0) R[n] += Ma.x;
n = bodyA.m_LM[4]; if (n >= 0) R[n] += Ma.y;
n = bodyA.m_LM[5]; if (n >= 0) R[n] += Ma.z;
// apply force and torque to body B
n = bodyB.m_LM[0]; if (n >= 0) R[n] -= F.x;
n = bodyB.m_LM[1]; if (n >= 0) R[n] -= F.y;
n = bodyB.m_LM[2]; if (n >= 0) R[n] -= F.z;
n = bodyB.m_LM[3]; if (n >= 0) R[n] -= Mb.x;
n = bodyB.m_LM[4]; if (n >= 0) R[n] -= Mb.y;
n = bodyB.m_LM[5]; if (n >= 0) R[n] -= Mb.z;
bodyA.m_Fr += F;
bodyA.m_Mr += Ma;
bodyB.m_Fr -= F;
bodyB.m_Mr -= Mb;
}
//-----------------------------------------------------------------------------
//! Stiffness matrix
//! TODO: Only the stiffness contribution in the were the axial forces are applied
//! to the center of mass has been implemented.
void FERigidAxialForce::StiffnessMatrix(FELinearSystem& LS)
{
// Get the rigid bodies
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& bodyA = *fem.GetRigidBody(m_ida);
FERigidBody& bodyB = *fem.GetRigidBody(m_idb);
// get the attachment position in global coordinates for body A
vec3d da0 = (m_brelative ? m_ra0 : m_ra0 - bodyA.m_r0);
vec3d da = bodyA.GetRotation()*da0;
vec3d pa = da + bodyA.m_rt;
// get the attachment position in global coordinates for body B
vec3d db0 = (m_brelative ? m_rb0 : m_rb0 - bodyB.m_r0);
vec3d db = bodyB.GetRotation()*db0;
vec3d pb = db + bodyB.m_rt;
// setup the axial unit vector
vec3d N = pb - pa;
double L = N.unit();
// calculate the force value
double f = -m_s / L;
// build the stiffness matrix components
mat3ds M = mat3dd(1.0) - dyad(N);
mat3da A(-da);
mat3da B(-db);
mat3da S(-N);
mat3d MA = M*A;
mat3d MB = M*B;
mat3d AM = A*M;
mat3d AMA = A*MA;
mat3d BMB = B*MB;
mat3d AMB = A*MB;
mat3d SA = S*A;
mat3d SB = S*B;
// put it all together
FEElementMatrix K; K.resize(12, 12); K.zero();
K.sub(0,0, M);
K.sub(0,3, MA);
K.add(0,6, M);
K.add(0,9, MB);
K.add(3,3, SA*L + AMA);
K.add(3,6, AM);
K.sub(3,9, AMB);
K.sub(6,6,M);
K.sub(6,9, MB);
K.add(9,9, SB*(-L) + BMB);
// since this is a symmetric matrix, fill the bottom triangular part
K.copy_ut();
// and multiply by f
K *= f;
// get the equation numbers
vector<int> lm(12);
lm[ 0] = bodyA.m_LM[0];
lm[ 1] = bodyA.m_LM[1];
lm[ 2] = bodyA.m_LM[2];
lm[ 3] = bodyA.m_LM[3];
lm[ 4] = bodyA.m_LM[4];
lm[ 5] = bodyA.m_LM[5];
lm[ 6] = bodyB.m_LM[0];
lm[ 7] = bodyB.m_LM[1];
lm[ 8] = bodyB.m_LM[2];
lm[ 9] = bodyB.m_LM[3];
lm[10] = bodyB.m_LM[4];
lm[11] = bodyB.m_LM[5];
// assemble into global matrix
K.SetIndices(lm);
LS.Assemble(K);
}
//=============================================================================
BEGIN_FECORE_CLASS(FERigidBodyForce, FERigidLoad)
ADD_PARAMETER(m_rigidMat, "rb")->setEnums("$(rigid_materials)")->setLongName("Rigid material");
ADD_PARAMETER(m_dof, "dof", 0, "Rx\0Ry\0Rz");
ADD_PARAMETER(m_force, "value")->SetFlags(FE_PARAM_ADDLC | FE_PARAM_VOLATILE)->setUnits(UNIT_FORCE);
ADD_PARAMETER(m_ntype, "load_type")->setEnums("LOAD\0FOLLOW\0TARGET");
ADD_PARAMETER(m_brelative, "relative");
END_FECORE_CLASS();
FERigidBodyForce::FERigidBodyForce(FEModel* pfem) : FERigidLoad(pfem)
{
m_rigidMat = -1;
m_ntype = FORCE_LOAD;
m_rid = -1;
m_brelative = false;
m_force0 = 0.0;
m_force = 0.0;
m_dof = 0;
}
void FERigidBodyForce::SetRigidMaterialID(int nid) { m_rigidMat = nid; }
void FERigidBodyForce::SetDOF(int bc) { m_dof = bc; }
void FERigidBodyForce::SetLoadType(int loadType) { m_ntype = loadType; }
void FERigidBodyForce::SetForce(double f) { m_force = f; }
//-----------------------------------------------------------------------------
bool FERigidBodyForce::Init()
{
// At this point the rigid ID's are still associated with the materials.
// We want to associate them with the rigid objects instead.
FEModel& fem = *GetFEModel();
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_rigidMat - 1));
if (pm == 0) return false;
// check the dof value
if ((m_dof < 0) || (m_dof >= 3)) return false;
return FEModelLoad::Init();
}
//-----------------------------------------------------------------------------
void FERigidBodyForce::Activate()
{
FEModelLoad::Activate();
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_rigidMat - 1));
m_rid = pm->GetRigidBodyID(); assert(m_rid >= 0);
FERigidBody& rb = *fem.GetRigidBody(m_rid);
if (m_ntype == FORCE_TARGET)
{
switch (m_dof)
{
case 0: m_force0 = rb.m_Fr.x; break;
case 1: m_force0 = rb.m_Fr.y; break;
case 2: m_force0 = rb.m_Fr.z; break;
}
}
if ((m_ntype == FORCE_LOAD) && m_brelative)
{
switch (m_dof)
{
case 0: m_force0 = rb.m_Fr.x; break;
case 1: m_force0 = rb.m_Fr.y; break;
case 2: m_force0 = rb.m_Fr.z; break;
}
}
}
//-----------------------------------------------------------------------------
void FERigidBodyForce::Serialize(DumpStream& ar)
{
FEModelLoad::Serialize(ar);
ar & m_ntype & m_dof & m_rigidMat & m_force & m_rid;
}
//-----------------------------------------------------------------------------
//! Residual
void FERigidBodyForce::LoadVector(FEGlobalVector& R)
{
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(m_rid);
double t = CurrentTime();
if (m_ntype == FORCE_FOLLOW)
{
// setup the force vector
vec3d f(0,0,0);
if (m_dof == 0) f.x = m_force;
else if (m_dof == 1) f.y = m_force;
else if (m_dof == 2) f.z = m_force;
// apply the rigid body rotation
f = rb.GetRotation()*f;
// add to the residual
int n;
n = rb.m_LM[0]; if (n >= 0) R[n] += f.x;
n = rb.m_LM[1]; if (n >= 0) R[n] += f.y;
n = rb.m_LM[2]; if (n >= 0) R[n] += f.z;
}
else
{
int I = rb.m_LM[m_dof];
if (I >= 0)
{
double incVal = 0.0;
if (m_ntype == FORCE_LOAD)
{
incVal = m_force + m_force0;
}
else if (m_ntype == FORCE_TARGET)
{
// get the current analysis step
FEAnalysis* pstep = fem.GetCurrentStep();
double t0 = pstep->m_tstart;
double t1 = pstep->m_tend;
double w = (t - t0) / (t1 - t0);
assert((w >= -0.0000001) && (w <= 1.0000001));
double f0 = m_force0, f1 = m_force;
double f = f0 * (1.0 - w) + f1 * w;
incVal = f;
}
R[I] += incVal;
}
}
}
//-----------------------------------------------------------------------------
//! Stiffness matrix
void FERigidBodyForce::StiffnessMatrix(FELinearSystem& LS)
{
// I think for follower forces I need to contribute to the stiffness matrix, but I'm not sure yet what.
}
//=============================================================================
BEGIN_FECORE_CLASS(FERigidBodyMoment, FERigidLoad)
ADD_PARAMETER(m_rigidMat, "rb")->setEnums("$(rigid_materials)")->setLongName("Rigid material");
ADD_PARAMETER(m_dof, "dof", 0, "Ru\0Rv\0Rw\0");
ADD_PARAMETER(m_value, "value")->SetFlags(FE_PARAM_ADDLC | FE_PARAM_VOLATILE)->setUnits(UNIT_MOMENT);
ADD_PARAMETER(m_brelative, "relative");
ADD_PARAMETER(m_ntype, "load_type")->setEnums("LOAD\0FOLLOW\0TARGET");
END_FECORE_CLASS();
FERigidBodyMoment::FERigidBodyMoment(FEModel* pfem) : FERigidLoad(pfem)
{
m_rigidMat = -1;
m_rid = -1;
m_brelative = false;
m_value0 = 0.0;
m_value = 0.0;
m_dof = 0;
m_ntype = MOMENT_LOAD;
}
void FERigidBodyMoment::SetRigidMaterialID(int nid) { m_rigidMat = nid; }
void FERigidBodyMoment::SetDOF(int bc) { m_dof = bc; }
void FERigidBodyMoment::SetValue(double f) { m_value = f; }
//-----------------------------------------------------------------------------
bool FERigidBodyMoment::Init()
{
// At this point the rigid ID's are still associated with the materials.
// We want to associate them with the rigid objects instead.
FEModel& fem = *GetFEModel();
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_rigidMat - 1));
if (pm == 0) return false;
// follower moments are not supported yet.
if (m_ntype == MOMENT_FOLLOW)
{
feLogError("Follower moments are not supported.");
return false;
}
return FEModelLoad::Init();
}
//-----------------------------------------------------------------------------
void FERigidBodyMoment::Activate()
{
FEModelLoad::Activate();
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_rigidMat - 1));
m_rid = pm->GetRigidBodyID(); assert(m_rid >= 0);
FERigidBody& rb = *fem.GetRigidBody(m_rid);
if (m_ntype == MOMENT_TARGET)
{
switch (m_dof)
{
case 0: m_value0 = rb.m_Mr.x; break;
case 1: m_value0 = rb.m_Mr.y; break;
case 2: m_value0 = rb.m_Mr.z; break;
}
}
if ((m_ntype == MOMENT_LOAD) && m_brelative)
{
switch (m_dof)
{
case 0: m_value0 = rb.m_Mr.x; break;
case 1: m_value0 = rb.m_Mr.y; break;
case 2: m_value0 = rb.m_Mr.z; break;
}
}
}
//-----------------------------------------------------------------------------
void FERigidBodyMoment::Serialize(DumpStream& ar)
{
FEModelLoad::Serialize(ar);
ar & m_value0 & m_rid;
}
//-----------------------------------------------------------------------------
//! Residual
void FERigidBodyMoment::LoadVector(FEGlobalVector& R)
{
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidBody& rb = *fem.GetRigidBody(m_rid);
double t = CurrentTime();
int I = rb.m_LM[m_dof + 3];
if (I >= 0)
{
double incVal = 0.0;
if (m_ntype == MOMENT_LOAD)
{
incVal = m_value + m_value0;
}
else if (m_ntype == MOMENT_TARGET)
{
// get the current analysis step
FEAnalysis* pstep = fem.GetCurrentStep();
double t0 = pstep->m_tstart;
double t1 = pstep->m_tend;
double w = (t - t0) / (t1 - t0);
assert((w >= -0.0000001) && (w <= 1.0000001));
double M0 = m_value0, M1 = m_value;
double M = M0 * (1.0 - w) + M1 * w;
incVal = M;
}
R[I] += incVal;
}
}
//-----------------------------------------------------------------------------
//! Stiffness matrix
void FERigidBodyMoment::StiffnessMatrix(FELinearSystem& LS)
{
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FERigidSolver.cpp | .cpp | 48,216 | 1,588 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidSolver.h"
#include "FESolidSolver2.h"
#include "FERigidMaterial.h"
#include "FERigidBody.h"
#include <FECore/FEModel.h>
#include "RigidBC.h"
#include <FECore/FEAnalysis.h>
#include <FECore/SparseMatrix.h>
#include <FECore/log.h>
#include <FECore/FEMaterial.h>
#include "FEMechModel.h"
#include <FECore/FELinearSystem.h>
#include "FESolidAnalysis.h"
FERigidSolver::FERigidSolver(FEModel* fem)
{
m_fem = dynamic_cast<FEMechModel*>(fem);
m_dofX = m_dofY = m_dofZ = -1;
m_bAllowMixedBCs = false;
}
int FERigidSolver::InitEquations(int neq)
{
// Next, we assign equation numbers to the rigid body degrees of freedom
if (m_fem == nullptr) return neq;
int nrb = m_fem->RigidBodies();
for (int i = 0; i<nrb; ++i)
{
FERigidBody& RB = *m_fem->GetRigidBody(i);
for (int j = 0; j<6; ++j)
{
int bcj = RB.m_BC[j];
int lmj = RB.m_LM[j];
if (bcj == DOF_OPEN ) { RB.m_LM[j] = neq; neq++; }
else if (bcj == DOF_PRESCRIBED) { RB.m_LM[j] = -neq - 2; neq++; }
else if (bcj == DOF_FIXED ) { RB.m_LM[j] = -1; }
else { assert(false); return -1; }
}
}
// get the DOF indices
m_dofX = m_fem->GetDOFIndex("x");
m_dofY = m_fem->GetDOFIndex("y");
m_dofZ = m_fem->GetDOFIndex("z");
m_dofVX = m_fem->GetDOFIndex("vx");
m_dofVY = m_fem->GetDOFIndex("vy");
m_dofVZ = m_fem->GetDOFIndex("vz");
m_dofU = m_fem->GetDOFIndex("u");
m_dofV = m_fem->GetDOFIndex("v");
m_dofW = m_fem->GetDOFIndex("w");
m_dofSX = m_fem->GetDOFIndex("sx");
m_dofSY = m_fem->GetDOFIndex("sy");
m_dofSZ = m_fem->GetDOFIndex("sz");
m_dofSVX = m_fem->GetDOFIndex("svx");
m_dofSVY = m_fem->GetDOFIndex("svy");
m_dofSVZ = m_fem->GetDOFIndex("svz");
int dofRU = m_fem->GetDOFIndex("Ru");
int dofRV = m_fem->GetDOFIndex("Rv");
int dofRW = m_fem->GetDOFIndex("Rw");
// we assign the rigid body equation number to
// Also make sure that the nodes are NOT constrained!
FEMesh& mesh = m_fem->GetMesh();
for (int i = 0; i<mesh.Nodes(); ++i)
{
FENode& node = mesh.Node(i);
if (node.m_rid >= 0)
{
FERigidBody& RB = *m_fem->GetRigidBody(node.m_rid);
node.m_ID[m_dofX] = (RB.m_LM[0] >= 0 ? -RB.m_LM[0] - 2 : RB.m_LM[0]);
node.m_ID[m_dofY] = (RB.m_LM[1] >= 0 ? -RB.m_LM[1] - 2 : RB.m_LM[1]);
node.m_ID[m_dofZ] = (RB.m_LM[2] >= 0 ? -RB.m_LM[2] - 2 : RB.m_LM[2]);
node.m_ID[dofRU] = (RB.m_LM[3] >= 0 ? -RB.m_LM[3] - 2 : RB.m_LM[3]);
node.m_ID[dofRV] = (RB.m_LM[4] >= 0 ? -RB.m_LM[4] - 2 : RB.m_LM[4]);
node.m_ID[dofRW] = (RB.m_LM[5] >= 0 ? -RB.m_LM[5] - 2 : RB.m_LM[5]);
if (node.HasFlags(FENode::SHELL) && node.HasFlags(FENode::RIGID_CLAMP)) {
node.m_ID[m_dofU] = (RB.m_LM[0] >= 0 ? -RB.m_LM[0] - 2 : RB.m_LM[0]);
node.m_ID[m_dofV] = (RB.m_LM[1] >= 0 ? -RB.m_LM[1] - 2 : RB.m_LM[1]);
node.m_ID[m_dofW] = (RB.m_LM[2] >= 0 ? -RB.m_LM[2] - 2 : RB.m_LM[2]);
node.m_ID[m_dofSX] = (RB.m_LM[0] >= 0 ? -RB.m_LM[0] - 2 : RB.m_LM[0]);
node.m_ID[m_dofSY] = (RB.m_LM[1] >= 0 ? -RB.m_LM[1] - 2 : RB.m_LM[1]);
node.m_ID[m_dofSZ] = (RB.m_LM[2] >= 0 ? -RB.m_LM[2] - 2 : RB.m_LM[2]);
}
}
}
return neq;
}
//-----------------------------------------------------------------------------
//! Serialization
void FERigidSolver::Serialize(DumpStream& ar)
{
if (ar.IsShallow()) return;
ar & m_dofX & m_dofY & m_dofZ;
ar & m_dofVX & m_dofVY & m_dofVZ;
ar & m_dofU & m_dofV & m_dofW;
ar & m_dofSX & m_dofSY & m_dofSZ;
ar & m_dofSVX & m_dofSVY & m_dofSVZ;
ar & m_bAllowMixedBCs;
}
//-----------------------------------------------------------------------------
//! return the FEModel
FEModel* FERigidSolver::GetFEModel()
{
return m_fem;
}
//-----------------------------------------------------------------------------
// \todo: eliminate need for ui parameter
void FERigidSolver::PrepStep(const FETimeInfo& timeInfo, vector<double>& ui)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
int NO = fem.RigidBodies();
for (int i = 0; i<NO; ++i) fem.GetRigidBody(i)->Init();
// calculate local rigid displacements
int NRBC = fem.RigidBCs();
for (int i = 0; i < NRBC; ++i)
{
FERigidBC& rbc = *fem.GetRigidBC(i);
if (rbc.IsActive()) rbc.InitTimeStep();
}
// calculate global rigid displacements
for (int i = 0; i<NO; ++i)
{
FERigidBody* prb = fem.GetRigidBody(i);
if (prb)
{
FERigidBody& RB = *prb;
if (RB.m_prb == 0)
{
// if all rotation dofs are fixed or prescribed, set the flag
if (m_bAllowMixedBCs==false)
{
RB.m_bpofr = false;
if (RB.m_pDC[3] || RB.m_pDC[4] || RB.m_pDC[5])
{
bool bpofr[3] = { false };
for (int j = 3; j<6; ++j) if (RB.m_pDC[j] || (RB.m_LM[j] < 0)) bpofr[j - 3] = true;
if (bpofr[0] && bpofr[1] && bpofr[2]) RB.m_bpofr = true;
else
{
feLogError("Rigid body rotations cannot mix prescribed and free components.\nRigid body: %d, Material: %d\n", RB.m_nID, RB.GetMaterialID());
throw "FATAL ERROR";
}
// see if all or none prescribed dofs are relative
bool br[3] = { false, false, false };
for (int j = 3; j < 6; ++j)
{
FERigidPrescribedBC* dc = RB.m_pDC[j];
if (dc && dc->GetRelativeFlag()) br[j - 3] = true;
}
bool bf = ((br[0] == br[1]) && (br[1] == br[2]) && (br[0] == br[2]));
if (bf==false)
{
feLogError("All or none rigid rotations must have relative flag set.\nRigid body: %d, Material: %d\n", RB.m_nID, RB.GetMaterialID());
throw "FATAL ERROR";
}
}
}
for (int j = 0; j<6; ++j) RB.m_du[j] = RB.m_dul[j];
}
else
{
double* dul = RB.m_dul;
vec3d dr = vec3d(dul[0], dul[1], dul[2]);
vec3d v = vec3d(dul[3], dul[4], dul[5]);
double w = sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
quatd dq = quatd(w, v);
FERigidBody* pprb = RB.m_prb;
vec3d r0 = RB.m_rt;
quatd Q0 = RB.GetRotation();
dr = Q0*dr;
dq = Q0*dq*Q0.Inverse();
while (pprb)
{
vec3d r1 = pprb->m_rt;
dul = pprb->m_dul;
quatd Q1 = pprb->GetRotation();
dr = r0 + dr - r1;
// grab the parent's local displacements
vec3d dR = vec3d(dul[0], dul[1], dul[2]);
v = vec3d(dul[3], dul[4], dul[5]);
w = sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
quatd dQ = quatd(w, v);
dQ = Q1*dQ*Q1.Inverse();
// update global displacements
quatd Qi = Q1.Inverse();
dr = dR + r1 + dQ*dr - r0;
dq = dQ*dq;
// move up in the chain
pprb = pprb->m_prb;
Q0 = Q1;
}
// set global displacements
double* du = RB.m_du;
du[0] = dr.x;
du[1] = dr.y;
du[2] = dr.z;
v = dq.GetVector();
w = dq.GetAngle();
du[3] = w*v.x;
du[4] = w*v.y;
du[5] = w*v.z;
}
}
}
// store rigid displacements in Ui vector
for (int i = 0; i<NO; ++i)
{
FERigidBody& RB = *fem.GetRigidBody(i);
for (int j = 0; j<6; ++j)
{
int I = -RB.m_LM[j] - 2;
if (I >= 0) ui[I] = RB.m_du[j];
}
}
for (int i = 0; i<NO; ++i)
{
FERigidBody& RB = *fem.GetRigidBody(i);
quatd q = RB.GetRotation()*RB.m_qp.Inverse();
q.MakeUnit();
// update RB variables
// translation
RB.m_rp = RB.m_rt;
RB.m_vp = RB.m_vt;
RB.m_ap = RB.m_at;
// rotation
RB.m_qp = RB.GetRotation();
RB.m_wp = RB.m_wt;
RB.m_alp = RB.m_alt;
// angular momentum
RB.m_hp = RB.m_ht;
RB.m_dhp = RB.m_dht;
// rigid body reaction force and moment
RB.m_Fp = RB.m_Fr;
RB.m_Mp = RB.m_Mr;
// estimate RB kinematics at current time
double dt = timeInfo.timeIncrement;
double beta = timeInfo.beta;
double gamma = timeInfo.gamma;
double a = 1.0 / (beta*dt);
double b = a / dt;
double c = 1.0 - 0.5 / beta;
// acceleration and velocity of center of mass
RB.m_at = RB.m_ap*c - RB.m_vp*a;
RB.m_vt = RB.m_vp + (RB.m_at*gamma + RB.m_ap*(1-gamma))*dt;
// angular acceleration and velocity of rigid body
vec3d vq = q.GetVector()*(2 * tan(q.GetAngle() / 2)); // Cayley transform
RB.m_wt = vq*(a*gamma) - RB.m_wp + (RB.m_wp + RB.m_alp*dt / 2.)*(2 - gamma / beta);
q.RotateVector(RB.m_wt);
RB.m_alt = vq*b - RB.m_wp*a + RB.m_alp*c;
q.RotateVector(RB.m_alt);
}
}
//-----------------------------------------------------------------------------
//! This function calculates the rigid stiffness matrices
void FERigidSolver::RigidStiffness(SparseMatrix& K, vector<double>& ui, vector<double>& F, const FEElementMatrix& ke, double alpha)
{
if (m_fem == nullptr) return;
const vector<int>& en = ke.Nodes();
int n = (int)en.size();
FEMesh& mesh = m_fem->GetMesh();
bool bclamped_shell = false;
for (int j = 0; j<n; ++j)
{
if (en[j] >= 0)
{
if (mesh.Node(en[j]).HasFlags(FENode::SHELL) && mesh.Node(en[j]).HasFlags(FENode::RIGID_CLAMP)) {
bclamped_shell = true;
break;
}
}
}
if (bclamped_shell)
RigidStiffnessShell(K, ui, F, en, ke.RowIndices(), ke.ColumnsIndices(), ke, alpha);
else
RigidStiffnessSolid(K, ui, F, en, ke.RowIndices(), ke.ColumnsIndices(), ke, alpha);
return;
}
//-----------------------------------------------------------------------------
//! This function calculates the rigid stiffness matrices
//! correct stiffness matrix for rigid-solid interfaces
void FERigidSolver::RigidStiffnessSolid(SparseMatrix& K, vector<double>& ui, vector<double>& F, const vector<int>& en, const vector<int>& elmi, const std::vector<int>& elmj, const matrix& ke, double alpha)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
if (fem.RigidBodies() == 0) return;
if (en.empty()) return;
int n = (int)en.size();
// get nodal DOFS
DOFS& fedofs = m_fem->GetDOFS();
int MAX_NDOFS = fedofs.GetTotalDOFS();
int ndof = ke.columns() / n;
matrix kij(ndof, ndof);
matrix KF(ndof, 6);
double KR[6][6];
FEMesh& mesh = m_fem->GetMesh();
// loop over columns
for (int j = 0; j<n; ++j)
{
if (en[j] >= 0)
{
FENode& nodej = mesh.Node(en[j]);
if (nodej.m_rid >= 0)
{
// this is a rigid interface node
// get the rigid body this node is attached to
FERigidBody& RBj = *fem.GetRigidBody(nodej.m_rid);
// get the rigid body equation nrs.
int* lmj = RBj.m_LM;
// get the relative distance to the center of mass
vec3d zj = nodej.m_rt - RBj.m_rt;
mat3d Zj; Zj.skew(zj);
// loop over rows
for (int i = 0; i < n; ++i)
{
// get the element sub-matrix
for (int k = 0; k < ndof; ++k)
for (int l = 0; l < ndof; ++l)
kij[k][l] = ke[ndof*i + k][ndof*j + l];
mat3d Kuu(kij[0][0], kij[0][1], kij[0][2],
kij[1][0], kij[1][1], kij[1][2],
kij[2][0], kij[2][1], kij[2][2]);
if (en[i] >= 0)
{
FENode& nodei = mesh.Node(en[i]);
if (nodei.m_rid >= 0)
{
// node i is also a rigid body node
// get the rigid body this node is attached to
FERigidBody& RBi = *fem.GetRigidBody(nodei.m_rid);
int* lmi = RBi.m_LM;
// get the relative distance (use alpha rule)
vec3d zi = (nodei.m_rt - RBi.m_rt)*alpha + (nodei.m_rp - RBi.m_rp)*(1 - alpha);
mat3d Zi; Zi.skew(zi);
mat3d M;
// Kuu transformation to Krr
M = Kuu;
KR[0][0] = M[0][0]; KR[0][1] = M[0][1]; KR[0][2] = M[0][2];
KR[1][0] = M[1][0]; KR[1][1] = M[1][1]; KR[1][2] = M[1][2];
KR[2][0] = M[2][0]; KR[2][1] = M[2][1]; KR[2][2] = M[2][2];
// Kuu transformation to Krq
M = Kuu * Zj*(-1);
KR[0][3] = M[0][0]; KR[0][4] = M[0][1]; KR[0][5] = M[0][2];
KR[1][3] = M[1][0]; KR[1][4] = M[1][1]; KR[1][5] = M[1][2];
KR[2][3] = M[2][0]; KR[2][4] = M[2][1]; KR[2][5] = M[2][2];
// Kuu transformation to Kqr
M = Zi * Kuu;
KR[3][0] = M[0][0]; KR[3][1] = M[0][1]; KR[3][2] = M[0][2];
KR[4][0] = M[1][0]; KR[4][1] = M[1][1]; KR[4][2] = M[1][2];
KR[5][0] = M[2][0]; KR[5][1] = M[2][1]; KR[5][2] = M[2][2];
// Kuu transformation to Kqq
M = Zi * Kuu*Zj*(-1);
KR[3][3] = M[0][0]; KR[3][4] = M[0][1]; KR[3][5] = M[0][2];
KR[4][3] = M[1][0]; KR[4][4] = M[1][1]; KR[4][5] = M[1][2];
KR[5][3] = M[2][0]; KR[5][4] = M[2][1]; KR[5][5] = M[2][2];
// add the stiffness components to the Krr matrix
for (int k = 0; k < 6; ++k)
for (int l = 0; l < 6; ++l)
{
int J = lmj[k];
int I = lmi[l];
if (I >= 0)
{
// multiply KR by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KR[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KR[l][k]);
}
}
// we still need to couple the non-rigid degrees of node i to the
// rigid dofs of node j
for (int k = 3; k < ndof; ++k) {
vec3d kpu(kij[k][0], kij[k][1], kij[k][2]);
vec3d m = kpu;
KF[k][0] = m.x; KF[k][1] = m.y; KF[k][2] = m.z;
m = Zj * kpu;
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (int k = 0; k < 6; ++k)
for (int l = 3; l < ndof; ++l)
{
int J = lmj[k];
int I = elmi[ndof*i + l];
if (I >= 0)
{
// multiply KF by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
// now the transpose location
for (int l = 3; l < ndof; ++l) {
vec3d kup(kij[0][l], kij[1][l], kij[2][l]);
vec3d m = Zi * kup;
KF[l][0] = kup.x; KF[l][1] = kup.y; KF[l][2] = kup.z;
KF[l][3] = m.x; KF[l][4] = m.y; KF[l][5] = m.z;
}
for (int k = 0; k < 6; ++k)
for (int l = 3; l < ndof; ++l)
{
int J = elmj[ndof*j + l];
int I = lmi[k];
if (I >= 0)
{
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
else
{
// node i is not a rigid body node
// add the stiffness components to the Kfr matrix
// Kij
for (int k = 0; k < ndof; ++k) {
vec3d kpu(kij[k][0], kij[k][1], kij[k][2]);
vec3d m = kpu;
KF[k][0] = m.x; KF[k][1] = m.y; KF[k][2] = m.z;
m = Zj * kpu;
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (int k = 0; k < 6; ++k)
for (int l = 0; l < ndof; ++l)
{
int J = lmj[k];
int I = elmi[ndof*i + l];
if (I >= 0)
{
// multiply KF by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
}
}
}
else
{
// loop over rows
for (int i = 0; i < n; ++i)
{
if (en[i] >= 0)
{
FENode& nodei = mesh.Node(en[i]);
if (nodei.m_rid >= 0)
{
// node i is a rigid body
// get the rigid body this node is attached to
FERigidBody& RBi = *fem.GetRigidBody(nodei.m_rid);
// get the rigid body equation nrs.
int* lmi = RBi.m_LM;
// get the relative distance (use alpha rule)
vec3d zi = (nodei.m_rt - RBi.m_rt)*alpha + (nodei.m_rp - RBi.m_rp)*(1 - alpha);
mat3d Zi; Zi.skew(zi);
// get the element sub-matrix
for (int k = 0; k < ndof; ++k)
for (int l = 0; l < ndof; ++l)
kij[k][l] = ke[ndof*i + k][ndof*j + l];
// add the stiffness components to the Krf matrix
// Kij
for (int k = 0; k < ndof; ++k) {
vec3d kup(kij[0][k], kij[1][k], kij[2][k]);
vec3d m = Zi * kup;
KF[k][0] = kup.x; KF[k][1] = kup.y; KF[k][2] = kup.z;
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (int k = 0; k < 6; ++k)
for (int l = 0; l < ndof; ++l)
{
int I = lmi[k];
int J = elmj[ndof*j + l];
if (I >= 0)
{
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
}
}
}
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the rigid stiffness matrices
//! correct stiffness matrix for rigid bodies accounting for rigid-body-deformable-shell interfaces
void FERigidSolver::RigidStiffnessShell(SparseMatrix& K, vector<double>& ui, vector<double>& F, const vector<int>& en, const vector<int>& elmi, const vector<int>& elmj, const matrix& ke, double alpha)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
if (fem.RigidBodies() == 0) return;
int i, j, k, l, n = (int)en.size();
// get nodal DOFS
DOFS& fedofs = m_fem->GetDOFS();
int MAX_NDOFS = fedofs.GetTotalDOFS();
vector< vector<double> > kij; kij.assign(MAX_NDOFS, vector<double>(MAX_NDOFS));
vector< vector<double> > KF; KF.assign(MAX_NDOFS, vector<double>(6));
double KR[6][6];
int *lmi, *lmj;
int I, J;
vec3d ai, aj, bi, bj;
mat3d Ai, Aj, Bi, Bj;
int ndof = ke.columns() / n;
FEMesh& mesh = m_fem->GetMesh();
// loop over columns
for (j = 0; j<n; ++j)
{
FENode& nodej = mesh.Node(en[j]);
if (nodej.m_rid >= 0)
{
// this is a rigid interface node
// get the rigid body this node is attached to
FERigidBody& RBj = *fem.GetRigidBody(nodej.m_rid);
// get the rigid body equation nrs.
lmj = RBj.m_LM;
// get the relative distance to the center of mass
aj = nodej.m_rt - RBj.m_rt;
Aj.skew(aj);
// get the shell director
bj = aj - nodej.m_dt;
Bj.skew(bj);
// loop over rows
for (i = 0; i<n; ++i)
{
// get the element sub-matrix
for (k = 0; k<ndof; ++k)
for (l = 0; l<ndof; ++l)
kij[k][l] = ke[ndof*i + k][ndof*j + l];
mat3d Kuu(kij[0][0], kij[0][1], kij[0][2],
kij[1][0], kij[1][1], kij[1][2],
kij[2][0], kij[2][1], kij[2][2]);
mat3d Kuw(kij[0][3], kij[0][4], kij[0][5],
kij[1][3], kij[1][4], kij[1][5],
kij[2][3], kij[2][4], kij[2][5]);
mat3d Kwu(kij[3][0], kij[3][1], kij[3][2],
kij[4][0], kij[4][1], kij[4][2],
kij[5][0], kij[5][1], kij[5][2]);
mat3d Kww(kij[3][3], kij[3][4], kij[3][5],
kij[4][3], kij[4][4], kij[4][5],
kij[5][3], kij[5][4], kij[5][5]);
FENode& nodei = mesh.Node(en[i]);
if (nodei.m_rid >= 0)
{
// node i is also a rigid body node
// get the rigid body this node is attached to
FERigidBody& RBi = *fem.GetRigidBody(nodei.m_rid);
lmi = RBi.m_LM;
// get the relative distance (use alpha rule)
ai = (nodei.m_rt - RBi.m_rt)*alpha + (nodei.m_rp - RBi.m_rp)*(1 - alpha);
Ai.skew(ai);
// get the shell director
bi = ai - nodei.m_dt;
Bi.skew(bi);
mat3d M;
// Kuu transformation
M = (Kuu + Kwu + Kuw + Kww);
KR[0][0] = M[0][0]; KR[0][1] = M[0][1]; KR[0][2] = M[0][2];
KR[1][0] = M[1][0]; KR[1][1] = M[1][1]; KR[1][2] = M[1][2];
KR[2][0] = M[2][0]; KR[2][1] = M[2][1]; KR[2][2] = M[2][2];
// Kuw transformation
M = ((Kuu + Kwu)*Aj + (Kuw + Kww)*Bj)*(-1);
KR[0][3] = M[0][0]; KR[0][4] = M[0][1]; KR[0][5] = M[0][2];
KR[1][3] = M[1][0]; KR[1][4] = M[1][1]; KR[1][5] = M[1][2];
KR[2][3] = M[2][0]; KR[2][4] = M[2][1]; KR[2][5] = M[2][2];
// Kwu transformation
M = (Ai*(Kuu + Kuw) + Bi*(Kwu + Kww));
KR[3][0] = M[0][0]; KR[3][1] = M[0][1]; KR[3][2] = M[0][2];
KR[4][0] = M[1][0]; KR[4][1] = M[1][1]; KR[4][2] = M[1][2];
KR[5][0] = M[2][0]; KR[5][1] = M[2][1]; KR[5][2] = M[2][2];
// Kww transformation
M = ((Ai*Kuu + Bi*Kwu)*Aj + (Ai*Kuw + Bi*Kww)*Bj)*(-1);
KR[3][3] = M[0][0]; KR[3][4] = M[0][1]; KR[3][5] = M[0][2];
KR[4][3] = M[1][0]; KR[4][4] = M[1][1]; KR[4][5] = M[1][2];
KR[5][3] = M[2][0]; KR[5][4] = M[2][1]; KR[5][5] = M[2][2];
// add the stiffness components to the Krr matrix
for (k = 0; k<6; ++k)
for (l = 0; l<6; ++l)
{
J = lmj[k];
I = lmi[l];
if (I >= 0)
{
// multiply KR by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KR[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KR[l][k]);
}
}
// we still need to couple the non-rigid degrees of node i to the
// rigid dofs of node j
for (k = 6; k<ndof; ++k) {
vec3d kpu(kij[k][0], kij[k][1], kij[k][2]);
vec3d kpw(kij[k][3], kij[k][4], kij[k][5]);
vec3d m = (kpu + kpw);
KF[k][0] = m.x; KF[k][1] = m.y; KF[k][2] = m.z;
m = (Aj*kpu + Bj*kpw);
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (k = 0; k<6; ++k)
for (l = 6; l<ndof; ++l)
{
J = lmj[k];
I = elmi[ndof*i + l];
if (I >= 0)
{
// multiply KF by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
// now the transpose location
for (l = 6; l<ndof; ++l) {
vec3d kup(kij[0][l], kij[1][l], kij[2][l]);
vec3d kwp(kij[3][l], kij[4][l], kij[5][l]);
vec3d m = kup + kwp;
KF[l][0] = m.x; KF[l][1] = m.y; KF[l][2] = m.z;
m = Ai*kup + Bi*kwp;
KF[l][3] = m.x; KF[l][4] = m.y; KF[l][5] = m.z;
}
for (k = 0; k<6; ++k)
for (l = 6; l<ndof; ++l)
{
J = elmj[ndof*j + l];
I = lmi[k];
if (I >= 0)
{
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
else
{
// node i is not a rigid body node
// add the stiffness components to the Kfr matrix
// Kij
for (k = 0; k<ndof; ++k) {
vec3d kpu(kij[k][0], kij[k][1], kij[k][2]);
vec3d kpw(kij[k][3], kij[k][4], kij[k][5]);
vec3d m = (kpu + kpw);
KF[k][0] = m.x; KF[k][1] = m.y; KF[k][2] = m.z;
m = (Aj*kpu + Bj*kpw);
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (k = 0; k<6; ++k)
for (l = 0; l<ndof; ++l)
{
J = lmj[k];
I = elmi[ndof*i + l];
if (I >= 0)
{
// multiply KF by alpha for alpha rule
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
}
}
else
{
// loop over rows
for (i = 0; i<n; ++i)
{
FENode& nodei = mesh.Node(en[i]);
if (nodei.m_rid >= 0)
{
// node i is a rigid body
// get the rigid body this node is attached to
FERigidBody& RBi = *fem.GetRigidBody(nodei.m_rid);
// get the rigid body equation nrs.
lmi = RBi.m_LM;
// get the relative distance (use alpha rule)
ai = (nodei.m_rt - RBi.m_rt)*alpha + (nodei.m_rp - RBi.m_rp)*(1 - alpha);
Ai.skew(ai);
// get the shell director
bi = ai - nodei.m_dt;
Bi.skew(bi);
// get the element sub-matrix
for (k = 0; k<ndof; ++k)
for (l = 0; l<ndof; ++l)
kij[k][l] = ke[ndof*i + k][ndof*j + l];
// add the stiffness components to the Krf matrix
// Kij
for (k = 0; k<ndof; ++k) {
vec3d kup(kij[0][k], kij[1][k], kij[2][k]);
vec3d kwp(kij[3][k], kij[4][k], kij[5][k]);
vec3d m = kup + kwp;
KF[k][0] = m.x; KF[k][1] = m.y; KF[k][2] = m.z;
m = Ai*kup + Bi*kwp;
KF[k][3] = m.x; KF[k][4] = m.y; KF[k][5] = m.z;
}
for (k = 0; k<6; ++k)
for (l = 0; l<ndof; ++l)
{
I = lmi[k];
J = elmj[ndof*j + l];
if (I >= 0)
{
if (J < -1) {
#pragma omp atomic
F[I] -= KF[l][k] * ui[-J - 2];
}
else if (J >= 0) K.add(I, J, KF[l][k]);
}
}
}
}
}
}
}
//-----------------------------------------------------------------------------
void FERigidSolver::AssembleResidual(int node_id, int dof, double f, vector<double>& R)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
FEMesh& mesh = m_fem->GetMesh();
// get the equation number
FENode& node = mesh.Node(node_id);
int n = node.m_ID[dof];
// assemble into global vector
if (n >= 0)
{
#pragma omp atomic
R[n] += f;
}
else if (node.m_rid >= 0)
{
// this is a rigid body node
FERigidBody& RB = *fem.GetRigidBody(node.m_rid);
// get the relative position
vec3d a = node.m_rt - RB.m_rt;
int* lm = RB.m_LM;
if (dof == m_dofX)
{
if (lm[0] >= 0) {
#pragma omp atomic
R[lm[0]] += f;
}
if (lm[4] >= 0) {
#pragma omp atomic
R[lm[4]] += a.z * f;
}
if (lm[5] >= 0) {
#pragma omp atomic
R[lm[5]] += -a.y * f;
}
}
else if (dof == m_dofY)
{
if (lm[1] >= 0) {
#pragma omp atomic
R[lm[1]] += f;
}
if (lm[3] >= 0) {
#pragma omp atomic
R[lm[3]] += -a.z * f;
}
if (lm[5] >= 0) {
#pragma omp atomic
R[lm[5]] += a.x * f;
}
}
else if (dof == m_dofZ)
{
if (lm[2] >= 0) {
#pragma omp atomic
R[lm[2]] += f;
}
if (lm[3] >= 0) {
#pragma omp atomic
R[lm[3]] += a.y * f;
}
if (lm[4] >= 0) {
#pragma omp atomic
R[lm[4]] += -a.x * f;
}
}
if (node.HasFlags(FENode::SHELL) && node.HasFlags(FENode::RIGID_CLAMP)) {
// get the shell director
vec3d d = node.m_dt;
vec3d b = a - d;
if (dof == m_dofSX)
{
if (lm[0] >= 0) {
#pragma omp atomic
R[lm[0]] += f;
}
if (lm[4] >= 0) {
#pragma omp atomic
R[lm[4]] += b.z * f;
}
if (lm[5] >= 0) {
#pragma omp atomic
R[lm[5]] += -b.y * f;
}
}
else if (dof == m_dofSY)
{
if (lm[1] >= 0) {
#pragma omp atomic
R[lm[1]] += f;
}
if (lm[3] >= 0) {
#pragma omp atomic
R[lm[3]] += -b.z * f;
}
if (lm[5] >= 0) {
#pragma omp atomic
R[lm[5]] += b.x * f;
}
}
else if (dof == m_dofSZ)
{
if (lm[2] >= 0) {
#pragma omp atomic
R[lm[2]] += f;
}
if (lm[3] >= 0) {
#pragma omp atomic
R[lm[3]] += b.y * f;
}
if (lm[4] >= 0) {
#pragma omp atomic
R[lm[4]] += -b.x * f;
}
}
}
}
}
//-----------------------------------------------------------------------------
void FERigidSolver::Residual()
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
int NRB = fem.RigidBodies();
for (int i = 0; i<NRB; ++i)
{
FERigidBody& RB = *fem.GetRigidBody(i);
RB.m_Fr = RB.m_Mr = vec3d(0, 0, 0);
}
}
//-----------------------------------------------------------------------------
void FERigidSolver::StiffnessMatrix(SparseMatrix& K, const FETimeInfo& tp)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
// we still need to set the diagonal elements to 1
// for the prescribed rigid body dofs.
int NRB = fem.RigidBodies();
for (int i = 0; i<NRB; ++i)
{
FERigidBody& rb = *fem.GetRigidBody(i);
for (int j = 0; j<6; ++j)
if (rb.m_LM[j] < -1)
{
int I = -rb.m_LM[j] - 2;
K.set(I, I, 1);
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the contribution to the mass matrix from the rigid bodies
void FERigidSolver::RigidMassMatrix(FELinearSystem& LS, const FETimeInfo& timeInfo)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
// element stiffness matrix
vector<int> lm;
FEElementMatrix ke;
// 6 dofs per rigid body
ke.resize(6, 6);
// Newmark integration rule
double dt = timeInfo.timeIncrement;
double alpham = timeInfo.alpham;
double beta = timeInfo.beta;
double gamma = timeInfo.gamma;
double a = 1. / (beta*dt*dt);
if (timeInfo.currentTime == 0)
{
a = alpham = 1;
}
for (int i=0; i<fem.RigidBodies(); ++i)
{
FERigidBody& RB = *fem.GetRigidBody(i);
// mass matrix
double M = RB.m_mass*a*alpham;
ke.zero();
ke[0][0] = M;
ke[1][1] = M;
ke[2][2] = M;
// evaluate mass moment of inertia at t
mat3d Rt = RB.GetRotation().RotationMatrix();
mat3ds Jt = (Rt*RB.m_moi*Rt.transpose()).sym();
// incremental rotation in spatial frame
quatd q = RB.GetRotation()*RB.m_qp.Inverse();
q.MakeUnit(); // clean-up roundoff errors
double theta = 2 * tan(q.GetAngle() / 2); // get theta from Cayley transform
vec3d e = q.GetVector();
// skew-symmetric tensor whose axial vector is the incremental rotation
mat3d qhat;
qhat.skew(e*theta);
// generate tensor T(theta)
mat3d T = mat3dd(1) + qhat / 2 + dyad(e*theta) / 4;
// skew-symmetric of angular momentum
mat3d hhat;
hhat.skew(RB.m_ht);
// skew-symmetric angular velocity
mat3d Omega; Omega.skew(RB.m_wt);
mat3d Dht; Dht.skew(RB.m_dht);
// rotational inertia stiffness
mat3d K = ((((Omega*gamma+mat3dd(1./dt))*Jt - hhat*gamma)/(beta*dt))*T - Dht)*alpham;
ke[3][3] = K(0, 0); ke[3][4] = K(0, 1); ke[3][5] = K(0, 2);
ke[4][3] = K(1, 0); ke[4][4] = K(1, 1); ke[4][5] = K(1, 2);
ke[5][3] = K(2, 0); ke[5][4] = K(2, 1); ke[5][5] = K(2, 2);
lm.assign(RB.m_LM, RB.m_LM + 6);
ke.SetIndices(lm);
LS.Assemble(ke);
}
}
//=================================================================================================
// FERigidSolverOld
//=================================================================================================
//-----------------------------------------------------------------------------
//! This function updates the rigid body linear and angular velocity by solving
//! an overdetermined system of linear equations using the least-square method.
void FERigidSolverOld::UpdateRigidKinematics()
{
// get the model and mesh
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
FEMesh& mesh = fem.GetMesh();
// loop over all rigid bodies
int NRB = fem.RigidBodies();
for (int j = 0; j<NRB; ++j)
{
// get the rigid body
FERigidBody& rb = *fem.GetRigidBody(j);
// right-hand side and least-square matrix
vector<double> r; r.assign(6, 0.0);
matrix m(6, 6); m.zero();
// we need to loop over all domains that define this rigid body
int ncnt = 0;
int NDOM = mesh.Domains();
for (int n = 0; n<NDOM; ++n)
{
FEDomain& dom = mesh.Domain(n);
FERigidMaterial* prm = dynamic_cast<FERigidMaterial*>(dom.GetMaterial());
if (prm)
{
if (prm->GetRigidBodyID() == j)
{
// now loop over all the nodes
int NN = dom.Nodes();
for (int i = 0; i<NN; ++i, ncnt++)
{
vec3d ri = dom.Node(i).m_rt - rb.m_rt;
vec3d vi = dom.Node(i).get_vec3d(m_dofVX, m_dofVY, m_dofVZ);
vec3d wi = ri ^ vi;
// right-hand side
r[0] += vi.x;
r[1] += vi.y;
r[2] += vi.z;
r[3] += wi.x;
r[4] += wi.y;
r[5] += wi.z;
// least-squares matrix
m[0][0] += 1.0;
m[1][1] += 1.0;
m[2][2] += 1.0;
m[0][4] += ri.z; m[0][5] += -ri.y;
m[1][3] += -ri.z; m[1][5] += ri.x;
m[2][3] += ri.y; m[2][4] += -ri.x;
m[3][4] += -ri.z; m[3][5] += ri.y;
m[4][3] += ri.z; m[4][5] += -ri.x;
m[5][3] += -ri.y; m[5][4] += ri.x;
m[3][3] += ri.y*ri.y + ri.z*ri.z; m[3][4] += -ri.x*ri.y; m[3][5] += -ri.x*ri.z;
m[4][4] += ri.x*ri.x + ri.z*ri.z; m[4][3] += -ri.x*ri.y; m[4][5] += -ri.y*ri.z;
m[5][5] += ri.x*ri.x + ri.y*ri.y; m[5][3] += -ri.x*ri.z; m[5][4] += -ri.y*ri.z;
}
}
}
}
// solve for the rigid body velocity (if we have enough nodes)
if (ncnt > 2)
{
vector<double> VR = r / m;
rb.m_vt = vec3d(VR[0], VR[1], VR[2]);
rb.m_wt = vec3d(VR[3], VR[4], VR[5]);
}
}
}
//-----------------------------------------------------------------------------
//! Updates the rigid body data
void FERigidSolverOld::UpdateRigidBodies(vector<double>& Ui, vector<double>& ui, bool bnewUpdate)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
const int NRB = fem.RigidBodies();
// first calculate the rigid body displacement increments
for (int i = 0; i<NRB; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
int *lm = RB.m_LM;
double* du = RB.m_du;
if (RB.m_prb == 0)
{
for (int j = 0; j<6; ++j)
{
du[j] = (lm[j] >= 0 ? Ui[lm[j]] + ui[lm[j]] : 0);
}
}
}
// for prescribed displacements, the displacement increments are evaluated differently
// TODO: Is this really necessary? Why can't the ui vector contain the correct values?
for (int i = 0; i < NRB; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
if (RB.m_prb == nullptr)
{
for (int j = 0; j < 6; ++j)
{
FERigidPrescribedBC* dc = RB.m_pDC[j];
if (dc && dc->IsActive())
{
int I = dc->GetBC();
RB.m_du[I] = dc->Value() - RB.m_Up[I];
}
}
}
}
// update the rigid bodies
for (int i = 0; i<NRB; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
double* du = RB.m_du;
if (bnewUpdate)
{
// This is the "new" update algorithm which addressesses a couple issues
// with the old method, namely that prescribed rotational dofs aren't update correctly.
// Unfortunately, it seems to produce worse convergence in some cases, especially with line search
// and it doesn't work when rigid bodies are used in a hierarchy
if (RB.m_prb) du = RB.m_dul;
RB.m_Ut[0] = RB.m_Up[0] + du[0];
RB.m_Ut[1] = RB.m_Up[1] + du[1];
RB.m_Ut[2] = RB.m_Up[2] + du[2];
RB.m_Ut[3] = RB.m_Up[3] + du[3];
RB.m_Ut[4] = RB.m_Up[4] + du[4];
RB.m_Ut[5] = RB.m_Up[5] + du[5];
RB.m_rt = RB.m_r0 + vec3d(RB.m_Ut[0], RB.m_Ut[1], RB.m_Ut[2]);
vec3d Rt(RB.m_Ut[3], RB.m_Ut[4], RB.m_Ut[5]);
RB.SetRotation(quatd(Rt));
}
else
{
// This is the "old" update algorithm which has some issues. It does not produce the correct
// rigid body orientation when the rotational degrees of freedom are prescribed.
RB.m_rt.x = RB.m_rp.x + du[0];
RB.m_rt.y = RB.m_rp.y + du[1];
RB.m_rt.z = RB.m_rp.z + du[2];
vec3d r = vec3d(du[3], du[4], du[5]);
double w = sqrt(r.x*r.x + r.y*r.y + r.z*r.z);
quatd dq = quatd(w, r);
quatd Q = dq*RB.m_qp;
Q.MakeUnit();
RB.SetRotation(Q);
if (RB.m_prb) du = RB.m_dul;
RB.m_Ut[0] = RB.m_Up[0] + du[0];
RB.m_Ut[1] = RB.m_Up[1] + du[1];
RB.m_Ut[2] = RB.m_Up[2] + du[2];
RB.m_Ut[3] = RB.m_Up[3] + du[3];
RB.m_Ut[4] = RB.m_Up[4] + du[4];
RB.m_Ut[5] = RB.m_Up[5] + du[5];
}
}
// we need to update the position of rigid nodes
fem.UpdateRigidMesh();
// Since the rigid nodes are repositioned we need to update the displacement DOFS
FEMesh& mesh = m_fem->GetMesh();
int N = mesh.Nodes();
for (int i = 0; i<N; ++i)
{
FENode& node = mesh.Node(i);
if (node.m_rid >= 0)
{
vec3d ut = node.m_rt - node.m_r0;
node.set_vec3d(m_dofX, m_dofY, m_dofZ, ut);
}
}
}
//=================================================================================================
// FERigidSolverNew
//=================================================================================================
//-----------------------------------------------------------------------------
void FERigidSolverNew::UpdateIncrements(vector<double>& Ui, vector<double>& ui, bool emap)
{
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
int nrb = fem.RigidBodies();
for (int i = 0; i<nrb; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
if (RB.m_prb == 0)
{
int *lm = RB.m_LM;
vec3d v;
quatd qUi;
// first do the displacements
for (int j = 0; j<3; ++j)
if (lm[j] >= 0) Ui[lm[j]] += ui[lm[j]];
// next, we do the rotations. We do this separately since
// they need to be interpreted differently than displacements
vec3d vUi(0, 0, 0);
vec3d vui(0, 0, 0);
if (lm[3] >= 0) { vUi.x = Ui[lm[3]]; vui.x = ui[lm[3]]; }
if (lm[4] >= 0) { vUi.y = Ui[lm[4]]; vui.y = ui[lm[4]]; }
if (lm[5] >= 0) { vUi.z = Ui[lm[5]]; vui.z = ui[lm[5]]; }
if (emap) qUi = quatd(vUi);
else qUi = quatd(2 * atan(vUi.norm() / 2), vUi); // Cayley transform
quatd qui(2 * atan(vui.norm() / 2), vui); // Cayley transform
quatd q = qui*qUi;
q.MakeUnit();
if (emap) v = q.GetVector()*q.GetAngle();
else v = q.GetVector()*(2 * tan(q.GetAngle() / 2)); // Cayley transform
if (lm[3] >= 0) Ui[lm[3]] = v.x;
if (lm[4] >= 0) Ui[lm[4]] = v.y;
if (lm[5] >= 0) Ui[lm[5]] = v.z;
}
}
}
//-----------------------------------------------------------------------------
//! Updates the rigid body data
void FERigidSolverNew::UpdateRigidBodies(vector<double>& Ui, vector<double>& ui)
{
// update rigid bodies
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
int nrb = fem.RigidBodies();
for (int i = 0; i<nrb; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
int *lm = RB.m_LM;
double* du = RB.m_du;
// first do the displacements
if (RB.m_prb == 0)
{
for (int j = 0; j<3; ++j)
{
FERigidPrescribedBC* pdc = RB.m_pDC[j];
if (pdc)
{
// TODO: do I need to take the line search step into account here?
du[j] = pdc->Value() - RB.m_Up[j];
}
else
{
du[j] = (lm[j] >= 0 ? Ui[lm[j]] + ui[lm[j]] : 0);
}
}
}
RB.m_rt.x = RB.m_rp.x + du[0];
RB.m_rt.y = RB.m_rp.y + du[1];
RB.m_rt.z = RB.m_rp.z + du[2];
// update RB center of mass translations
if (RB.m_prb) du = RB.m_dul;
RB.m_Ut[0] = RB.m_Up[0] + du[0];
RB.m_Ut[1] = RB.m_Up[1] + du[1];
RB.m_Ut[2] = RB.m_Up[2] + du[2];
// next, we do the rotations. We do this seperatly since
// they need to be interpreted differently than displacements
if (RB.m_prb == 0)
{
if (RB.m_bpofr) {
// if all rotation components are known (prescribed or fixed)
// evaluate net increment from load curve
double Ut[3] = { 0 };
for (int j = 3; j<6; ++j) {
if (RB.m_pDC[j]) {
Ut[j - 3] = RB.m_pDC[j]->Value();
}
}
quatd qUt(vec3d(Ut[0], Ut[1], Ut[2]));
RB.SetRotation(qUt);
RB.m_Ut[3] = Ut[0];
RB.m_Ut[4] = Ut[1];
RB.m_Ut[5] = Ut[2];
}
else
{
// rotation components are either free or fixed
vec3d vUi(0, 0, 0); // initialize total increment so far
vec3d vui(0, 0, 0); // initialize current increment
if (lm[3] >= 0) { vUi.x = Ui[lm[3]]; vui.x = ui[lm[3]]; }
if (lm[4] >= 0) { vUi.y = Ui[lm[4]]; vui.y = ui[lm[4]]; }
if (lm[5] >= 0) { vUi.z = Ui[lm[5]]; vui.z = ui[lm[5]]; }
quatd qUi(2 * atan(vUi.norm() / 2), vUi); // Cayley transform
quatd qui(2 * atan(vui.norm() / 2), vui); // Cayley transform
quatd qdu = qui*qUi; // quaternion of net increment
qdu.MakeUnit(); // clean-up roundoff errors
quatd Q = qdu*RB.m_qp;
Q.MakeUnit();
// update at the current time step
RB.SetRotation(Q);
// update RB rotations
vec3d vUt = Q.GetRotationVector();
RB.m_Ut[3] = vUt.x;
RB.m_Ut[4] = vUt.y;
RB.m_Ut[5] = vUt.z;
}
}
}
// Newmark rule
FETimeInfo& timeInfo = GetFEModel()->GetTime();
double alpham = timeInfo.alpham;
double beta = timeInfo.beta;
double gamma = timeInfo.gamma;
double dt = timeInfo.timeIncrement;
double a = 1.0 / (beta*dt);
double b = a / dt;
double c = 1.0 - 0.5 / beta;
for (int i = 0; i<nrb; ++i)
{
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(i);
// acceleration and velocity of center of mass
RB.m_at = (RB.m_rt - RB.m_rp)*b - RB.m_vp*a + RB.m_ap*c;
RB.m_vt = RB.m_vp + (RB.m_ap*(1.0 - gamma) + RB.m_at*gamma)*dt;
// angular acceleration and velocity of rigid body
quatd q = RB.GetRotation()*RB.m_qp.Inverse();
q.MakeUnit();
vec3d vq = q.GetVector()*(2 * tan(q.GetAngle() / 2)); // Cayley transform
RB.m_wt = vq*(a*gamma) - RB.m_wp + (RB.m_wp + RB.m_alp*dt / 2.)*(2 - gamma / beta);
q.RotateVector(RB.m_wt);
RB.m_alt = vq*b - RB.m_wp*a + RB.m_alp*c;
q.RotateVector(RB.m_alt);
// evaluate mass moment of inertia at t
mat3d Rt = RB.GetRotation().RotationMatrix();
mat3ds Jt = (Rt*RB.m_moi*Rt.transpose()).sym();
// evaluate angular momentum and its rate of change at current time
RB.m_ht = Jt*RB.m_wt;
RB.m_dht = (RB.m_ht - RB.m_hp)/(gamma*dt) + RB.m_dhp*(1-1./gamma);
}
// update the mesh' nodes
fem.UpdateRigidMesh();
// Since the rigid nodes are repositioned we need to update the displacement DOFS
FEMesh& mesh = m_fem->GetMesh();
int N = mesh.Nodes();
for (int i = 0; i<N; ++i)
{
FENode& node = mesh.Node(i);
if (node.m_rid >= 0)
{
vec3d ut = node.m_rt - node.m_r0;
node.set_vec3d(m_dofX, m_dofY, m_dofZ, ut);
if (node.HasFlags(FENode::SHELL) && node.HasFlags(FENode::RIGID_CLAMP)) {
// get the rigid body
FERigidBody& RB = *fem.GetRigidBody(node.m_rid);
// evaluate the director in the current configuration
vec3d d = RB.GetRotation()*node.m_d0 - node.m_d0;
// evaluate the back face displacement increments
node.set_vec3d(m_dofSX, m_dofSY, m_dofSZ, ut - d);
}
}
}
}
//-----------------------------------------------------------------------------
//! evaluate inertia forces
void FERigidSolverNew::InertialForces(FEGlobalVector& R, const FETimeInfo& timeInfo)
{
// Newmark rule
double alpham = timeInfo.alpham;
if (m_fem == nullptr) return;
FEMechModel& fem = *m_fem;
int nrb = fem.RigidBodies();
// calculate rigid body inertial forces
for (int i = 0; i<nrb; ++i)
{
FERigidBody& RB = *fem.GetRigidBody(i);
// 6 dofs per rigid body
vector<double> fe(6);
vector<int> LM(6);
// rate of change of linear momentum = mass*acceleration
vec3d F = (RB.m_at*alpham + RB.m_ap*(1-alpham))*RB.m_mass;
fe[0] = -F.x;
fe[1] = -F.y;
fe[2] = -F.z;
// evaluate mass moment of inertia at t and tp
mat3d Rt = RB.GetRotation().RotationMatrix();
mat3ds Jt = (Rt*RB.m_moi*Rt.transpose()).sym();
RB.m_ht = Jt*RB.m_wt;
// evaluate rate of change of angular momentum
RB.m_dht = (RB.m_wt ^ RB.m_ht) + Jt*RB.m_alt;
vec3d M = (RB.m_dht*alpham + RB.m_dhp*(1-alpham));
fe[3] = -M.x;
fe[4] = -M.y;
fe[5] = -M.z;
// pack the equation numbers
LM[0] = RB.m_LM[0];
LM[1] = RB.m_LM[1];
LM[2] = RB.m_LM[2];
LM[3] = RB.m_LM[3];
LM[4] = RB.m_LM[4];
LM[5] = RB.m_LM[5];
R.Assemble(LM, fe);
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEDamageNeoHookean.h | .h | 2,637 | 76 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEElasticMaterial.h"
#include "FEDamageMaterialPoint.h"
//-----------------------------------------------------------------------------
// This material is a first attempt to include damage in hyper-elastic materials.
// It assumes the simple damage model as defined in Simo, CMAME 60 (1987), 153-173
//-----------------------------------------------------------------------------
class FEDamageNeoHookean : public FEElasticMaterial
{
public:
FEDamageNeoHookean(FEModel* pfem);
public:
double m_E; //!< Young's modulus
double m_v; //!< Poisson's ratio
double m_alpha; //!< damage parameter alpha
double m_beta; //!< damage parameter beta
protected:
double m_lam;
double m_mu;
public:
//! calculate stress at material point
virtual mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
virtual tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
virtual double StrainEnergyDensity(FEMaterialPoint& pt) override;
//! data initialization and checking
bool Init() override;
// returns a pointer to a new material point object
FEMaterialPointData* CreateMaterialPointData() override;
// calculate damage reduction factor
double Damage(FEMaterialPoint& pt);
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEElasticMaterialPoint.cpp | .cpp | 14,926 | 421 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEElasticMaterialPoint.h"
//-----------------------------------------------------------------------------
FEElasticMaterialPoint::FEElasticMaterialPoint(FEMaterialPointData* mp) : FEMaterialPointData(mp)
{
m_F.unit();
m_J = 1;
m_s.zero();
m_v = m_a = vec3d(0, 0, 0);
m_buncoupled = false;
m_Wt = m_Wp = 0;
m_p = 0;
}
//-----------------------------------------------------------------------------
FEMaterialPointData* FEElasticMaterialPoint::Copy()
{
FEElasticMaterialPoint* pt = new FEElasticMaterialPoint(*this);
if (m_pNext) pt->m_pNext = m_pNext->Copy();
return pt;
}
//-----------------------------------------------------------------------------
void FEElasticMaterialPoint::Init()
{
m_F.unit();
m_J = 1;
m_s.zero();
m_v = m_a = vec3d(0, 0, 0);
m_L.zero();
m_Wt = m_Wp = 0;
m_p = 0;
// don't forget to initialize the base class
FEMaterialPointData::Init();
}
//-----------------------------------------------------------------------------
void FEElasticMaterialPoint::Serialize(DumpStream& ar)
{
FEMaterialPointData::Serialize(ar);
ar & m_F & m_J & m_s & m_v & m_a & m_L & m_Wt & m_Wp & m_p;
ar & m_buncoupled;
}
//-----------------------------------------------------------------------------
//! Calculates the right Cauchy-Green tensor at the current material point
mat3ds FEElasticMaterialPoint::RightCauchyGreen() const
{
// get the right Cauchy-Green tensor
// C = Ft*F
const mat3d& F = m_F;
mat3ds C;
C.xx() = F[0][0]*F[0][0]+F[1][0]*F[1][0]+F[2][0]*F[2][0]; // = C[0][0]
C.yy() = F[0][1]*F[0][1]+F[1][1]*F[1][1]+F[2][1]*F[2][1]; // = C[1][1]
C.zz() = F[0][2]*F[0][2]+F[1][2]*F[1][2]+F[2][2]*F[2][2]; // = C[2][2]
C.xy() = F[0][0]*F[0][1]+F[1][0]*F[1][1]+F[2][0]*F[2][1]; // = C[0][1]
C.yz() = F[0][1]*F[0][2]+F[1][1]*F[1][2]+F[2][1]*F[2][2]; // = C[1][2]
C.xz() = F[0][0]*F[0][2]+F[1][0]*F[1][2]+F[2][0]*F[2][2]; // = C[0][2]
return C;
}
//-----------------------------------------------------------------------------
//! Calculates the left Cauchy-Green tensor at the current material point
mat3ds FEElasticMaterialPoint::LeftCauchyGreen() const
{
// get the left Cauchy-Green tensor
// b = F*Ft
const mat3d& F = m_F;
mat3ds b;
b.xx() = F[0][0]*F[0][0]+F[0][1]*F[0][1]+F[0][2]*F[0][2]; // = b[0][0]
b.yy() = F[1][0]*F[1][0]+F[1][1]*F[1][1]+F[1][2]*F[1][2]; // = b[1][1]
b.zz() = F[2][0]*F[2][0]+F[2][1]*F[2][1]+F[2][2]*F[2][2]; // = b[2][2]
b.xy() = F[0][0]*F[1][0]+F[0][1]*F[1][1]+F[0][2]*F[1][2]; // = b[0][1]
b.yz() = F[1][0]*F[2][0]+F[1][1]*F[2][1]+F[1][2]*F[2][2]; // = b[1][2]
b.xz() = F[0][0]*F[2][0]+F[0][1]*F[2][1]+F[0][2]*F[2][2]; // = b[0][2]
return b;
}
//-----------------------------------------------------------------------------
//! Calculates the right Cauchy-Green tensor at the current material point
mat3ds FEElasticMaterialPoint::DevRightCauchyGreen() const
{
double Jm23 = pow(m_J, -2.0/3.0);
// get the deviatoric right Cauchy-Green tensor
// C = Ft*F
const mat3d& F = m_F;
mat3ds C;
C.xx() = Jm23*(F[0][0]*F[0][0]+F[1][0]*F[1][0]+F[2][0]*F[2][0]); // = C[0][0]
C.yy() = Jm23*(F[0][1]*F[0][1]+F[1][1]*F[1][1]+F[2][1]*F[2][1]); // = C[1][1]
C.zz() = Jm23*(F[0][2]*F[0][2]+F[1][2]*F[1][2]+F[2][2]*F[2][2]); // = C[2][2]
C.xy() = Jm23*(F[0][0]*F[0][1]+F[1][0]*F[1][1]+F[2][0]*F[2][1]); // = C[0][1]
C.yz() = Jm23*(F[0][1]*F[0][2]+F[1][1]*F[1][2]+F[2][1]*F[2][2]); // = C[1][2]
C.xz() = Jm23*(F[0][0]*F[0][2]+F[1][0]*F[1][2]+F[2][0]*F[2][2]); // = C[0][2]
return C;
}
//-----------------------------------------------------------------------------
//! Calculates the left Cauchy-Green tensor at the current material point
mat3ds FEElasticMaterialPoint::DevLeftCauchyGreen() const
{
double Jm23 = pow(m_J, -2.0/3.0);
// get the left Cauchy-Green tensor
// b = F*Ft
const mat3d& F = m_F;
mat3ds b;
b.xx() = Jm23*(F[0][0]*F[0][0]+F[0][1]*F[0][1]+F[0][2]*F[0][2]); // = b[0][0]
b.yy() = Jm23*(F[1][0]*F[1][0]+F[1][1]*F[1][1]+F[1][2]*F[1][2]); // = b[1][1]
b.zz() = Jm23*(F[2][0]*F[2][0]+F[2][1]*F[2][1]+F[2][2]*F[2][2]); // = b[2][2]
b.xy() = Jm23*(F[0][0]*F[1][0]+F[0][1]*F[1][1]+F[0][2]*F[1][2]); // = b[0][1]
b.yz() = Jm23*(F[1][0]*F[2][0]+F[1][1]*F[2][1]+F[1][2]*F[2][2]); // = b[1][2]
b.xz() = Jm23*(F[0][0]*F[2][0]+F[0][1]*F[2][1]+F[0][2]*F[2][2]); // = b[0][2]
return b;
}
//-----------------------------------------------------------------------------
//! Calculates the right stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::RightStretch() const
{
// get the right stretch tensor
mat3ds C = RightCauchyGreen();
double l2[3];
vec3d v[3];
C.eigen2(l2, v);
mat3ds U = dyad(v[0])*sqrt(l2[0]) + dyad(v[1])*sqrt(l2[1]) + dyad(v[2])*sqrt(l2[2]);
return U;
}
//-----------------------------------------------------------------------------
//! Calculates the left stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::LeftStretch() const
{
// get the left stretch tensor
mat3ds B = LeftCauchyGreen();
double l2[3];
vec3d v[3];
B.eigen2(l2, v);
mat3ds V = dyad(v[0])*sqrt(l2[0]) + dyad(v[1])*sqrt(l2[1]) + dyad(v[2])*sqrt(l2[2]);
return V;
}
//-----------------------------------------------------------------------------
//! Calculates the right stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::RightStretchInverse() const
{
// get the right stretch tensor
mat3ds C = RightCauchyGreen();
double l2[3];
vec3d v[3];
C.eigen2(l2, v);
mat3ds U = dyad(v[0])/sqrt(l2[0]) + dyad(v[1])/sqrt(l2[1]) + dyad(v[2])/sqrt(l2[2]);
return U;
}
//-----------------------------------------------------------------------------
//! Calculates the left stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::LeftStretchInverse() const
{
// get the left stretch tensor
mat3ds B = LeftCauchyGreen();
double l2[3];
vec3d v[3];
B.eigen2(l2, v);
mat3ds V = dyad(v[0])/sqrt(l2[0]) + dyad(v[1])/sqrt(l2[1]) + dyad(v[2])/sqrt(l2[2]);
return V;
}
//-----------------------------------------------------------------------------
//! Calculates the right stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::RightHencky() const
{
// get the right stretch tensor
mat3ds C = RightCauchyGreen();
double l2[3];
vec3d v[3];
C.eigen2(l2, v);
mat3ds H = dyad(v[0])*log(l2[0])/2 + dyad(v[1])*log(l2[1])/2 + dyad(v[2])*log(l2[2])/2;
return H;
}
//-----------------------------------------------------------------------------
//! Calculates the left stretch tensor at the current material point
mat3ds FEElasticMaterialPoint::LeftHencky() const
{
// get the left stretch tensor
mat3ds B = LeftCauchyGreen();
double l2[3];
vec3d v[3];
B.eigen2(l2, v);
mat3ds h = dyad(v[0])*log(l2[0])/2 + dyad(v[1])*log(l2[1])/2 + dyad(v[2])*log(l2[2])/2;
return h;
}
//-----------------------------------------------------------------------------
//! Calculates the rotation tensor at the current material point
mat3d FEElasticMaterialPoint::Rotation() const
{
return m_F*RightStretchInverse();
}
//-----------------------------------------------------------------------------
//! Calculates the Lagrangian strain at the current material point
mat3ds FEElasticMaterialPoint::Strain() const
{
// get the right Cauchy-Green tensor
// C = Ft*F
const mat3d& F = m_F;
mat3ds C;
C.xx() = F[0][0]*F[0][0]+F[1][0]*F[1][0]+F[2][0]*F[2][0]; // = C[0][0]
C.yy() = F[0][1]*F[0][1]+F[1][1]*F[1][1]+F[2][1]*F[2][1]; // = C[1][1]
C.zz() = F[0][2]*F[0][2]+F[1][2]*F[1][2]+F[2][2]*F[2][2]; // = C[2][2]
C.xy() = F[0][0]*F[0][1]+F[1][0]*F[1][1]+F[2][0]*F[2][1]; // = C[0][1]
C.yz() = F[0][1]*F[0][2]+F[1][1]*F[1][2]+F[2][1]*F[2][2]; // = C[1][2]
C.xz() = F[0][0]*F[0][2]+F[1][0]*F[1][2]+F[2][0]*F[2][2]; // = C[0][2]
// calculate the Lagrangian strain
// E = 1/2*(C - 1)
mat3ds E = (C - mat3dd(1))*0.5;
return E;
}
//-----------------------------------------------------------------------------
//! Calculates the small-strain tensor from the deformation gradient
mat3ds FEElasticMaterialPoint::SmallStrain() const
{
// caculate small strain tensor
const mat3d& F = m_F;
return mat3ds(F[0][0] - 1.0, F[1][1] - 1.0, F[2][2] - 1.0, 0.5*(F[0][1] + F[1][0]), 0.5*(F[0][2] + F[2][0]), 0.5*(F[1][2] + F[2][1]));
}
//-----------------------------------------------------------------------------
//! Calculates the Almansi strain tensor
mat3ds FEElasticMaterialPoint::AlmansiStrain() const
{
// caculate small strain tensor
mat3ds B = LeftCauchyGreen();
return (mat3dd(1)-B.inverse())/2.;
}
//-----------------------------------------------------------------------------
//! Calculates the 2nd PK stress from the Cauchy stress stored in the point
mat3ds FEElasticMaterialPoint::pull_back(const mat3ds& A) const
{
const mat3d& F = m_F;
double J = m_J;
mat3d Fi = F.inverse();
mat3d P = Fi*A;
return mat3ds(J*(P[0][0]*Fi[0][0]+P[0][1]*Fi[0][1]+P[0][2]*Fi[0][2]),
J*(P[1][0]*Fi[1][0]+P[1][1]*Fi[1][1]+P[1][2]*Fi[1][2]),
J*(P[2][0]*Fi[2][0]+P[2][1]*Fi[2][1]+P[2][2]*Fi[2][2]),
J*(P[0][0]*Fi[1][0]+P[0][1]*Fi[1][1]+P[0][2]*Fi[1][2]),
J*(P[1][0]*Fi[2][0]+P[1][1]*Fi[2][1]+P[1][2]*Fi[2][2]),
J*(P[0][0]*Fi[2][0]+P[0][1]*Fi[2][1]+P[0][2]*Fi[2][2]));
}
//-----------------------------------------------------------------------------
mat3ds FEElasticMaterialPoint::push_forward(const mat3ds& A) const
{
const mat3d& F = m_F;
mat3d P = F*A;
double Ji = 1 / m_J;
return mat3ds(Ji*(P[0][0]*F[0][0]+P[0][1]*F[0][1]+P[0][2]*F[0][2]),
Ji*(P[1][0]*F[1][0]+P[1][1]*F[1][1]+P[1][2]*F[1][2]),
Ji*(P[2][0]*F[2][0]+P[2][1]*F[2][1]+P[2][2]*F[2][2]),
Ji*(P[0][0]*F[1][0]+P[0][1]*F[1][1]+P[0][2]*F[1][2]),
Ji*(P[1][0]*F[2][0]+P[1][1]*F[2][1]+P[1][2]*F[2][2]),
Ji*(P[0][0]*F[2][0]+P[0][1]*F[2][1]+P[0][2]*F[2][2]));
}
//-----------------------------------------------------------------------------
// This function converts the spatial tangent to the material tangent
tens4ds FEElasticMaterialPoint::pull_back(const tens4ds& c) const
{
const mat3d& F = m_F;
mat3d Fi = F.inverse();
double J = F.det();
double C[6][6] = {0};
for (int i=0; i<3; ++i)
for (int j=0; j<3; ++j)
for (int k=0; k<3; ++k)
for (int l=0; l<3; ++l)
{
C[0][0] += J*Fi[0][i]*Fi[0][j]*Fi[0][k]*Fi[0][l]*c(i,j,k,l);
C[0][1] += J*Fi[0][i]*Fi[0][j]*Fi[1][k]*Fi[1][l]*c(i,j,k,l);
C[0][2] += J*Fi[0][i]*Fi[0][j]*Fi[2][k]*Fi[2][l]*c(i,j,k,l);
C[0][3] += J*Fi[0][i]*Fi[0][j]*Fi[0][k]*Fi[1][l]*c(i,j,k,l);
C[0][4] += J*Fi[0][i]*Fi[0][j]*Fi[1][k]*Fi[2][l]*c(i,j,k,l);
C[0][5] += J*Fi[0][i]*Fi[0][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
C[1][1] += J*Fi[1][i]*Fi[1][j]*Fi[1][k]*Fi[1][l]*c(i,j,k,l);
C[1][2] += J*Fi[1][i]*Fi[1][j]*Fi[2][k]*Fi[2][l]*c(i,j,k,l);
C[1][3] += J*Fi[1][i]*Fi[1][j]*Fi[0][k]*Fi[1][l]*c(i,j,k,l);
C[1][4] += J*Fi[1][i]*Fi[1][j]*Fi[1][k]*Fi[2][l]*c(i,j,k,l);
C[1][5] += J*Fi[1][i]*Fi[1][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
C[2][2] += J*Fi[2][i]*Fi[2][j]*Fi[2][k]*Fi[2][l]*c(i,j,k,l);
C[2][3] += J*Fi[2][i]*Fi[2][j]*Fi[0][k]*Fi[1][l]*c(i,j,k,l);
C[2][4] += J*Fi[2][i]*Fi[2][j]*Fi[1][k]*Fi[2][l]*c(i,j,k,l);
C[2][5] += J*Fi[2][i]*Fi[2][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
C[3][3] += J*Fi[0][i]*Fi[1][j]*Fi[0][k]*Fi[1][l]*c(i,j,k,l);
C[3][4] += J*Fi[0][i]*Fi[1][j]*Fi[1][k]*Fi[2][l]*c(i,j,k,l);
C[3][5] += J*Fi[0][i]*Fi[1][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
C[4][4] += J*Fi[1][i]*Fi[2][j]*Fi[1][k]*Fi[2][l]*c(i,j,k,l);
C[4][5] += J*Fi[1][i]*Fi[2][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
C[5][5] += J*Fi[0][i]*Fi[2][j]*Fi[0][k]*Fi[2][l]*c(i,j,k,l);
}
return tens4ds(C);
}
//-----------------------------------------------------------------------------
// This function converts the material tangent to the spatial tangent
tens4ds FEElasticMaterialPoint::push_forward(const tens4ds& C) const
{
const mat3d& F = m_F;
double Ji = 1/F.det();
double c[6][6] = {0};
for (int i=0; i<3; ++i)
for (int j=0; j<3; ++j)
for (int k=0; k<3; ++k)
for (int l=0; l<3; ++l)
{
c[0][0] += Ji*F[0][i]*F[0][j]*F[0][k]*F[0][l]*C(i,j,k,l);
c[0][1] += Ji*F[0][i]*F[0][j]*F[1][k]*F[1][l]*C(i,j,k,l);
c[0][2] += Ji*F[0][i]*F[0][j]*F[2][k]*F[2][l]*C(i,j,k,l);
c[0][3] += Ji*F[0][i]*F[0][j]*F[0][k]*F[1][l]*C(i,j,k,l);
c[0][4] += Ji*F[0][i]*F[0][j]*F[1][k]*F[2][l]*C(i,j,k,l);
c[0][5] += Ji*F[0][i]*F[0][j]*F[0][k]*F[2][l]*C(i,j,k,l);
c[1][1] += Ji*F[1][i]*F[1][j]*F[1][k]*F[1][l]*C(i,j,k,l);
c[1][2] += Ji*F[1][i]*F[1][j]*F[2][k]*F[2][l]*C(i,j,k,l);
c[1][3] += Ji*F[1][i]*F[1][j]*F[0][k]*F[1][l]*C(i,j,k,l);
c[1][4] += Ji*F[1][i]*F[1][j]*F[1][k]*F[2][l]*C(i,j,k,l);
c[1][5] += Ji*F[1][i]*F[1][j]*F[0][k]*F[2][l]*C(i,j,k,l);
c[2][2] += Ji*F[2][i]*F[2][j]*F[2][k]*F[2][l]*C(i,j,k,l);
c[2][3] += Ji*F[2][i]*F[2][j]*F[0][k]*F[1][l]*C(i,j,k,l);
c[2][4] += Ji*F[2][i]*F[2][j]*F[1][k]*F[2][l]*C(i,j,k,l);
c[2][5] += Ji*F[2][i]*F[2][j]*F[0][k]*F[2][l]*C(i,j,k,l);
c[3][3] += Ji*F[0][i]*F[1][j]*F[0][k]*F[1][l]*C(i,j,k,l);
c[3][4] += Ji*F[0][i]*F[1][j]*F[1][k]*F[2][l]*C(i,j,k,l);
c[3][5] += Ji*F[0][i]*F[1][j]*F[0][k]*F[2][l]*C(i,j,k,l);
c[4][4] += Ji*F[1][i]*F[2][j]*F[1][k]*F[2][l]*C(i,j,k,l);
c[4][5] += Ji*F[1][i]*F[2][j]*F[0][k]*F[2][l]*C(i,j,k,l);
c[5][5] += Ji*F[0][i]*F[2][j]*F[0][k]*F[2][l]*C(i,j,k,l);
}
return tens4ds(c);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FECubicCLE.cpp | .cpp | 7,726 | 241 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FECubicCLE.h"
#include <FECore/log.h>
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FECubicCLE, FEElasticMaterial)
ADD_PARAMETER(m_lp1, "lp1")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_lm1, "lm1")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_l2 , "l2")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_mu , FE_RANGE_GREATER_OR_EQUAL(0.0), "mu")->setUnits(UNIT_PRESSURE);
ADD_PROPERTY(m_Q, "mat_axis")->SetFlags(FEProperty::Optional);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Check material parameters.
bool FECubicCLE::Validate()
{
if (FEElasticMaterial::Validate() == false) return false;
// Evaluate Lame coefficients
double lam[3][3];
double mu[3];
mu[0] = m_mu;
mu[1] = m_mu;
mu[2] = m_mu;
lam[0][0] = m_lm1; lam[0][1] = m_l2 ; lam[0][2] = m_l2;
lam[1][0] = m_l2 ; lam[1][1] = m_lm1; lam[1][2] = m_l2;
lam[2][0] = m_l2 ; lam[2][1] = m_l2 ; lam[2][2] = m_lm1;
// check that stiffness matrix is positive definite
mat3ds c(lam[0][0]+2*mu[0],lam[1][1]+2*mu[1],lam[2][2]+2*mu[2],lam[0][1],lam[1][2],lam[0][2]);
double l[3];
c.exact_eigen(l);
if ((l[0] < 0) || (l[1] < 0) || (l[2] < 0))
{
feLogError("Stiffness matrix is not positive definite.");
return false;
}
// repeat check with all tensile diagonal first lamé constants
lam[0][0] = m_lp1; lam[1][1] = m_lp1; lam[2][2] = m_lp1;
// check that compliance matrix is positive definite
c = mat3ds(lam[0][0]+2*mu[0],lam[1][1]+2*mu[1],lam[2][2]+2*mu[2],lam[0][1],lam[1][2],lam[0][2]);
c.exact_eigen(l);
if ((l[0] < 0) || (l[1] < 0) || (l[2] < 0))
{
feLogError("Stiffness matrix is not positive definite.");
return false;
}
return true;
}
//-----------------------------------------------------------------------------
//! Calculates the stress
mat3ds FECubicCLE::Stress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// Evaluate Lame coefficients
double lam[3][3];
double mu[3];
mu[0] = m_mu;
mu[1] = m_mu;
mu[2] = m_mu;
lam[0][0] = m_lm1; lam[0][1] = m_l2 ; lam[0][2] = m_l2;
lam[1][0] = m_l2 ; lam[1][1] = m_lm1; lam[1][2] = m_l2;
lam[2][0] = m_l2 ; lam[2][1] = m_l2 ; lam[2][2] = m_lm1;
int i,j;
vec3d a0; // texture direction in reference configuration
mat3ds A0[3]; // texture tensor in reference configuration
double AE[3]; // E:A
mat3ds E = pt.Strain();
mat3d F = pt.m_F;
double J = pt.m_J;
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
for (i=0; i<3; i++) { // Perform sum over all three texture directions
// Copy the texture direction in the reference configuration to a0
a0.x = Q[0][i]; a0.y = Q[1][i]; a0.z = Q[2][i];
A0[i] = dyad(a0);
AE[i] = a0*(E*a0);
}
lam[0][0] = (AE[0] >= 0) ? m_lp1 : m_lm1;
lam[1][1] = (AE[1] >= 0) ? m_lp1 : m_lm1;
lam[2][2] = (AE[2] >= 0) ? m_lp1 : m_lm1;
mat3ds s; s.zero();
for (i=0; i<3; ++i) {
s += (A0[i]*E).sym()*(mu[i]);
for (j=0; j<3; ++j) {
s += A0[j]*(lam[i][j]*AE[i]);
}
}
s = (F*s*F.transpose()).sym()/J;
return s;
}
//-----------------------------------------------------------------------------
//! Calculates the elasticity tensor
tens4ds FECubicCLE::Tangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// Evaluate Lame coefficients
double lam[3][3];
double mu[3];
mu[0] = m_mu;
mu[1] = m_mu;
mu[2] = m_mu;
lam[0][0] = m_lm1; lam[0][1] = m_l2 ; lam[0][2] = m_l2;
lam[1][0] = m_l2 ; lam[1][1] = m_lm1; lam[1][2] = m_l2;
lam[2][0] = m_l2 ; lam[2][1] = m_l2 ; lam[2][2] = m_lm1;
int i,j;
vec3d a0; // texture direction in reference configuration
mat3ds A[3]; // texture tensor in current configuration
double AE[3]; // E:A
mat3ds E = pt.Strain();
mat3d F = pt.m_F;
double J = pt.m_J;
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
for (i=0; i<3; i++) { // Perform sum over all three texture directions
// Copy the texture direction in the reference configuration to a0
a0.x = Q[0][i]; a0.y = Q[1][i]; a0.z = Q[2][i];
A[i] = dyad(F*a0);
AE[i] = a0*(E*a0);
}
lam[0][0] = (AE[0] >= 0) ? m_lp1 : m_lm1;
lam[1][1] = (AE[1] >= 0) ? m_lp1 : m_lm1;
lam[2][2] = (AE[2] >= 0) ? m_lp1 : m_lm1;
tens4ds c;
c.zero();
mat3ds B = pt.LeftCauchyGreen();
for (i=0; i<3; ++i) {
c += dyad4s(A[i], B)*mu[i];
for (j=0; j<3; ++j) {
c += dyad1s(A[i],A[j])*lam[i][j]/2;
}
}
c /= J;
return c;
}
//-----------------------------------------------------------------------------
//! Calculates the strain energy density
double FECubicCLE::StrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// Evaluate Lame coefficients
double lam[3][3];
double mu[3];
mu[0] = m_mu;
mu[1] = m_mu;
mu[2] = m_mu;
lam[0][0] = m_lm1; lam[0][1] = m_l2 ; lam[0][2] = m_l2;
lam[1][0] = m_l2 ; lam[1][1] = m_lm1; lam[1][2] = m_l2;
lam[2][0] = m_l2 ; lam[2][1] = m_l2 ; lam[2][2] = m_lm1;
int i,j;
vec3d a0; // texture direction in reference configuration
mat3ds A0; // texture tensor in reference configuration
double AE[3], AE2[3]; // Ka
mat3ds E = pt.Strain();
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
for (i=0; i<3; i++) { // Perform sum over all three texture directions
// Copy the texture direction in the reference configuration to a0
a0.x = Q[0][i]; a0.y = Q[1][i]; a0.z = Q[2][i];
A0 = dyad(a0);
AE[i] = a0*(E*a0);
AE2[i] = a0*(E*E*a0);
}
lam[0][0] = (AE[0] >= 0) ? m_lp1 : m_lm1;
lam[1][1] = (AE[1] >= 0) ? m_lp1 : m_lm1;
lam[2][2] = (AE[2] >= 0) ? m_lp1 : m_lm1;
double W = 0;
for (i=0; i<3; ++i) {
W += AE2[i]*mu[i];
for (j=0; j<3; ++j) {
W += AE[i]*AE[j]*lam[i][j]/2;
}
}
return W;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FETransIsoMREstrada.h | .h | 2,831 | 77 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2022 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEUncoupledMaterial.h"
#include "FEUncoupledFiberExpLinear.h"
#include "FEActiveContractionMaterial.h"
#include <FECore/FEModelParam.h>
//-----------------------------------------------------------------------------
//! Transversely Isotropic Mooney-Rivlin-Estrada material based on doi: 10.1115/1.4044030
//! This material has an isotopric Mooney-Rivlin basis and single preferred
//! fiber direction.
class FETransIsoMREstrada: public FEUncoupledMaterial
{
public:
enum { MAX_TERMS = 3 };
public:
FETransIsoMREstrada(FEModel* pfem);
public:
FEParamDouble c1; //!< Mooney-Rivlin coefficient C1
FEParamDouble c2; //!< Mooney-Rivlin coefficient C2
public:
//! calculate deviatoric stress at material point
mat3ds DevStress(FEMaterialPoint& pt) override;
//! calculate deviatoric tangent stiffness at material point
tens4ds DevTangent(FEMaterialPoint& pt) override;
//! calculate deviatoric strain energy density at material point
double DevStrainEnergyDensity(FEMaterialPoint& pt) override;
//! create material point data
FEMaterialPointData* CreateMaterialPointData() override;
// update force-velocity material point
void UpdateSpecializedMaterialPoints(FEMaterialPoint& mp, const FETimeInfo& tp) override;
protected:
FEFiberExpLinearUC m_fib;
FEActiveContractionMaterial* m_ac;
FEVec3dValuator* m_fiber;
// declare parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FENewtonianViscousSolidUC.h | .h | 2,103 | 57 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEUncoupledMaterial.h"
class FENewtonianViscousSolidUC : public FEUncoupledMaterial
{
public:
FENewtonianViscousSolidUC(FEModel* pfem);
public:
double m_kappa; //!< bulk viscosity
double m_mu; //!< shear viscosity
bool m_secant_tangent; //!< flag for using secant tangent calculation
public:
//! calculate stress at material point
mat3ds DevStress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
tens4ds DevTangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
double DevStrainEnergyDensity(FEMaterialPoint& pt) override;
bool UseSecantTangent() override { return m_secant_tangent; }
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FESurfaceAttractionBodyForce.h | .h | 2,181 | 64 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEBodyForce.h"
#include <FECore/FESurface.h>
//-----------------------------------------------------------------------------
//! This class defines a surface attraction body force
class FESurfaceAttractionBodyForce : public FEBodyForce
{
public:
FESurfaceAttractionBodyForce(FEModel* pfem);
vec3d force(FEMaterialPoint& mp) override;
double divforce(FEMaterialPoint& mp) override;
mat3d stiffness(FEMaterialPoint& mp) override;
// initialize
bool Init() override;
private:
vector< vector<vec3d> > m_q; //!< projection points
public:
FESurface* m_s; //!< the attractive surface
public:
double m_blt; //!< boundary layer thickness
double m_bsf; //!< body force scale factor
double m_stol; //!< search tolerance
double m_sradius; //!< search radius
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FERigidBody.h | .h | 5,222 | 153 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/fecore_enum.h>
#include <FECore/vec3d.h>
#include <FECore/quatd.h>
#include <FECore/FECoreBase.h>
#include "febiomech_api.h"
//-----------------------------------------------------------------------------
class FEModel;
class FERigidPrescribedBC;
//-----------------------------------------------------------------------------
//! rigid body class
//! \todo perhaps the rigid body should store a list of domains it uses.
//! That way, we can have multiple domains per RB using multiple
//! materials.
class FEBIOMECH_API FERigidBody : public FECoreBase
{
FECORE_SUPER_CLASS(FEOBJECT_ID)
FECORE_BASE_CLASS(FERigidBody)
public:
// Constructor
FERigidBody(FEModel* pfem);
//! desctructor
virtual ~FERigidBody();
//! Set the center of mass directly
void SetCOM(vec3d rc);
//! Update the mass of the rigid body
void UpdateMass();
//! Update total mass and center of mass
void UpdateCOM();
//! Update the moment of intertia
void UpdateMOI();
//! reset rigid body data
void Reset();
//! initialize data
bool Init() override;
//! serialize data to archive
void Serialize(DumpStream& ar) override;
//! get the material ID
int GetMaterialID() { return m_mat; }
//! incremental compound rotation from Cayley transform
vec3d CayleyIncrementalCompoundRotation();
public:
const quatd& GetRotation() const { return m_qt; }
quatd GetPreviousRotation() const { return m_qp; }
void SetRotation(const quatd& q)
{
m_qt = q;
m_qt.GetEuler(m_euler.x, m_euler.y, m_euler.z);
}
public:
int m_nID; //!< ID of rigid body
int m_mat; //!< material ID (TODO: Since rigid bodies can have multiple materials, I want to remove this)
double m_mass; //!< total mass of rigid body
mat3ds m_moi; //!< mass moment of inertia about center of mass
vec3d m_Fr, m_Mr; //!< reaction force and torque
vec3d m_Fp, m_Mp; //!< reaction force and torque at the end of the previous step
vec3d m_r0; //!< initial position of rigid body
vec3d m_rp; //!< previous position of rigid body
vec3d m_rt; //!< current position of rigid body
vec3d m_vp; //!< previous velocity of rigid body
vec3d m_vt; //!< current velocity of rigid body
vec3d m_ap; //!< previous acceleration of rigid body
vec3d m_at; //!< current acceleration of rigid body
quatd m_qp; //!< previous orientation of rigid body
private:
// TODO: This is a hack!I only need this so I can access the euler angles directly from
// the optimization module. Need to figure out a better way.
quatd m_qt; //!< current orientation of rigid body
vec3d m_euler; //!< Euler angles of rotation
public:
vec3d m_wp; //!< previous angular velocity of rigid body
vec3d m_wt; //!< current angular velocity of rigid body
vec3d m_alp; //!< previous angular acceleration of rigid body
vec3d m_alt; //!< current angular acceleration of rigid body
vec3d m_hp; //!< previous angular momentum
vec3d m_ht; //!< current angular momentum
vec3d m_dhp; //!< previous time rate of change of angular momentum
vec3d m_dht; //!< current time rate of change of angular momentum
int m_BC[6]; //!< DOF types
int m_LM[6]; //!< dof equation numbers
double m_Up[6]; //!< previous displacement/rotation vector
double m_Ut[6]; //!< total displacement/rotation vector
double m_du[6]; //!< incremental displacement vector
double m_dul[6]; //!< displacement in local coordinates system
bool m_bpofr; //!< flag for all or none of rotation dofs prescribed/fixed
public:
FERigidPrescribedBC* m_pDC[6]; //!< active displacement constraints
FERigidBody* m_prb; //!< parent rigid body
public:
// return the helical axis relative to the ground
void InstantaneousHelicalAxis(vec3d& omega, vec3d& s, double& tdot);
void FiniteHelicalAxis(vec3d& omega, vec3d& s, double& tdot);
public:
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEPressureRobinBC.cpp | .cpp | 5,587 | 168 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEPressureRobinBC.h"
#include "FEBioMech.h"
#include <FECore/FEFacetSet.h>
#include <FECore/FEModel.h>
//-----------------------------------------------------------------------------
// Parameter block for pressure loads
BEGIN_FECORE_CLASS(FEPressureRobinBC, FESurfaceLoad)
ADD_PARAMETER(m_epsk , "spring_eps")->setUnits("P/L");
ADD_PARAMETER(m_epsc , "dashpot_eps")->setUnits("P.t/L");
ADD_PARAMETER(m_bshellb , "shell_bottom");
END_FECORE_CLASS()
//-----------------------------------------------------------------------------
//! constructor
FEPressureRobinBC::FEPressureRobinBC(FEModel* pfem) : FESurfaceLoad(pfem)
{
m_epsk = 0.0;
m_epsc = 0.0;
m_bshellb = false;
}
//-----------------------------------------------------------------------------
bool FEPressureRobinBC::Init()
{
FESurface& surf = GetSurface();
surf.SetShellBottom(m_bshellb);
// get the degrees of freedom
m_dof.Clear();
if (m_bshellb == false)
{
m_dof.AddVariable(FEBioMech::GetVariableName(FEBioMech::DISPLACEMENT));
}
else
{
m_dof.AddVariable(FEBioMech::GetVariableName(FEBioMech::SHELL_DISPLACEMENT));
}
if (m_dof.IsEmpty()) return false;
return FESurfaceLoad::Init();
}
//-----------------------------------------------------------------------------
void FEPressureRobinBC::Update()
{
FETimeInfo tp = GetFEModel()->GetTime();
FESurface& surf = GetSurface();
for (int i=0; i<surf.Elements(); ++i) {
FESurfaceElement& el = surf.Element(i);
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n) {
FEMaterialPoint* mp = el.GetMaterialPoint(n);
mp->Update(tp);
}
}
surf.Update(tp);
}
//-----------------------------------------------------------------------------
void FEPressureRobinBC::LoadVector(FEGlobalVector& R)
{
if (GetFEModel()->GetTime().currentTime == 0) return;
double dt = GetFEModel()->GetTime().timeIncrement;
// evaluate the integral
FESurface& surf = GetSurface();
surf.LoadVector(R, m_dof, false, [&](FESurfaceMaterialPoint& pt, const FESurfaceDofShape& dof_a, std::vector<double>& val) {
// evaluate pressure at this material point
vec3d n = (pt.dxr ^ pt.dxs);
double J = n.unit();
double epsk = m_epsk(pt);
double epsc = m_epsc(pt);
vec3d u = pt.m_rt - pt.m_r0;
vec3d udot = (dt > 0) ? (pt.m_rt - pt.m_rp)/dt : vec3d(0,0,0);
double un = u*n;
double vn = udot*n;
// prescribe a pressure only when the boundary is moving in the direction of the normal
double p = (un > 0) ? epsk*un + epsc*vn : 0;
if (m_bshellb) p = -p;
// force vector
vec3d t = -n*p;
double Na = dof_a.shape;
val[0] = Na*t.x*J;
val[1] = Na*t.y*J;
val[2] = Na*t.z*J;
});
}
//-----------------------------------------------------------------------------
void FEPressureRobinBC::StiffnessMatrix(FELinearSystem& LS)
{
if (GetFEModel()->GetTime().currentTime == 0) return;
double dt = GetFEModel()->GetTime().timeIncrement;
// evaluate the integral
FESurface& surf = GetSurface();
surf.LoadStiffness(LS, m_dof, m_dof, [&](FESurfaceMaterialPoint& pt, const FESurfaceDofShape& dof_a, const FESurfaceDofShape& dof_b, matrix& kab) {
// evaluate pressure at this material point
vec3d n = (pt.dxr ^ pt.dxs);
double J = n.unit();
mat3dd I(1);
double epsk = m_epsk(pt);
double epsc = m_epsc(pt);
vec3d u = pt.m_rt - pt.m_r0;
vec3d udot = (dt > 0) ? (pt.m_rt - pt.m_rp)/dt : vec3d(0,0,0);
double un = u*n;
double vn = udot*n;
double p = (un > 0) ? epsk*un + epsc*vn : 0;
if (m_bshellb) p = -p;
double Na = dof_a.shape;
double dNar = dof_a.shape_deriv_r;
double dNas = dof_a.shape_deriv_s;
double Nb = dof_b.shape;
double dNbr = dof_b.shape_deriv_r;
double dNbs = dof_b.shape_deriv_s;
mat3da Ab = mat3da(pt.dxs*(dNbr/J)-pt.dxr*(dNbs/J));
mat3d Kab = (n & n)*(J*Na*Nb)*(epsk+epsc/dt)
+(n & (Ab*(u*epsk+udot*epsc))*(Na*J))
+(mat3da(pt.dxr*dNbs - pt.dxs*dNbr)*(Na*p));
// prescribe a pressure only when the boundary is moving in the direction of the normal
if (un > 0) kab.set(0, 0, Kab);
});
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEMaxStressCriterion.cpp | .cpp | 2,158 | 72 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEMaxStressCriterion.h"
#include "FEElasticMaterial.h"
#include <FECore/FEElement.h>
BEGIN_FECORE_CLASS(FEStressCriterion, FEMeshAdaptorCriterion)
ADD_PARAMETER(m_metric, "metric");
END_FECORE_CLASS();
FEStressCriterion::FEStressCriterion(FEModel* fem) : FEMeshAdaptorCriterion(fem)
{
m_metric = 0;
}
bool FEStressCriterion::GetMaterialPointValue(FEMaterialPoint& mp, double& value)
{
FEElasticMaterialPoint* ep = mp.ExtractData<FEElasticMaterialPoint>();
if (ep == nullptr) return false;
mat3ds s = ep->m_s;
// get the metric
value = 0.0;
switch (m_metric)
{
case 0: value = s.effective_norm(); break;
case 1:
{
mat3ds devs = s.dev();
double l[3], lmax;
devs.exact_eigen(l);
lmax = l[0];
if (l[1] > lmax) lmax = l[1];
if (l[2] > lmax) lmax = l[2];
value = lmax;
}
break;
default:
return false;
}
return true;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEReactiveVEMaterialPoint.h | .h | 3,082 | 83 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FECore/FEMaterialPoint.h"
#include "FEReactiveViscoelastic.h"
#include "FEUncoupledReactiveViscoelastic.h"
#include <deque>
class FEReactiveViscoelasticMaterial;
class FEUncoupledReactiveViscoelasticMaterial;
//-----------------------------------------------------------------------------
//! Material point data array for reactive viscoelastic materials
//!
class FEReactiveViscoelasticMaterialPoint : public FEMaterialPointArray
{
public:
//! constructor
FEReactiveViscoelasticMaterialPoint();
//! Copy material point data
FEMaterialPointData* Copy();
};
//-----------------------------------------------------------------------------
//! Material point data for reactive viscoelastic materials
class FEReactiveVEMaterialPoint : public FEMaterialPointData
{
public:
//! olverloaded constructors
FEReactiveVEMaterialPoint(FEMaterialPointData*pt) : FEMaterialPointData(pt) {}
//! copy material point data
FEMaterialPointData* Copy() override;
//! Initialize material point data
void Init() override;
//! Update material point data
void Update(const FETimeInfo& timeInfo) override;
//! Serialize data to archive
void Serialize(DumpStream& ar) override;
public:
// multigenerational material data
deque <mat3ds> m_Uv; //!< right stretch tensor at tv (when generation u starts breaking)
deque <double> m_Jv; //!< determinant of Uv (store for efficiency)
deque <double> m_v; //!< time tv when generation starts breaking
deque <double> m_f; //!< mass fraction when generation starts breaking
public:
// weak bond recruitment parameters
double m_Et; //!< trial strain value at time t
deque <double> m_wv; //!< total mass fraction of weak bonds
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEDamageTransIsoMooneyRivlin.cpp | .cpp | 15,815 | 605 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEDamageTransIsoMooneyRivlin.h"
FETIMRDamageMaterialPoint::FETIMRDamageMaterialPoint(FEMaterialPointData*pt) : FEMaterialPointData(pt) {}
FEMaterialPointData* FETIMRDamageMaterialPoint::Copy()
{
FETIMRDamageMaterialPoint* pt = new FETIMRDamageMaterialPoint(*this);
if (m_pNext) pt->m_pNext = m_pNext->Copy();
return pt;
}
void FETIMRDamageMaterialPoint::Init()
{
FEMaterialPointData::Init();
// intialize data to zero
m_MEmax = 0;
m_MEtrial = 0;
m_Dm = 0;
m_FEmax = 0;
m_FEtrial = 0;
m_Df = 0;
}
void FETIMRDamageMaterialPoint::Update(const FETimeInfo& timeInfo)
{
FEMaterialPointData::Update(timeInfo);
m_MEmax = max(m_MEmax, m_MEtrial);
m_FEmax = max(m_FEmax, m_FEtrial);
}
void FETIMRDamageMaterialPoint::Serialize(DumpStream& ar)
{
FEMaterialPointData::Serialize(ar);
ar & m_MEtrial & m_MEmax & m_Dm;
ar & m_FEtrial & m_FEmax & m_Df;
}
// define the material parameters
BEGIN_FECORE_CLASS(FEDamageTransIsoMooneyRivlin, FEUncoupledMaterial)
ADD_PARAMETER(m_c1, FE_RANGE_GREATER(0.0), "c1")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_c2, "c2")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_c3, "c3")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_c4, FE_RANGE_GREATER(0.0), "c4");
ADD_PARAMETER(m_Mbeta, "Mbeta");
ADD_PARAMETER(m_Msmin, "Msmin");
ADD_PARAMETER(m_Msmax, "Msmax");
ADD_PARAMETER(m_Fbeta, "Fbeta");
ADD_PARAMETER(m_Fsmin, "Fsmin");
ADD_PARAMETER(m_Fsmax, "Fsmax");
ADD_PROPERTY(m_Q, "mat_axis")->SetFlags(FEProperty::Optional);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEDamageTransIsoMooneyRivlin::FEDamageTransIsoMooneyRivlin(FEModel* pfem) : FEUncoupledMaterial(pfem)
{
}
//-----------------------------------------------------------------------------
FEMaterialPointData* FEDamageTransIsoMooneyRivlin::CreateMaterialPointData()
{
return new FETIMRDamageMaterialPoint(new FEElasticMaterialPoint);
}
//-----------------------------------------------------------------------------
mat3ds FEDamageTransIsoMooneyRivlin::DevStress(FEMaterialPoint& mp)
{
// matrix stress
mat3ds sm = MatrixStress(mp);
// matrix reduction factor
double gm = MatrixDamage(mp);
// fiber stress
mat3ds sf = FiberStress(mp);
// fiber reduction factor
double gf = FiberDamage(mp);
return sm*gm + sf*gf;
}
//-----------------------------------------------------------------------------
//! Calculate the deviatoric stress
mat3ds FEDamageTransIsoMooneyRivlin::MatrixStress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// determinant of deformation gradient
double J = pt.m_J;
// calculate deviatoric left Cauchy-Green tensor
mat3ds B = pt.DevLeftCauchyGreen();
// calculate square of B
mat3ds B2 = B.sqr();
// Invariants of B (= invariants of C)
// Note that these are the invariants of Btilde, not of B!
double I1 = B.tr();
// --- TODO: put strain energy derivatives here ---
//
// W = C1*(I1 - 3) + C2*(I2 - 3)
//
// Wi = dW/dIi
double W1 = m_c1;
double W2 = m_c2;
// ---
// calculate T = F*dW/dC*Ft
// T = F*dW/dC*Ft
mat3ds T = B*(W1 + W2*I1) - B2*W2;
return T.dev()*(2.0/J);
}
//-----------------------------------------------------------------------------
// Calculate the fiber stress
mat3ds FEDamageTransIsoMooneyRivlin::FiberStress(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
mat3d& F = pt.m_F;
double J = pt.m_J;
double Jm13 = pow(J, -1.0/3.0);
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
// get the initial fiber direction
vec3d a0 = Q.col(0);
// calculate the current material axis lam*a = F*a0;
vec3d a = F*a0;
// normalize material axis and store fiber stretch
double lam, lamd;
lam = a.unit();
lamd = lam*Jm13; // i.e. lambda tilde
// invariant I4
double I4 = lamd*lamd;
// strain energy derivative
double W4 = (I4 - 1)*m_c3*exp(m_c4*(I4-1)*(I4-1));
// calculate dyad of a: AxA = (a x a)
mat3ds AxA = dyad(a);
// calculate FdWf/dCFt = I4*W4*(a x a)
mat3ds T = AxA*(W4*I4);
// return stress
return T.dev()*(2.0/J);
}
//-----------------------------------------------------------------------------
tens4ds FEDamageTransIsoMooneyRivlin::DevTangent(FEMaterialPoint& mp)
{
// matrix tangent
tens4ds Cm = MatrixTangent(mp);
// matrix damage
double gm = MatrixDamage(mp);
// fiber tangent
tens4ds Cf = FiberTangent(mp);
// fiber damage
double gf = FiberDamage(mp);
return Cm*gm + Cf*gf;
}
//-----------------------------------------------------------------------------
//! Calculate the deviatoric tangent
tens4ds FEDamageTransIsoMooneyRivlin::MatrixTangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// determinant of deformation gradient
double J = pt.m_J;
double Ji = 1.0/J;
// calculate deviatoric left Cauchy-Green tensor: B = F*Ft
mat3ds B = pt.DevLeftCauchyGreen();
// calculate square of B
mat3ds B2 = B.sqr();
// Invariants of B (= invariants of C)
double I1 = B.tr();
double I2 = 0.5*(I1*I1 - B2.tr());
// --- TODO: put strain energy derivatives here ---
// Wi = dW/dIi
double W1, W2;
W1 = m_c1;
W2 = m_c2;
// ---
// calculate dWdC:C
double WC = W1*I1 + 2*W2*I2;
// calculate C:d2WdCdC:C
double CWWC = 2*I2*W2;
// deviatoric cauchy-stress, trs = trace[s]/3
mat3ds T = B * (W1 + W2 * I1) - B2 * W2;
mat3ds devs = T.dev() * (2.0 / J);
// Identity tensor
mat3ds I(1,1,1,0,0,0);
tens4ds IxI = dyad1s(I);
tens4ds I4 = dyad4s(I);
tens4ds BxB = dyad1s(B);
tens4ds B4 = dyad4s(B);
// d2W/dCdC:C
mat3ds WCCxC = B*(W2*I1) - B2*W2;
tens4ds cw = (BxB - B4)*(W2*4.0*Ji) - dyad1s(WCCxC, I)*(4.0/3.0*Ji) + IxI*(4.0/9.0*Ji*CWWC);
tens4ds c = dyad1s(devs, I)*(-2.0/3.0) + (I4 - IxI/3.0)*(4.0/3.0*Ji*WC) + cw;
return c;
}
//-----------------------------------------------------------------------------
// Fiber material tangent
//
tens4ds FEDamageTransIsoMooneyRivlin::FiberTangent(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
mat3d& F = pt.m_F;
double J = pt.m_J;
double Jm13 = pow(J, -1.0/3.0);
double Ji = 1.0/J;
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
// get initial local material axis
vec3d a0 = Q.col(0);
// calculate current local material axis
vec3d a = F*a0;
double lam = a.unit();
// deviatoric stretch
double lamd = lam*Jm13;
double I4 = lamd*lamd;
// strain energy derivative
double W4 = (I4 - 1)*m_c3*exp(m_c4*(I4-1)*(I4-1));
double W44 = m_c3*exp(m_c4*(I4 - 1)*(I4 - 1)) + 2*m_c3*m_c4*(I4 - 1)*(I4 - 1)*exp(m_c4*(I4 - 1)*(I4 - 1));
// calculate dWdC:C
double WC = W4*I4;
// calculate C:d2WdCdC:C
double CWWC = W44*I4*I4;
mat3dd I(1); // Identity
tens4ds IxI = dyad1s(I);
tens4ds Id4 = dyad4s(I);
mat3ds AxA = dyad(a);
tens4ds AxAxAxA = dyad1s(AxA);
tens4ds cw = AxAxAxA*(4.0*Ji*W44*I4*I4) - dyad1s(I, AxA)*(4.0/3.0*Ji*W44*I4*I4);
tens4ds c = (Id4 - IxI/3.0)*(4.0/3.0*Ji*WC) + IxI*(4.0/9.0*Ji*CWWC) + cw;
// see if we need to add the stress
FETIMRDamageMaterialPoint& dp = *mp.ExtractData<FETIMRDamageMaterialPoint>();
if (dp.m_FEtrial > dp.m_FEmax)
{
mat3ds devs = pt.m_s.dev();
double dg = FiberDamageDerive(mp);
c += dyad1s(devs)*(J*dg/dp.m_FEtrial);
}
return c;
}
//-----------------------------------------------------------------------------
double FEDamageTransIsoMooneyRivlin::DevStrainEnergyDensity(FEMaterialPoint& mp)
{
// matrix sed
double sedm = MatrixStrainEnergyDensity(mp);
// matrix reduction factor
double gm = MatrixDamage(mp);
// fiber sed
double sedf = FiberStrainEnergyDensity(mp);
// fiber reduction factor
double gf = FiberDamage(mp);
return sedm*gm + sedf*gf;
}
//-----------------------------------------------------------------------------
//! Calculate the matrix strain energy density
double FEDamageTransIsoMooneyRivlin::MatrixStrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate deviatoric left Cauchy-Green tensor
mat3ds B = pt.DevLeftCauchyGreen();
// calculate square of B
mat3ds B2 = B.sqr();
// Invariants of B (= invariants of C)
// Note that these are the invariants of Btilde, not of B!
double I1 = B.tr();
double I2 = 0.5*(I1*I1 - B2.tr());
// --- TODO: put strain energy derivatives here ---
//
// W = C1*(I1 - 3) + C2*(I2 - 3)
//
double sed = m_c1*(I1 - 3) + m_c2*(I2 - 3);
return sed;
}
//-----------------------------------------------------------------------------
// Calculate the fiber strain energy density
double FEDamageTransIsoMooneyRivlin::FiberStrainEnergyDensity(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
mat3d& F = pt.m_F;
double J = pt.m_J;
double Jm13 = pow(J, -1.0/3.0);
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
// get the initial fiber direction
vec3d a0 = Q.col(0);
// calculate the current material axis lam*a = F*a0;
vec3d a = F*a0;
// normalize material axis and store fiber stretch
double lam, lamd;
lam = a.unit();
lamd = lam*Jm13; // i.e. lambda tilde
// invariant I4
double I4 = lamd*lamd;
// strain energy derivative
double sed = 0.5*m_c3/m_c4*(exp(m_c4*(I4-1)*(I4-1))-1);
// return sed
return sed;
}
//-----------------------------------------------------------------------------
// Calculate damage reduction factor for matrix
double FEDamageTransIsoMooneyRivlin::MatrixDamage(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate right Cauchy-Green tensor
mat3ds C = pt.DevRightCauchyGreen();
mat3ds C2 = C.sqr();
// Invariants
double I1 = C.tr();
double I2 = 0.5*(I1*I1 - C2.tr());
// strain-energy value
double SEF = m_c1*(I1 - 3) + m_c2*(I2 - 3);
// get the damage material point data
FETIMRDamageMaterialPoint& dp = *mp.ExtractData<FETIMRDamageMaterialPoint>();
// calculate trial-damage parameter
dp.m_MEtrial = sqrt(2.0*fabs(SEF));
// calculate damage parameter
double Es = max(dp.m_MEtrial, dp.m_MEmax);
// calculate reduction parameter
double g = 1.0;
if (Es < m_Msmin) g = 1.0;
else if (Es > m_Msmax) g = 0.0;
else
{
double F = (Es - m_Msmin)/(m_Msmin - m_Msmax);
g = 1.0 - (1.0 - m_Mbeta + m_Mbeta*F*F)*(F*F);
}
dp.m_Dm = 1-g;
return g;
}
//-----------------------------------------------------------------------------
// Calculate damage reduction factor for matrix
double FEDamageTransIsoMooneyRivlin::MatrixDamageDerive(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate right Cauchy-Green tensor
mat3ds C = pt.DevRightCauchyGreen();
mat3ds C2 = C.sqr();
// Invariants
double I1 = C.tr();
double I2 = 0.5*(I1*I1 - C2.tr());
// strain-energy value
double SEF = m_c1*(I1 - 3) + m_c2*(I2 - 3);
// get the damage material point data
FETIMRDamageMaterialPoint& dp = *mp.ExtractData<FETIMRDamageMaterialPoint>();
// calculate trial-damage parameter
dp.m_MEtrial = sqrt(2.0*fabs(SEF));
// calculate damage parameter
double Es = max(dp.m_MEtrial, dp.m_MEmax);
// calculate reduction parameter
double dg = 0.0;
if (Es < m_Msmin) dg = 0.0;
else if (Es > m_Msmax) dg = 0.0;
else
{
double h = m_Msmax - m_Msmin;
double F = (Es - m_Msmin)/h;
dg = -2.0*F/h*(1 - m_Mbeta + m_Mbeta*F*F)-(F*F)*(2.0*m_Mbeta*F/h);
}
return dg;
}
//-----------------------------------------------------------------------------
// Calculate damage reduction factor for fibers
double FEDamageTransIsoMooneyRivlin::FiberDamage(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
mat3d& F = pt.m_F;
double J = pt.m_J;
double Jm13 = pow(J, -1.0/3.0);
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
// get the initial fiber direction
vec3d a0 = Q.col(0);
// calculate the current material axis lam*a = F*a0;
vec3d a = F*a0;
// normalize material axis and store fiber stretch
double lam, lamd;
lam = a.unit();
lamd = lam*Jm13; // i.e. lambda tilde
// invariant I4
double I4 = lamd*lamd;
// strain energy value
double SEF = 0.5*m_c3/m_c4*(exp(m_c4*(I4-1)*(I4-1))-1);
// get the damage material point data
FETIMRDamageMaterialPoint& dp = *mp.ExtractData<FETIMRDamageMaterialPoint>();
// calculate trial-damage parameter
dp.m_FEtrial = sqrt(2.0*fabs(SEF));
// calculate damage parameter
double Es = max(dp.m_FEtrial, dp.m_FEmax);
// calculate reduction parameter
double g = 1.0;
if (Es < m_Fsmin) g = 1.0;
else if (Es > m_Fsmax) g = 0.0;
else
{
double F = (Es - m_Fsmin)/(m_Fsmin - m_Fsmax);
g = 1.0 - (1.0 - m_Fbeta + m_Fbeta*F*F)*(F*F);
}
dp.m_Df = 1-g;
return g;
}
//-----------------------------------------------------------------------------
// Calculate damage reduction factor for fibers
double FEDamageTransIsoMooneyRivlin::FiberDamageDerive(FEMaterialPoint &mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
mat3d& F = pt.m_F;
double J = pt.m_J;
double Jm13 = pow(J, -1.0/3.0);
// get the local coordinate systems
mat3d Q = GetLocalCS(mp);
// get the initial fiber direction
vec3d a0 = Q.col(0);
// calculate the current material axis lam*a = F*a0;
vec3d a = F*a0;
// normalize material axis and store fiber stretch
double lam, lamd;
lam = a.unit();
lamd = lam*Jm13; // i.e. lambda tilde
// invariant I4
double I4 = lamd*lamd;
// strain energy value
double SEF = 0.5*m_c3/m_c4*(exp(m_c4*(I4-1)*(I4-1))-1);
// get the damage material point data
FETIMRDamageMaterialPoint& dp = *mp.ExtractData<FETIMRDamageMaterialPoint>();
// calculate trial-damage parameter
dp.m_FEtrial = sqrt(2.0*fabs(SEF));
// calculate damage parameter
double Es = max(dp.m_FEtrial, dp.m_FEmax);
// calculate reduction parameter
double dg = 0.0;
if (Es < m_Fsmin) dg = 0.0;
else if (Es > m_Fsmax) dg = 0.0;
else
{
double h = m_Fsmin - m_Fsmax;
double F = (Es - m_Fsmin)/h;
dg = -2.0*F/h*(1 - m_Fbeta + m_Fbeta*F*F)-(F*F)*(2.0*m_Fbeta*F/h);
}
return dg;
}
//-----------------------------------------------------------------------------
//! damage
double FEDamageTransIsoMooneyRivlin::Damage(FEMaterialPoint& pt)
{
return MatrixDamage(pt) + FiberDamage(pt);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FERigidConnector.cpp | .cpp | 6,475 | 180 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidConnector.h"
#include "FERigidBody.h"
#include "FEMechModel.h"
#include "FERigidMaterial.h"
#include <FECore/FEMaterial.h>
#include <FECore/log.h>
//-----------------------------------------------------------------------------
BEGIN_FECORE_CLASS(FERigidConnector, FENLConstraint);
ADD_PARAMETER(m_nRBa, "body_a")->setEnums("$(rigid_materials)");
ADD_PARAMETER(m_nRBb, "body_b")->setEnums("$(rigid_materials)");
END_FECORE_CLASS();
int FERigidConnector::m_ncount = 0;
//-----------------------------------------------------------------------------
FERigidConnector::FERigidConnector(FEModel* pfem) : FENLConstraint(pfem)
{
m_F = m_M = vec3d(0, 0, 0);
m_rbA = m_rbB = 0;
};
//-----------------------------------------------------------------------------
FERigidConnector::~FERigidConnector() {}
//-----------------------------------------------------------------------------
bool FERigidConnector::Init()
{
// do base class first
if (FENLConstraint::Init() == false) return false;
// When the rigid spring is read in, the ID's correspond to the rigid materials.
// Now we want to make the ID's refer to the rigid body ID's
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
FERigidMaterial* pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_nRBa - 1));
if (pm == nullptr)
{
feLogError("Rigid connector %d (spring) does not connect two rigid bodies\n", m_nID + 1);
return false;
}
m_nRBa = pm->GetRigidBodyID();
pm = dynamic_cast<FERigidMaterial*>(fem.GetMaterial(m_nRBb - 1));
if (pm == nullptr)
{
feLogError("Rigid connector %d (spring) does not connect two rigid bodies\n", m_nID);
return false;
}
m_nRBb = pm->GetRigidBodyID();
// get the actual rigid bodies
m_rbA = fem.GetRigidBody(m_nRBa);
m_rbB = fem.GetRigidBody(m_nRBb);
return true;
}
//-----------------------------------------------------------------------------
void FERigidConnector::BuildMatrixProfile(FEGlobalMatrix& M)
{
vector<int> lm(12);
int* lm1 = m_rbA->m_LM;
int* lm2 = m_rbB->m_LM;
for (int j=0; j<6; ++j) lm[j ] = lm1[j];
for (int j=0; j<6; ++j) lm[j+6] = lm2[j];
M.build_add(lm);
}
//-----------------------------------------------------------------------------
void FERigidConnector::Serialize(DumpStream& ar)
{
FENLConstraint::Serialize(ar);
ar & m_nID;
ar & m_nRBa & m_nRBb;
ar & m_F & m_M;
if (ar.IsLoading())
{
// get the actual rigid bodies
FEMechModel& fem = static_cast<FEMechModel&>(*GetFEModel());
m_rbA = fem.GetRigidBody(m_nRBa);
m_rbB = fem.GetRigidBody(m_nRBb);
}
}
//-----------------------------------------------------------------------------
// return the instantaneous helical axis of Body b relative to Body a, in ground CS
void FERigidConnector::InstantaneousHelicalAxis(vec3d& omega, vec3d& s, double& tdot)
{
double dt = GetFEModel()->GetTime().timeIncrement;
// incremental rotation in spatial frame
vec3d oma = (m_rbA->m_wp + m_rbA->m_wt)/2;
vec3d omb = (m_rbB->m_wp + m_rbB->m_wt)/2;
vec3d va = (m_rbA->m_vp + m_rbA->m_vt)/2;
vec3d vb = (m_rbB->m_vp + m_rbB->m_vt)/2;
// get the relative motion
omega = (omb - oma);
vec3d rdot = vb - va;
double rdm = rdot.norm();
vec3d n(omega); n.unit();
vec3d w(omega);
tdot = rdot*n;
vec3d ra = (m_rbA->m_rt + m_rbA->m_rp)/2;
vec3d rb = (m_rbB->m_rt + m_rbB->m_rp)/2;
vec3d r = rb - ra; // midpoint value of r
double w2 = w*w;
s = (w2 > 0) ? (w ^ (rdot - n*tdot + (r ^ w)))/(w*w) : vec3d(0,0,0);
if ((w2 == 0) && (rdm > 0)) {
tdot = rdm;
n = rdot.Normalize();
omega = n;
}
// now transform the helical axis to be represented relative to the ground
s -= m_rbB->m_rt;
omega = m_rbB->GetRotation().Inverse()*omega;
}
//-----------------------------------------------------------------------------
// return the helical axis of Body b relative to Body a, in ground CS
void FERigidConnector::FiniteHelicalAxis(vec3d& omega, vec3d& s, double& tdot)
{
// incremental rotation in spatial frame
quatd oma = m_rbA->GetRotation()*m_rbA->GetPreviousRotation().Inverse();
quatd omb = m_rbB->GetRotation()*m_rbB->GetPreviousRotation().Inverse();
// clean-up roundoff errors
oma.MakeUnit();
omb.MakeUnit();
vec3d rda = (m_rbA->m_rt - m_rbA->m_rp);
vec3d rdb = (m_rbB->m_rt - m_rbB->m_rp);
// get the relative motion
quatd dQ = omb - oma; // TODO: Is this valid for rotations?
omega = dQ.GetRotationVector();
vec3d rdot = rdb - rda;
double rdm = rdot.norm();
vec3d n(omega); n.unit();
vec3d w(omega);
tdot = rdot*n;
vec3d ra = (m_rbA->m_rt + m_rbA->m_rp)/2;
vec3d rb = (m_rbB->m_rt + m_rbB->m_rp)/2;
vec3d r = rb - ra; // midpoint value of r
double w2 = w*w;
s = (w2 > 0) ? (w ^ (rdot - n*tdot + (r ^ w)))/(w*w) : vec3d(0,0,0);
if ((w2 == 0) && (rdm > 0)) {
tdot = rdm;
n = rdot.Normalize();
omega = n;
}
// now transform the helical axis to be represented relative to the ground
s -= m_rbB->m_rt;
omega = m_rbB->GetRotation().Inverse()*omega;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FENodalForce.h | .h | 2,019 | 58 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FENodalLoad.h>
#include "febiomech_api.h"
//-----------------------------------------------------------------------------
// Class that implements an equivalent nodal force load.
// This load will be applied directly to the load vector of the system
class FEBIOMECH_API FENodalForce : public FENodalLoad
{
public:
FENodalForce(FEModel* fem);
// set the value
void SetValue(const vec3d& v);
protected: // required functions of FENodalLoad
// Set the dof list
bool SetDofList(FEDofList& dofList) override;
// get the nodal values
void GetNodalValues(int inode, std::vector<double>& val) override;
private:
FEParamVec3 m_f; //!< the applied force
bool m_shellBottom;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEABUnconstrained.h | .h | 1,979 | 60 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2019 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEBioMech/FEUncoupledMaterial.h"
class FEABUnconstrained : public FEElasticMaterial
{
//public:
//enum { MAX_TERMS = 6 };
public:
FEABUnconstrained(FEModel* pfem);
//! calculate the stress
mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate the tangent
tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
double StrainEnergyDensity(FEMaterialPoint& pt) override;
protected:
void EigenValues(mat3ds& A, double l[3], vec3d r[3], const double eps = 0);
double m_eps;
public:
//FEParamDouble m_ksi;
double m_N;
int m_term;
FEParamDouble m_ksi;
FEParamDouble m_kappa;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEPRLig.h | .h | 2,071 | 61 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEElasticMaterial.h"
class FEPRLig : public FEElasticMaterial
{
public:
FEPRLig(FEModel* pfem);
public:
double m_c1; //!< fiber constant c1
double m_c2; //!< fiber constant c2
double m_u; //!< Lame Coefficient mu of the matrix
double m_m; //!< Poisson's ratio slope
double m_v0; //!< initial Poisson's ratio
double m_k; //!< Penalty for the volumetric strain energy
public:
//! calculate stress at material point
mat3ds Stress(FEMaterialPoint& pt) override;
//! calculate tangent stiffness at material point
tens4ds Tangent(FEMaterialPoint& pt) override;
//! calculate strain energy density at material point
double StrainEnergyDensity(FEMaterialPoint& pt) override;
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/triangle_sphere.h | .h | 743,619 | 347 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
const int NST20 = 20;
const double AREA20[NST20] = {
0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718,0.628318530718
};
const double PHI20[NST20] = {
2.48923451381,2.48923451381,2.48923451381,2.48923451381,2.48923451381,0.652358139784,0.652358139784,0.652358139784,0.652358139784,0.652358139784,1.38208579601,1.75950685758,1.75950685758,1.75950685758,1.38208579601,1.38208579601,1.75950685758,1.75950685758,1.38208579601,1.38208579601
};
const double THETA20[NST20] = {
2.51327412287,-1.25663706144,0,3.76991118431,1.25663706144,0.628318530718,4.39822971503,3.14159265359,-0.628318530718,1.88495559215,3.14159265359,2.51327412287,3.76991118431,0,0.628318530718,-0.628318530718,-1.25663706144,1.25663706144,4.39822971503,1.88495559215
};
const int NST34 = 34;
const double AREA34[NST34] = {
0.383935577992,0.363384852082,0.404286699707,0.399662586846,0.354335283849,0.352347120947,0.393903444368,0.379809289616,0.348615415676,0.362162027018,0.352706956245,0.334201951381,0.38550990319,0.353366062299,0.353210862208,0.390916630874,0.350536536666,0.334426717588,0.401460216421,0.403845317927,0.339702141107,0.395964760734,0.354184187245,0.35253909316,0.379408560901,0.394927777324,0.35332404861,0.391201373908,0.379167729391,0.339928651639,0.397540807177,0.35214902586,0.352731483864,0.380977520538
};
const double PHI34[NST34] = {
0.992311860958,0.540938308295,0.740973555387,1.21706836975,1.4250943943,1.48988159961,2.21160798775,1.64632156581,1.61309409716,0.272718163585,1.12766830359,0.692114402353,0.331284915403,0.825383424239,1.24305999687,1.18761290633,1.81917628368,1.21867315735,1.21642807486,0.887592308181,2.54850378579,2.24712659371,1.71737990968,1.6503477742,2.04868066283,2.75219649767,1.90134757641,1.78830605485,2.14096763772,2.56416958122,2.86656487935,2.31787616339,2.01399005833,2.09881196833
};
const double THETA34[NST34] = {
2.84381372042,2.45969310542,1.44397272665,1.45316745591,2.50154805757,1.95763275851,0.161250110851,0.427494793002,0.976186514632,3.82722948119,-1.34124680328,0.591757041849,-0.374424949851,-0.786805077371,-0.366748217522,0.210267741996,4.21323110868,3.42427462827,4.33893673216,3.93695829964,-1.24684183905,-0.465522391576,-0.637552827163,-1.18265444754,-1.5544160045,3.8807156385,2.7749120359,3.32757398959,3.7256260405,0.797024363447,2.2253590719,2.35938161601,1.80394081727,1.20832067743
};
const int NST60 = 60;
const double AREA60[NST60] = {
0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239,0.209439510239
};
const double PHI60[NST60] = {
2.77901624839,2.77901624839,2.77901624839,2.77901624839,2.77901624839,0.362576405201,0.362576405201,0.362576405201,0.362576405201,0.362576405201,2.397020341,2.11317043701,1.73299308984,2.11317043701,1.73299308984,0.744572312593,1.02842221657,1.40859956375,1.02842221657,1.40859956375,2.397020341,2.11317043701,1.73299308984,1.73299308984,2.11317043701,2.397020341,2.11317043701,2.11317043701,1.73299308984,1.73299308984,0.744572312593,1.02842221657,1.40859956375,1.40859956375,1.02842221657,0.744572312593,1.02842221657,1.02842221657,1.40859956375,1.40859956375,2.11317043701,2.397020341,2.11317043701,1.73299308984,1.73299308984,2.11317043701,2.397020341,1.73299308984,2.11317043701,1.73299308984,1.02842221657,0.744572312593,1.02842221657,1.40859956375,1.40859956375,1.02842221657,0.744572312593,1.40859956375,1.40859956375,1.02842221657
};
const double THETA60[NST60] = {
1.88495559215,4.39822971503,-0.628318530718,3.14159265359,0.628318530718,1.25663706144,-1.25663706144,3.76991118431,0,2.51327412287,3.14159265359,3.54640644495,2.9287380957,2.73677886223,3.35444721148,0,-0.404813791358,0.21285455789,0.404813791358,-0.21285455789,-0.628318530718,-0.22350473936,-0.415463972828,-0.841173088608,-1.03313232208,0.628318530718,1.03313232208,0.22350473936,0.415463972828,0.841173088608,3.76991118431,3.36509739295,3.55705662642,3.9827657422,4.17472497567,2.51327412287,2.10846033151,2.91808791423,2.72612868076,2.30041956498,-1.4801418008,4.39822971503,3.99341592367,4.61108427292,4.18537515714,2.28976938351,1.88495559215,2.09781015004,1.4801418008,1.67210103426,4.62173445439,-1.25663706144,-0.851823270078,-1.04378250355,-1.46949161933,0.851823270078,1.25663706144,1.04378250355,1.46949161933,1.66145085279
};
const int NST74 = 74;
const double AREA74[NST74] = {
0.172194497108,0.172616214738,0.156384928339,0.158507077935,0.181989031701,0.164489052852,0.170463214221,0.16791900153,0.174140795926,0.167638690642,0.163799740359,0.167974639108,0.174154539066,0.171879495364,0.166744662057,0.169537017558,0.185616681294,0.168799231951,0.168829055331,0.158481556172,0.17671435797,0.172868926325,0.18167436801,0.185611507665,0.15636355032,0.172247969404,0.18070564458,0.167150673674,0.181726232028,0.165314830546,0.169961200128,0.172654595308,0.171222346552,0.171246768459,0.167601272159,0.169450198726,0.167629614669,0.169508601315,0.165328142768,0.169914886884,0.164214499781,0.167677242098,0.17192283869,0.190385295886,0.16381928312,0.167103261273,0.180784609354,0.190430641824,0.164227106766,0.168116666569,0.180247005644,0.181982148896,0.172609862041,0.176818987391,0.158837157007,0.158858544541,0.168442689446,0.168486647778,0.160628620296,0.168636058657,0.159225581499,0.160273422768,0.168645193049,0.16061638219,0.168661465192,0.160240964724,0.159275111334,0.168607230802,0.166728581783,0.169458074264,0.168183535321,0.180160965744,0.170522960063,0.164487167827
};
const double PHI74[NST74] = {
1.37637747565,1.77848403736,1.40219574588,1.67945305427,1.92268587646,2.31568591025,2.34029288949,1.74919536568,2.0904221287,2.65976168911,2.07826715601,2.07982156114,2.31224176828,2.79200030874,2.9309419527,2.58144952406,1.1534990749,1.13996555245,1.30505558926,1.40234552605,1.73756509933,2.00215145978,0.19103172404,0.7696420396,0.731695622618,0.498670411242,1.59204101919,1.71932119701,1.11126669369,1.22012811405,0.987522913199,0.592108360768,1.55921318852,1.69204624116,1.47866187997,1.13117589437,1.16637514167,0.932676730736,0.469112235723,0.572650532114,1.92280468579,2.18769815342,2.51317688672,1.56555227458,1.48104448229,1.13721016656,0.824791654243,2.36395408104,2.73274234576,2.89973890344,2.54482479876,1.37368120261,1.07179674998,0.466803260621,0.786073451869,0.194230542378,0.801816920121,0.552063943806,1.31992333966,1.39377623123,1.09644735409,0.791733455504,0.941592618213,2.21540832028,1.8284785983,1.70848167882,1.96385985674,2.30044204202,2.31792447645,2.31575385231,1.98922622439,1.69986240845,1.98690641289,1.69868183315
};
const double THETA74[NST74] = {
4.23372155256,3.77350281851,3.84608000918,3.18484837654,3.45809438838,3.39077080754,2.91506076853,0.250156160968,0.316825916633,-0.143154113368,-0.84076048198,-0.426340636629,-0.106690018794,0.818610130238,2.33492710176,2.48483746082,3.5931710259,2.89909309915,3.22927360111,2.61469093203,2.80180069559,2.654831488,1.308041588,2.831818526,2.32376205684,1.78656726746,-1.30884279106,-0.960196437309,4.45822975191,-1.41123318914,-1.12411539369,-1.08459745398,-0.0945343132877,-0.363600184289,-0.696117769684,-0.744259801597,-0.0547273435112,-0.357678326852,0.321737854417,-0.353212976842,0.992995023213,0.714451163504,1.03342605354,0.861716307267,0.493572491076,0.334686032515,0.575808887909,-1.15430788691,-0.98649181298,4.15257530946,3.87038000761,2.24934454968,2.09486017238,4.63887041185,4.26918611221,3.70514048067,3.73735278376,3.33042501982,1.08705818641,1.47334175658,1.68393403727,1.42390002369,0.995745287995,-1.55050565608,-1.56134266036,4.37856330849,4.10130884779,4.24511018959,1.55945328606,2.04234454148,1.3922866091,1.63240927868,2.21673002442,2.01964818044
};
const int NST196 = 196;
const double AREA196[NST196] = {
0.0638972311061,0.0668894692436,0.0649858303874,0.0616304009286,0.0652668671976,0.065266527635,0.0663350077825,0.0619973712494,0.0659695136296,0.0677211405895,0.0640119463478,0.0658673121802,0.0638707648582,0.0613608629933,0.0624495545788,0.060868522918,0.0674482226427,0.0671445089851,0.064837595448,0.062626039322,0.0617571980229,0.0626253474998,0.0657849326183,0.0650523303174,0.0644063159435,0.0632107557901,0.0661364206817,0.0670360363369,0.0641293778863,0.0611082806036,0.0663154376387,0.0631159265005,0.0644200031677,0.0639622415538,0.0624689285189,0.0670199827974,0.0618141056617,0.0661940957789,0.0626199310979,0.0661333082831,0.0630759889626,0.0646358006381,0.0632064948448,0.0657527651672,0.0650919188211,0.0614645705149,0.068038372082,0.0621728888174,0.0621604388567,0.0624503500411,0.0615810462997,0.0623772508079,0.0628872780195,0.0643338947915,0.0629750384363,0.0673882292199,0.0633495486256,0.0659467764361,0.0645347447336,0.0639615118178,0.0634791780095,0.0646338089292,0.0632190912109,0.0650657772645,0.0610130299864,0.0649286976652,0.0645341052298,0.0615521843399,0.0631564345319,0.0635087658748,0.0641850864396,0.0648102851225,0.0639681320617,0.0640018140136,0.0669712301109,0.0640833922652,0.0639546643343,0.065864856972,0.0629714016573,0.0647429367746,0.0649855121913,0.0656913043705,0.0610866775775,0.0627823095172,0.0650003056205,0.0638208777769,0.0613889570916,0.0638986821682,0.0648972457364,0.0657808734732,0.0647655104122,0.0642512111769,0.0624994214407,0.0675120161824,0.0654779359653,0.0651195316694,0.0613319113968,0.0681258859813,0.0635523806897,0.0634059245265,0.0635785126812,0.0635843220386,0.0672131922246,0.0674297560572,0.0633540087023,0.0633556232024,0.0622259647217,0.0621016756343,0.0625175919109,0.0615427568012,0.0625274688479,0.0663983992939,0.0617283672137,0.0649753513125,0.0644470747974,0.0668101556072,0.0612965420155,0.0671188646658,0.066844693631,0.0639306465074,0.0635281786511,0.0620441236157,0.0620105509386,0.0620206299095,0.0620323741906,0.0619472652273,0.0613419067267,0.0645874503395,0.0625951627553,0.0682956166143,0.0618125564724,0.0660826280633,0.0635518632664,0.0625994172267,0.0636431475865,0.0656899318151,0.0614506375482,0.069319385953,0.0626899203954,0.0639075010672,0.0610870417725,0.0659135629029,0.0648390635504,0.0645356233343,0.0615356150467,0.0651728841148,0.0647208956059,0.0614134063328,0.0632181648813,0.0671536214318,0.0664316351668,0.0634431678513,0.0635170076154,0.064137433268,0.0619366174429,0.0662827425601,0.0632340633187,0.0666931621427,0.0634852057939,0.0655424402549,0.0627586118204,0.0637870642746,0.0659670181209,0.0649179542241,0.0643158934673,0.0664030078897,0.0615439641304,0.0646235217071,0.0619671421584,0.0648177739233,0.0624309475518,0.0683794315543,0.0649214754714,0.0610500616617,0.0616095715887,0.0648169853985,0.0651418225484,0.0655188258374,0.0620442301568,0.0630219105744,0.0663489073152,0.0647882352238,0.0621295964819,0.066430603159,0.0626539499938,0.0640667376352,0.0637282714912,0.0654284504408,0.0610327460579,0.0665293001472,0.064299664322,0.0627676549845,0.0670393417749,0.0614484705382,0.0640106207734,0.0660463769293
};
const double PHI196[NST196] = {
1.80836671617,1.29832776991,0.94228751199,0.732905150597,2.19377370325,2.31639125438,0.966431658401,0.818889029927,1.37953490986,1.22925672388,1.05037045195,1.25926285733,1.18709403222,0.88111579647,1.10552091779,1.14838705952,1.31124258856,1.64990671373,1.36519575348,1.94572963976,1.57512415122,1.72009677992,2.12963710354,2.04756241373,2.04486196597,2.17108671434,2.11519971854,2.40247205336,0.602805457992,0.370214502354,0.265896414357,0.459050383423,2.3993218573,2.15960844178,2.14015125695,2.04323188674,2.36132260345,2.49982090068,2.37013126348,2.52237961342,2.72859268381,2.74927033539,2.45912165436,2.23865900628,2.25771531208,1.80552440002,1.68742933601,2.01869423775,2.0624576012,1.78824900142,1.68895467049,1.85577193941,1.39354056866,1.31843835311,1.45381725971,1.66974915202,1.45011354454,1.52010206323,2.32743187247,2.49552311052,2.71562823291,2.69941844724,2.31356410972,2.46836390872,2.23761848557,2.41885969296,2.36272762192,0.508161558671,0.590138992775,1.03121493528,1.10234167365,0.926146424803,1.33503863901,1.17749089228,1.48878894412,1.43103441945,1.23125592847,1.62364221231,2.03308212549,0.973514445626,1.69088311595,1.47606327184,1.06048610543,1.26774168139,1.10204828398,1.4265683055,1.33466591432,0.539478631249,0.772476502065,0.921903797273,0.875826122064,0.0895315987298,0.137851673947,0.327797088242,1.06443825113,1.27434703233,1.41698102098,1.34733271759,0.985625000209,1.12914259348,2.00882415627,1.96242175598,1.73300599931,1.8216024004,1.59791619364,1.553833713,1.71835252331,1.83555509629,1.49357365456,1.46983162977,1.68364939523,0.715958399061,0.948251487118,0.823591668672,0.64799502201,1.08545745922,1.02755896126,2.67811597869,2.86835724998,2.87289785746,3.07601049864,2.33993349868,2.40693462402,2.63558623579,2.49463322079,2.71176455438,1.77092556584,2.00337323549,1.70664796972,1.62778226531,1.93596754464,2.09347795197,1.5277243242,1.58761099372,1.87774948053,1.68226789429,1.96065151405,1.82328089079,1.78984467507,1.71260908411,1.87922075866,2.62444258213,2.81122931044,2.99553578578,2.55642150561,2.81834768778,2.62662967867,2.13211709458,1.76745276656,1.98062982002,1.12495708594,1.45562363485,1.35664636459,1.3539172001,0.729157727476,0.531935703048,0.625937913466,0.762894289957,0.391524660781,0.314600928392,0.737166675241,0.674089966637,0.478384402152,0.290930734262,1.0267248652,1.11358749938,1.16258939196,1.37316397925,2.00580168006,1.79674329049,2.12955413302,2.02811677239,2.12481846107,2.00872828191,2.42642342061,2.36143083527,2.24969869344,2.07292286777,1.01616262327,0.717088536216,0.785989747102,1.14922105765,0.882725643433,1.08160587844,0.432245579661,0.413317952937,0.80375186523,0.659586646746,0.794396809397,0.634598863078,1.68355379272,1.79551428286,1.44970886684,1.35309487299,1.4792185133,1.6857176227
};
const double THETA196[NST196] = {
-1.39879016116,4.29290552688,-0.937064908269,-0.945764591142,0.869098980069,0.690132440686,4.00870550433,3.82380312656,0.133015465789,0.599313147326,-0.686521809384,-0.682918425682,0.172434683271,0.423138512991,0.411658556429,0.826635878645,0.992875148352,-1.23314119079,-0.886905027792,-0.96884804196,-0.869354478659,-1.04471898523,4.27325532862,4.50345754587,-1.35099218529,-1.53568741585,-1.09978895672,-1.49114157014,-0.622642130078,-0.637223824463,-0.0122066818501,0.286428223023,2.99803767246,2.96752777002,2.5384756761,2.74233298388,2.15165335374,1.90767868759,2.46926237165,2.68651765489,1.95644177919,2.53906368875,3.2944324046,3.76584122856,3.48887883771,2.7481727468,2.95028166459,3.14501287265,3.39061927511,3.12744171073,3.33923410152,3.50062744154,-0.480259347054,-0.280261383655,-0.0955986160253,-0.115072124391,0.560337364087,0.332811467341,-0.966088665087,-1.15358840735,-1.00046483975,-0.495079531284,-0.656905027578,-0.426289208525,1.15963296772,1.33027812736,1.62841713147,3.46452720013,3.87637290747,2.57254124801,4.42729833968,4.2979258923,4.05520263476,3.91130051605,3.37808403709,3.60568728296,3.66232850164,1.34933038882,1.25389783742,1.72062116747,2.5624323531,2.57770111415,1.30135084276,1.21086041804,1.55989690753,1.38396784491,1.59913908711,0.714237250946,0.678104317038,0.891467913842,1.16206278221,0.980860351692,3.7366501396,3.17053219172,-1.1609736903,-1.11483105316,-1.28202865411,-1.50653839836,-1.42055632555,4.68832861271,3.85934507402,4.07417898369,4.1234102221,3.70891434698,3.76977202055,3.97532239097,4.69341175964,4.49919725968,4.63742602288,4.40643541284,4.32299331985,-0.376787542551,-0.447800956207,0.126996343883,0.00339147810881,-0.246137658807,-0.0156009829997,3.45024745599,-1.52694920829,3.07068782174,3.97148448643,4.24701962691,3.94122471399,3.87663179939,4.50847308402,4.36225610912,-0.316895021078,-0.34084997707,-0.682444583324,-0.495236001174,-0.731694944088,-0.575115932759,0.938202810665,0.728783458353,1.07319603318,1.11700351484,0.839544182254,0.675566688733,0.0735329036302,0.294226246794,0.463895962205,0.335725758055,0.0408824865674,0.662965888283,0.739559114522,1.38708455103,1.13181546416,1.67766181592,1.53839731511,1.49197997337,2.78805152743,2.96980789241,2.78285090759,3.18564748945,4.4485884031,4.2418379763,-1.25866365282,-1.50771503471,-1.24790804871,4.48019766728,1.65781415434,1.3329621944,1.15233580815,1.53197984437,2.14960463908,1.96547091301,2.37163917892,2.37807131896,2.32927203473,2.34494634088,2.11105553679,1.90941226796,-0.144943351745,0.0670534847881,0.162117270986,-0.139931312373,0.392525929233,0.321756086501,3.00977844775,3.30463633459,3.02426735215,3.21838405974,3.53138794426,3.47196174541,2.62748473851,2.08062052909,2.50204962909,2.7205217448,2.18801705959,1.96178119228,1.75043866232,1.93156157162,1.77544514533,1.97567098299,2.16404739813,2.14589799835
};
const int NST210 = 210;
const double AREA210[NST210] = {
0.0617261268408,0.0572021838321,0.0585417938648,0.0579280011801,0.0628324889081,0.0600692862341,0.0609854756845,0.0591470501748,0.058467055142,0.0572211510884,0.058526820186,0.0584063297697,0.0629212944849,0.058485970962,0.0587998679634,0.0597919176565,0.0617154681067,0.0593629151904,0.0584048672317,0.0584563269676,0.0565036549011,0.0604426835554,0.0616212055909,0.0567587686408,0.0590195766734,0.0626737849368,0.0604578213511,0.0580331450718,0.0601845861277,0.0609650862119,0.0602381574602,0.0614350575904,0.057675434257,0.0614435647344,0.0601357747143,0.0606436947824,0.058516660023,0.0603949705967,0.0612807382314,0.058676514521,0.062078711286,0.0591027958568,0.0627753295078,0.0568733542969,0.0614661025879,0.0599697922713,0.0578262691074,0.0604992858605,0.0573446399649,0.0608952893807,0.0575454564564,0.0596462828169,0.0584359546775,0.0613956781304,0.0581551890517,0.0596317463966,0.0568177903081,0.0624661475829,0.0594039733269,0.0595157041224,0.0625432382959,0.0589886090546,0.0599593815068,0.0614006997236,0.0609971295995,0.059644376798,0.0575743926486,0.0576005519456,0.0614582203163,0.0579799506881,0.0572147898719,0.0632280691993,0.0573247291651,0.0577851114325,0.0609633833708,0.0598527056738,0.061395890046,0.0588336341589,0.0589329561808,0.0588594830734,0.0575033699712,0.0636153242894,0.0614667698898,0.059836059967,0.0609490477428,0.0599427215578,0.060992235703,0.0617394120729,0.0597898915972,0.0616086081686,0.0599585833968,0.0603997301358,0.0579381733046,0.0613763590138,0.0607981981826,0.060961085144,0.0584203973588,0.0599616864129,0.0572786402672,0.0598138660989,0.0588934323424,0.0600343770278,0.0602415630196,0.0583684733324,0.0607680389403,0.062993320632,0.0574086256585,0.0584923329581,0.0601812167544,0.0579784139407,0.0573779165296,0.0630017327435,0.0583718210939,0.0585171184189,0.058155534865,0.0613669118278,0.0579409057712,0.062817072186,0.0613784399263,0.0597049728596,0.0585632128005,0.0586823214224,0.0628116061211,0.0572428072035,0.0629258462517,0.0584716026651,0.0590894912888,0.062075774712,0.0605919214638,0.0586325221713,0.058894588923,0.0595104634257,0.0625367518162,0.0590212952343,0.0567714437982,0.0594129165014,0.062469960423,0.0614876120822,0.0600550869591,0.0604977268336,0.0617609855461,0.059978943823,0.0608883354762,0.0596841192514,0.0607528377946,0.0573074068185,0.059779199051,0.0578427640479,0.0621323486405,0.0578323006126,0.0587510828722,0.0629538807279,0.0586873422163,0.0627785760775,0.0568780687601,0.0579805899646,0.061716254378,0.0593746734986,0.0629321845602,0.0578386572947,0.0589624905788,0.0620820432839,0.0628970090094,0.0584960013579,0.056514592837,0.0615457759188,0.0604177830247,0.0604087851543,0.0616301921087,0.0590449330796,0.0601335773987,0.0576854913489,0.0580541040744,0.0604638351777,0.0602104325046,0.0609567743297,0.0612931762639,0.0603727593784,0.0585154840033,0.0602179813966,0.0606605959591,0.0607402992078,0.0624186049465,0.0596818112761,0.0605764843196,0.0586418303659,0.0629173567506,0.0584563520542,0.0596765598385,0.0599895918732,0.0624447935436,0.0586029827012,0.0616856101553,0.0575607114475,0.0597098614745,0.0583943402342,0.0567541791485,0.062639679851,0.0572141888902,0.0632281967766,0.0584620551142,0.0613922234501,0.0591338295615,0.0613816159532,0.0574750795995,0.0635785441598,0.0578159100694,0.0572651244042,0.0628414012199,0.0587136259924
};
const double PHI210[NST210] = {
1.64205163325,1.69576891668,1.55302696835,1.65786003915,1.81035172201,2.95259004663,2.1249446318,0.741493568919,0.723553593224,1.93599048719,2.14282114279,1.25007811366,1.04182127262,1.02635892657,1.89145345108,1.79361677253,1.35938818867,1.42485102221,1.14838278674,0.99705814157,0.879634603933,0.661399804237,1.19669679328,0.901890653771,1.25556457096,1.09770289637,0.579064320031,0.621791804787,0.844020570294,0.984616886048,1.33441999678,1.06374203844,0.964463053263,0.832904133211,0.787902716094,0.384126785123,0.193770593424,0.230221614714,0.0258511719668,2.29424459936,1.57959835114,1.66096165612,2.02038929766,1.87437724004,2.7967870441,2.57806523377,2.54229714419,2.74506583765,2.56484307545,2.76896456441,2.79822718898,2.40784507977,2.39643720059,2.3985253715,2.01370066215,2.17944064897,2.24307873494,2.16227518747,2.26993357228,2.49615785582,2.59775839819,2.44354220202,0.689805061893,0.57833006518,0.229284323085,0.360440748487,1.0073335915,1.41544068882,1.36449124173,1.28860835751,0.959186224399,1.07431141218,1.3581705353,0.934410333228,1.24797450007,1.05837374614,1.18734698209,1.36397470589,1.57816229938,1.21923419499,1.55309323497,1.57152650421,2.17261512819,2.38703490527,2.39338068556,1.42189920262,1.40660925281,1.7655980271,1.57984248649,0.806267324898,0.818214934415,0.596523173251,0.386029486161,2.73802075954,2.51135842722,1.72581766695,1.45542742879,1.51104402873,2.19551383769,2.07767437816,1.8662363286,2.1120863193,0.924544541244,0.690862683385,0.463363640366,0.815794901293,0.763338309699,0.575726556235,0.39331749424,1.9457428196,1.32072054276,1.16256974512,1.21952868619,1.52597051393,0.397865345695,0.623162592102,0.528110489743,0.336544697462,0.771426356384,0.723598572609,1.64128627014,2.0707360693,1.92155721418,1.72141391838,2.28106769262,2.40959460303,2.28062500769,2.47147745477,2.51885325753,2.33072695699,2.79251702411,0.616314122133,0.806705678975,0.815716331747,0.661954521122,0.405339624566,0.4521778649,0.925064218937,1.0589084659,1.03320964047,1.28856108935,1.39045917049,1.26440078704,1.0242404107,1.19744440575,1.03369958106,1.21646246586,1.39237158135,1.40225505447,1.76758417533,1.93700633118,1.76454410323,1.9499660554,2.14730644024,2.13545656816,1.98608460922,1.6168700403,1.78783418139,2.05458452062,2.3685657813,2.00855332643,2.15563926497,1.61093369862,1.80538304526,1.54683911135,1.93510725406,1.84878497536,1.65814535928,1.09766452354,1.26262357329,1.14102277134,1.02812642169,1.44663233161,1.37207112602,1.33295478463,1.14864395093,1.89770419679,1.82155289681,1.74645486036,1.59454684036,1.52214661489,1.44352702927,1.75186435933,1.62439043882,1.72292328059,1.94695209096,2.07866750423,1.97770340891,2.69636664599,2.87665546543,2.63360042872,2.73120366038,3.09064928718,2.93583934137,1.67302751761,1.63464142831,1.47493025448,1.45193138294,2.18301658924,2.00211427025,1.82023680452,1.8367515343,2.19174625482,2.0262701945,2.59972261129,2.41393475512,2.24074845605,2.57216772373,2.37119677121,2.22279345708
};
const double THETA210[NST210] = {
2.3098846686,2.51498827854,2.68012833101,0.0253666627587,0.169392501915,0.657387339984,0.490992496048,2.65116816848,2.99039328198,-1.33637194821,-1.25929241163,-0.820476371327,-0.914252056679,-1.14541300435,2.61460431107,2.16523771779,2.05625646871,2.2600818858,2.00125526765,2.17173043291,-0.74576225749,-0.774975400854,1.37253440654,1.67259232958,1.61581745265,1.76047374954,0.966195650031,1.31010293167,1.39389491435,1.24123813693,1.25316102984,0.485401641265,0.965288700881,0.534975301238,0.805233885293,0.745276341802,1.21251649094,-0.764791583187,-1.12050850745,3.41360652402,3.05851654701,2.88457603863,3.00851756579,2.85098373261,0.161582322815,0.369567296303,-0.39571709708,-0.42610149364,-1.17299105175,-1.05040359745,1.26023224126,1.6191403593,-0.133349902,0.15804166089,0.0978082156619,0.257530292958,1.16067774104,0.919665482458,0.691073140548,0.68949601478,1.0575356908,1.27195547124,3.53384992091,3.21130754361,3.5834542682,3.03368656478,3.92616241998,3.77002143123,2.64946743748,2.43191979551,2.60811904911,2.40408063841,3.06261372911,3.06693442885,2.8588724022,2.844681848,4.07671837497,3.99066661754,-1.52993974539,-1.26792675509,4.10440742845,4.31203289817,-1.03235218752,-0.654603856943,-0.93371694055,-0.948376107971,-1.17259391141,-1.20673370066,-1.30175727126,-1.26120094063,-1.50510564814,-1.08064272864,-1.25879854111,1.86229151811,1.88769911124,1.95660042833,1.69543596408,1.90082692269,1.64348140361,1.8453758932,1.79774553277,1.3867140271,-0.463593331996,0.2993046879,0.285856421731,0.041182803929,-0.243671501861,-0.410145218339,-0.216522785756,0.916946204154,1.01696649562,0.873326483872,0.649257589157,0.956032860751,2.45251451828,2.41164607697,1.67153574443,1.8714005006,2.13046071178,1.8582050896,3.76128011224,3.85059706488,4.0269999738,3.9668915638,3.90980617712,3.67880926501,-1.4912014996,-1.51903458212,4.38233131068,4.19517607477,2.37620326197,3.83849032401,4.0337289192,4.30668850618,4.53228423379,4.00956877064,4.51110072448,3.50625848105,3.6827104587,3.28074139158,3.62143125874,3.42060521145,3.25877645417,4.42868725391,4.32026717414,4.67694501915,-1.49811204608,4.4350505116,4.65698916594,4.39365473246,-1.5703398017,4.61773603201,4.25255832151,4.34731261372,4.59255061866,-0.889545282254,-0.855347040364,-0.980104266793,2.49810713195,2.15703945805,2.24630581705,2.09035935479,1.53255344431,1.57641652788,1.32967977034,1.36736049108,1.13238464709,1.14075761621,-0.411900644574,-0.595308140516,0.277774073429,0.0706636747074,0.0726806696981,0.258746996198,-0.129780691837,-0.149468007419,0.535945714201,0.735798218433,0.381562620205,0.765355530577,0.420094078399,0.607744191893,3.60197558083,3.4114790067,3.24402822918,3.23324483432,3.42444692424,3.62831376894,4.22893605183,4.67549316729,3.74614924369,3.3674029025,4.22950188064,3.03273391803,-0.198591200116,-0.638277362782,-0.301397371083,-0.510682787489,-0.534757890292,-0.653251989401,-0.533215802892,-0.298009885792,-0.26480792881,-0.153162415167,2.62995761815,2.4684206133,2.63803785048,3.04010873968,3.12922806285,2.92481792802
};
const int NST396 = 396;
const double AREA396[NST396] = {
0.03196806835,0.0307724814763,0.0326670909823,0.0316753895894,0.03241593564,0.0318400794937,0.0325723045501,0.0316902612656,0.0313380298612,0.0304442548717,0.0329109704209,0.0316294159061,0.0311261854815,0.0324481846991,0.0302529332871,0.0299337495325,0.0336586239237,0.0298606799971,0.038943019973,0.0313518618684,0.0324459235281,0.0300835348858,0.032919542974,0.030007112045,0.0339456101877,0.031439248786,0.0311274136036,0.0308412242929,0.0332299213076,0.0318391625081,0.0307473344078,0.0327271256857,0.0320582010291,0.0317433101989,0.0315504238471,0.0315502765064,0.0329668656051,0.0307051346218,0.0314888481773,0.0326729310569,0.0313903090479,0.0328447962789,0.0312767914791,0.0317042423325,0.0328018064884,0.0310766125467,0.0317446089275,0.0327723364577,0.0316257100321,0.0303708758793,0.0309141591621,0.0310952382243,0.0302798893944,0.0308007312497,0.0327397848397,0.0315083013587,0.0325358857685,0.0319347878067,0.0321014582275,0.032970012598,0.0294522431313,0.0318511860402,0.0321735593042,0.0317112070203,0.0319092112013,0.0316329736358,0.0307040867842,0.0306476131915,0.0308413200566,0.0304029429484,0.0333360012636,0.0303345472719,0.0307816747325,0.0310187657823,0.0336805232324,0.030452737782,0.0308530647428,0.0314817165838,0.0324917977933,0.0321975864164,0.0322787063524,0.032131488421,0.0313014745753,0.032024567557,0.0323005973735,0.0308533426957,0.030761375968,0.0304687609196,0.0328390590568,0.0314926720471,0.0323383202758,0.031274873493,0.0319807975883,0.0319575858874,0.0299756554502,0.0326093302885,0.030577241214,0.0380165862533,0.0336345019351,0.0310158066808,0.0313364596216,0.0325033809997,0.0310069926698,0.0327023874213,0.0306648669175,0.0331308246036,0.0316587111431,0.0316290706979,0.0312239071564,0.0318444879588,0.0313310499878,0.0326993452984,0.0319956577793,0.0323353884764,0.031139279012,0.0318422796366,0.031488419299,0.0317694166571,0.0325892444505,0.0315655265794,0.0322149103406,0.0318590285214,0.0321988505034,0.0321150233477,0.0312783897417,0.0314978456415,0.0308145540461,0.0319389362847,0.0305842802071,0.0304751069434,0.0303407069125,0.0309307558749,0.0312477297644,0.0329290265655,0.0304135212529,0.0327095998468,0.0318167332071,0.0322522842709,0.0311297488753,0.0313816509232,0.0317180516934,0.0313433164486,0.031234905619,0.0328214865829,0.0312255669176,0.0332255183054,0.0327989491842,0.0309694878391,0.031226670151,0.0323111999794,0.0327167412032,0.031385334616,0.032328856459,0.0325014437715,0.0318304554517,0.0318672729691,0.0318016591845,0.0314340208606,0.0323390971949,0.0306674931114,0.0320663397708,0.0327848186549,0.0334842664009,0.031650894515,0.031044259039,0.032426730159,0.0318835323752,0.031932534153,0.032123778789,0.031383197724,0.0313208234634,0.0328927228934,0.0319576405568,0.0311663378929,0.0317523680796,0.031391973863,0.0309971828016,0.0323414232078,0.0315839127426,0.0324004692026,0.0314150856752,0.0307800163387,0.032834147999,0.031808738222,0.031655069784,0.0323372575461,0.03002487425,0.0316408645269,0.0319456214575,0.0320576490491,0.0324915309134,0.0310442404533,0.0314989764372,0.0311289313323,0.031855686058,0.0313448749221,0.0316085724141,0.0318854131335,0.0329953570563,0.0317759351331,0.0309336870324,0.0326655163441,0.0318016069401,0.0317647839363,0.0311175453967,0.0320308170714,0.032119204769,0.031264618296,0.0320172078262,0.0320723692976,0.0322087189005,0.0316590903441,0.0322845740305,0.0317335423549,0.0310281091071,0.0304268850935,0.0331252581373,0.0308080108274,0.0317667212385,0.0326650019839,0.0312366672035,0.0324600392685,0.0301425063795,0.0305081962146,0.0306387982171,0.0312662513038,0.0300178583765,0.0304862962875,0.0324863640379,0.0335447409856,0.0308724659125,0.0317489484094,0.0308301367763,0.0318638768295,0.0331208227813,0.0313004376747,0.0311332290901,0.0310870703121,0.0311057145924,0.0331623093442,0.0313980020344,0.029995772295,0.0324180209079,0.031055061027,0.030518750923,0.0329702883695,0.0310360502093,0.0328873948018,0.0305873140198,0.0322710005692,0.0309229268826,0.0328371562254,0.0315999428187,0.0322659138972,0.0312670341958,0.0311668524703,0.0326672952385,0.0297563832912,0.0336979069779,0.0315124209716,0.032117704645,0.0302264892837,0.0323117122241,0.0321733819469,0.0320926545123,0.0309395063436,0.0331193552439,0.0309339094277,0.0305028805452,0.0329795725317,0.0318733256954,0.0333498422757,0.0318489477896,0.032861365092,0.0312299493823,0.0312764709868,0.0325225197675,0.0330937604043,0.0306935680727,0.0312378311115,0.0322687370109,0.031857647371,0.0311325778664,0.0321099153684,0.0321593297224,0.0317731416173,0.0320959937696,0.0301597393625,0.032420414026,0.0304356824728,0.0328472759056,0.0313759407128,0.0317236405112,0.0325905593951,0.0310072231131,0.0318237805372,0.0320668938192,0.0320413439128,0.0316171356179,0.0324894629487,0.03286636986,0.0310258885552,0.0327809345445,0.031272363915,0.0325601836509,0.0326020913087,0.0313420807296,0.0316103856774,0.0318864546126,0.0315831993899,0.0323906971195,0.0328880274412,0.0315266328732,0.0320219870382,0.0309247504999,0.033227062701,0.0309841400221,0.0309614505782,0.0303308291027,0.0312634025704,0.0314136225711,0.0302883287319,0.0326226568884,0.0303145772644,0.0329859873399,0.0319066766656,0.0311712542463,0.0309737471274,0.0333330127418,0.0313757270155,0.030933370407,0.0326489853417,0.0333350285315,0.0316133563944,0.0307919537013,0.0326898482914,0.0317186371716,0.0332078927676,0.0310222651778,0.0326850446859,0.0314299624938,0.031412241056,0.0327099745256,0.0310583622241,0.0322798738471,0.0316147893588,0.0312112154822,0.0329953333098,0.0310051159533,0.032236563216,0.0317650427946,0.0308034153633,0.0325879614426,0.0308239041695,0.0305579741665,0.0334965959073,0.0304723714499,0.0317272809071,0.0323531238259,0.0311920205473,0.0323627164706,0.0326259036942,0.0307573090302,0.0318530716458,0.03230015494,0.0312356351217,0.0324697891176,0.0309473562468,0.0305052914482,0.0333881565102,0.0327027978552,0.0304401523955,0.031966884925,0.0325524307364,0.0319887962319,0.0319682287202,0.0306708152369,0.032373562358,0.0312290681946,0.0317476091343,0.0327822735816,0.0319771327094,0.0314941880356,0.0311844250801,0.0327073658651,0.0308447664465,0.0305961093274,0.0309767782876,0.0305810178556,0.0308007887344,0.0304984092436,0.0308613805317,0.0305237462805,0.0305747855136,0.0306106529603,0.0308269037684
};
const double PHI396[NST396] = {
2.31176052497,0.696785381799,1.26730066,1.41299632057,1.52601790063,1.50079731645,0.775639585955,0.435847923935,0.581910041599,0.837524756219,0.697660808152,0.650714932317,0.888189413513,0.812527781427,0.314181108795,0.391954236848,0.396118112416,0.0794623070853,0.202185899367,0.186753495252,0.338428563595,0.161379184414,0.30559673095,0.459391806863,0.517718908522,1.45387779152,1.2990637431,1.50525316265,1.49167317972,1.81030593945,1.04803871295,1.92814462286,1.66858401143,1.76512334192,1.67144971628,1.7909592956,1.48857132891,1.63425644758,2.17352033451,2.12458949333,1.65121572249,1.79754025429,2.34332732387,2.19737877394,2.12713449724,2.0968365024,0.854692620619,1.0124522328,1.15939952474,1.0030725586,0.916133241006,1.15632542176,1.17168419701,1.02711253342,0.948959210375,1.51270808094,1.52062129106,1.26831403289,1.40091050632,0.456965478185,0.32015255276,0.490129245876,0.346494294942,0.574989217298,0.429714156186,0.914059332287,1.14784167592,0.867337286872,0.858076781153,0.551464985608,0.613171705703,0.764042190623,0.54343606281,0.577929553359,0.769388604386,0.683596319248,1.35319666546,1.23906885126,1.35988061229,1.21740663206,1.64639883387,1.65326547226,1.78680610482,1.86253861326,2.02837239074,1.79138734028,1.65326858106,1.68881591235,1.13532036251,1.07443044207,1.17989900745,1.29301455888,2.15789536711,2.04144494827,2.12576615189,1.98020105939,2.37642869741,2.24309328244,2.33625527902,1.34741736534,2.05838246415,1.92267875337,2.19474801031,2.19810634856,1.59388777332,1.62267094885,1.71656412252,1.86400372621,1.77496575107,1.89426882882,2.31928601496,2.46260322377,2.1264833159,1.97150452213,1.94798592265,2.72232881227,2.57354541606,2.99603855532,3.00136900511,2.83796512203,1.75822014365,1.64014222598,1.89456770068,2.16307814052,2.43884813992,2.55653218888,1.98518913089,2.1277584552,1.01477773256,1.00822806796,1.88303141384,1.98576513015,2.05925892802,1.90971327622,1.5202758141,1.6547449955,1.6373892574,1.5167944079,1.78174483646,1.79596176859,2.22172919178,2.07734269049,1.94646351176,1.94145923617,2.73608647634,2.73960850572,2.48295059454,2.59339797312,2.08325095155,2.22227743697,1.26520612642,1.22173063964,1.36026769806,1.12053712269,1.09829258493,1.22190257114,1.37776749941,1.26111725606,1.5712875067,1.0266920436,0.893336439274,1.3712570788,1.12483708553,1.22211089045,1.09306209718,1.2910478717,1.42476870382,1.11631511601,1.06676988672,1.449771098,0.936314060352,0.964648146386,1.07602787105,1.09163836884,0.659414320464,0.526859267083,0.811911689083,0.797927770303,0.704981606838,0.562873589921,0.829198058417,0.78924436294,0.876041791699,0.678644861875,0.632951094183,0.564831814146,0.123017001608,0.269966193751,0.169807589087,0.322465894021,0.389680059315,0.411664384201,0.728096159587,0.586058656447,0.864771919022,0.862014772549,0.732397018757,0.594739937965,0.846916496037,0.870863430152,0.992103011174,1.00062089176,0.425435021745,0.564623769417,0.439190189339,0.593368212513,0.715898571219,0.700351112435,0.72302764987,0.772486533884,1.01710743794,1.3113148681,1.16111297043,1.77144805314,1.91370255831,2.02419348936,2.04675901517,1.61847563217,1.62086056626,1.75689129124,1.87786559618,1.76519790435,1.88378732653,2.0190105833,1.95602062484,2.06905691542,2.21849590339,2.18381440884,1.38813271973,1.59049753297,1.43586247662,1.33497090301,1.64615624215,1.54390315194,1.4951636962,1.5488616194,1.59729132853,1.70338407446,1.75079233708,1.80424877721,2.33167022,2.41070695686,2.30782548391,2.47249915878,2.13177411287,2.27635980261,2.04068949643,2.08062867781,2.24564024092,2.26920588791,2.34907929689,2.49312295534,2.70098271424,2.85549736761,2.56078104076,2.74270059303,2.60280545857,2.49628252718,2.48347462691,2.62615241007,2.7635171918,2.59681628973,2.74937161546,1.73807928124,1.59827006103,1.58606200037,1.71818227886,2.15760627088,2.25560824354,2.2876639813,2.01493330104,1.13077690085,1.38084074082,1.38486134993,1.26490307779,1.12625865823,1.25577733428,1.93829459795,1.89712750559,1.81366226064,2.44165521039,2.29506571102,2.27697516462,2.33785138039,2.40594939038,2.54576442129,2.39082087556,2.3010866836,2.14458049228,1.91734856658,2.05930957492,2.16191845626,2.08503070171,1.9183449732,1.85114038973,2.48477118988,2.34601016357,2.59543757575,2.30787674523,2.53572503191,2.3920042891,0.954414959859,0.824344560586,0.673190988701,0.670602038639,0.988306605106,0.838811125455,1.11300122308,1.09417597452,0.818364169072,0.949826443206,1.84599357322,1.9996108456,2.01828907951,1.72218455552,1.75111256124,1.89308845029,1.3843921634,1.26619702982,1.52488866549,1.34459333957,1.50593400833,1.38588361215,1.5079723174,1.44893068153,1.20419342163,1.71582827889,1.83639514791,1.84883958191,1.69414129196,1.30283348825,1.44304154412,1.30142254085,1.57723027195,1.43214018816,1.56746223346,0.917284988669,1.1776549164,1.02047305606,1.50121846428,1.47917964055,1.32896052958,2.5053054119,2.35503579713,2.27035706687,2.24672756588,2.79547488062,2.95556649655,2.96396829628,2.81193859628,1.85270292566,2.10577150347,1.99284804991,1.84476876448,2.09978361572,1.97922051903,1.7438798564,1.48117556358,1.61891659507,1.7375966849,2.62401045801,2.71288124931,2.56723913424,2.53182872808,1.17255587961,0.980731507507,0.998114056929,1.29588473473,1.10587368579,1.24691718189,0.987199791866,0.926368717584,1.03933387921,1.20013412338,2.42405587056,2.42679633471,2.54892490199,2.69865938298,2.55773310729,2.70484906098,1.62875388525,1.53919788753,1.65858323704,1.38880328479,1.36364811454,1.48478363959,2.76725055687,2.82709730345,2.84275386461,3.00403327366,2.98319561957,1.13191993571,1.23385640099,1.22198071564,1.37673049277,1.38359121376
};
const double THETA396[NST396] = {
0.553414398579,-1.46680480798,3.19185953489,3.10677317961,3.1914837276,3.35686814715,2.98877217408,-1.12363409936,-1.03685227222,-1.15213283879,-1.22323609443,-0.784922264222,-0.956189863155,-0.786192405505,1.42448328374,1.01546851901,0.625931087037,1.5603395751,1.82782980013,-0.778899767247,-0.787527664044,0.151967437922,0.244571413549,1.63630584209,1.90426767204,1.50119676711,1.44614038868,3.83869608563,3.68213941956,-0.688405530599,-0.962261685846,-1.3985132466,-1.48158335601,-1.36774457859,3.11509809976,3.20145408165,1.66094721759,1.72747857406,0.601096228029,0.793747937775,0.0518067800135,-0.023995315774,0.326566922594,0.971106186227,1.30257443391,1.13356266269,-1.53727124322,2.68897157331,2.60231016969,3.16387657158,3.00082598453,3.10373314017,2.92844436547,2.85481736472,3.89876643038,-0.0361175165889,-0.199292669235,-0.263582709924,-0.313640943589,2.23000348396,2.40453454764,2.94252108588,2.88410511533,4.65906104804,-1.50862969316,-0.624328978866,-0.379284602795,0.136376804354,0.478483106896,0.545430844609,0.288013293243,0.297813293728,1.12726316592,1.41083317729,2.07712552284,1.8881072705,3.60932550961,3.36554549869,3.44382667866,3.69681232148,3.9233724526,4.08898861767,4.18461600917,-0.823341875558,-0.840767160841,-0.1686657108,-0.25395300564,-0.410208045204,-0.831207409441,-0.66379863812,-0.546562904832,-0.866031234745,4.50115287374,4.38150490816,4.68134619831,-1.56025542802,-1.44453481533,-1.4263910316,-0.948129849994,-1.02276893737,4.20569145034,4.11144237937,3.93137236624,4.1203233827,4.5516028652,4.40456821546,4.65183387708,4.60612501294,4.34342431258,4.44271297558,3.79838553014,3.86438577859,2.93649127591,2.99368205233,3.14422896414,3.73985387172,3.66561319498,4.403514793,-0.63482506635,-0.570652346497,1.96540432745,1.89300229567,1.86370187554,1.66402297435,1.88864950231,2.07936895242,2.66814277518,2.76752888127,0.22978027942,0.423915081812,0.682069637054,0.812087863168,0.467477359034,0.527251818838,0.280102616627,0.199462083245,0.514456237608,0.442639976718,0.433178848604,0.278857398993,0.209563191116,0.296567157691,0.0470280027431,0.205056844662,-0.190889463105,0.234021374966,0.220874767174,0.390384867859,-0.0541666553725,0.0109349217212,1.29421229937,0.968767285324,0.703499349572,0.529884700702,0.711574335669,0.796938677949,0.533972097744,0.448145691724,1.41232818553,4.27557202393,4.5780605498,3.92212964984,4.13854303376,3.85544725333,3.96063420487,4.45478988144,4.57927220951,4.44165399155,4.57666155712,2.46700475182,3.70611967315,3.33417783727,3.61455334211,3.44576673129,3.71379514823,3.54744827303,3.39290946941,3.60382603869,3.21392463529,3.23983594077,4.03012793321,4.4008242198,4.23358853084,3.95895414116,4.39654836058,4.15233339889,3.52804416946,3.3583250748,4.57855267445,4.46634264953,3.68679125539,4.09226279736,2.29437806227,2.40263137297,2.42136691789,2.61182346885,2.7579361343,2.6942941403,-0.0515576004261,-0.441423159555,-0.143410341807,-0.317789181651,-0.0909872633567,0.0130777875215,-0.465005775075,-0.547734726266,-0.375195568882,-0.148788093063,1.45699095261,1.68032124545,2.3490005665,2.38056839044,2.44645906181,3.8582771236,3.94849591509,3.69505415559,3.85859502752,3.59947056109,3.43780475179,3.68894621092,3.61771507026,3.36045358883,3.44989142829,-1.27465141613,-1.11946920972,-0.992644517625,-1.06290050962,-1.25902851931,-0.745539909745,-0.517708842462,-0.476936513068,-0.591714752689,-0.666926953687,-0.778805134969,-1.05006471464,-1.19716631209,-0.927287748597,-1.22000553298,-0.949186479929,-1.09582479067,4.22659748348,4.59642991522,4.43833062907,4.11595888822,3.5636897925,3.58868181186,3.40741731843,3.25923448804,2.48975625871,2.67483831377,2.32688176607,2.33797582139,2.03030197517,4.49782943037,4.55744195121,4.13849332495,4.27324831799,-1.26981907913,-1.02958796615,-1.44417960967,-1.35308933686,-0.820012678235,-0.909103968521,2.13866510858,2.22979382122,2.39358360541,2.47574703556,1.84788837149,2.15033055432,1.9627035981,1.94041362928,0.158729246705,0.0246872833503,0.195508723414,0.271046067853,-0.030925743913,-0.0864323733494,1.10579132549,0.960982580816,1.22000476067,1.65490840088,1.5564405091,1.35590924202,0.966784189508,0.738822605206,0.69232155951,1.18718019161,-0.729864010367,-0.701157454783,-0.273792064013,-0.234271968516,-0.378206453491,-0.549177468287,-0.555847263842,-0.426606211557,-0.0529160495018,-0.13109764163,-0.259967587619,-0.345798780264,-0.550599923544,-0.547114290947,0.794569446828,0.67108652452,0.738039153187,0.979922320882,1.35386554554,1.29438565282,1.23727018664,1.06640171106,1.08783369873,0.982242842493,1.36854555179,1.42006294332,1.58641163313,1.47088556883,1.62794705717,1.68936573855,4.07165987851,4.17981333022,4.15185609817,4.33175366093,4.31043686019,4.70002858749,-1.46300795453,-1.32555302809,4.70817953218,2.63784589704,2.89230859788,2.73184678687,2.9543395849,2.68795870798,2.6213022856,2.85129965886,2.70795558138,2.94072487906,2.86610758503,1.68676685763,1.56032717634,1.52833448263,1.98973596441,2.15496912228,2.23033779162,3.40447628604,3.40144280014,3.05113015897,3.2290986715,2.38125717074,2.44236412773,3.34760958725,3.38073004416,2.21955299147,2.21745625451,2.12528374601,2.39407330714,2.40778344334,2.48972267473,0.918253772112,0.777605240312,0.681601383135,0.753512919597,0.957832210892,1.64516785318,1.50216296014,1.22305437473,-1.44286561188,-1.2556631844,-1.41227329364,-1.31595026923,-1.13338656686,-1.15904240957,1.86550912598,2.04703799761,2.18285309119,2.134022404,2.76158631682,2.97991358575,2.59698272757,2.68500622191,3.14919709708,3.06219485542,1.00909268071,1.2555633819,1.16736648247,1.19429187601,1.03684533286,0.941636681709,0.956757715176,1.39815897235,0.514195987453,0.436231460551,1.57552687306,1.85308094522,1.98379325327,1.70770498523,1.75204248748,1.91639528377
};
const int NST410 = 410;
const double AREA410[NST410] = {
0.0299129824597,0.0307320240289,0.0309153261461,0.0299696286292,0.0319534183687,0.0294691475196,0.030023485182,0.0303026642568,0.0308562736467,0.0298191461686,0.0311331473389,0.030612002736,0.0307907608038,0.0319426978796,0.0309633508536,0.0306973265997,0.0301794958262,0.0305731407362,0.0311035896528,0.0308408536944,0.0309598498266,0.0309392594887,0.0318102128804,0.0309601109884,0.0299417024093,0.0304855959924,0.0313938609109,0.0302074249079,0.0306246022142,0.0318000823921,0.029998410983,0.0297420498881,0.0310306646117,0.0304270638651,0.0320652589326,0.0297625264347,0.0290255316998,0.0316085515414,0.0296115775697,0.0325747085322,0.0295452794979,0.0302729706974,0.0286061602708,0.0310961935849,0.0308494547391,0.0310935787133,0.0312587957644,0.0309131648657,0.0316958038622,0.0303013470206,0.0312245227667,0.030272519866,0.0309710741949,0.0303570951594,0.030893364684,0.0299311903796,0.0309800310946,0.0302318339392,0.0303718081532,0.0297274128963,0.0308124659236,0.0300514293267,0.0317377640383,0.0308039356793,0.0308764943404,0.0300617889642,0.0314358583758,0.029765762832,0.0316050043829,0.0304439199212,0.0301702717785,0.0312268294637,0.0303051984036,0.0307298918567,0.0306690421719,0.0306571926243,0.0304507918055,0.0302169963709,0.0316185008885,0.0314752830163,0.0315320734599,0.030902351624,0.0311638658398,0.0307933033015,0.0304434756777,0.0299480034398,0.0292859714715,0.0308249397375,0.0304907401372,0.0292091807266,0.0295931275008,0.0313919805121,0.0301248316218,0.0305154385749,0.0317658060508,0.0317187173641,0.0301446816851,0.0318398401571,0.0301952898698,0.0303795504453,0.0316384004301,0.0321805731835,0.0294645187812,0.0320609447599,0.0290485445939,0.0317996897304,0.0292303503153,0.02965929487,0.0332441387196,0.0309247859261,0.030816087616,0.0309984490658,0.0308799605778,0.0308306155927,0.0310129302208,0.030939213497,0.0319028673155,0.0291278976722,0.0294659816308,0.0300411609629,0.0315313513416,0.0308916659388,0.0306849685504,0.0315292465398,0.0298874496687,0.0306026312778,0.030470431744,0.030236039873,0.0295412956344,0.0317172390244,0.0292569707308,0.0322127054158,0.0297760026204,0.0316530681698,0.0294459780912,0.0310295751943,0.0306835665842,0.0311185578547,0.030069126698,0.0297826622024,0.0296354513127,0.030052286933,0.0295516536586,0.0316589367617,0.030056586263,0.0312072025853,0.0305813024071,0.0309921633675,0.0301914266726,0.030020424037,0.0316523873737,0.0295361647593,0.0295354979509,0.0299823489676,0.0319934365347,0.0291096087685,0.029923329285,0.031364411003,0.0316809046034,0.0316222272502,0.0301206268156,0.0298315945889,0.0291388312107,0.0299357224509,0.0312065035374,0.0302518564518,0.0301406174903,0.0308157270653,0.0308016705586,0.0306678812575,0.0302485507401,0.030792207603,0.029930570345,0.0311923445463,0.0301768036651,0.0298608399015,0.0295616841075,0.0313346099056,0.0301475700746,0.0312543461898,0.030176680937,0.0314060305622,0.0309896311177,0.0305024650262,0.0292679273851,0.0310759052233,0.0307527669866,0.0316129079446,0.030965034841,0.0313615577728,0.030669334324,0.0316084260038,0.0308816976349,0.0303145889298,0.0313658887989,0.0302449343788,0.0303395279741,0.0312519695258,0.0314380679724,0.0301170433977,0.0306686669286,0.0311095918031,0.0297020132732,0.0304355910579,0.0310651613969,0.0311802663682,0.0312936431483,0.0321310877235,0.0307458684122,0.0307460898388,0.0309950219528,0.0301877309588,0.0302151325138,0.0298547396812,0.0315109254777,0.0295627515854,0.0317062929798,0.0300104451315,0.0306010981062,0.0313361122384,0.0302241548151,0.0294489936194,0.0297907436981,0.0296230594953,0.0296774361447,0.0294817024298,0.0315989105478,0.0304229551128,0.0310896515175,0.0304268939309,0.0294646882226,0.0297483700194,0.0298926457858,0.0298403537265,0.0315778618945,0.0296071357864,0.0305690333738,0.0320621713813,0.0309874780337,0.0300963605887,0.0311910002725,0.0315032172952,0.0301617286562,0.0313181522078,0.0303186449238,0.0304486253852,0.0313165487644,0.0298299854575,0.0314776121318,0.030076500068,0.0300246910773,0.031328761322,0.0304409717027,0.0300274109162,0.0308390895042,0.0319496844781,0.0301255915414,0.0310881160854,0.0290815572054,0.0299847138934,0.0319559816127,0.0295477924393,0.0322169961222,0.0318203226009,0.0298167547018,0.0314530549827,0.0293415855739,0.0323375971545,0.0314010899119,0.0303801069701,0.0312816502259,0.0305253300803,0.0309496656844,0.030987357797,0.0299486991471,0.0311547833035,0.029439104906,0.0333708611358,0.0303004975337,0.03163179902,0.0300136282978,0.0311251878812,0.0309338554975,0.0298105010126,0.0317726110973,0.0298309022899,0.0299813436874,0.0313329131616,0.031225375632,0.0307152065066,0.0299870375341,0.0315669213318,0.0310069265204,0.0309555520175,0.0316736587337,0.0308349894336,0.0310102490455,0.0289813978977,0.0316981825778,0.0309273367437,0.0304082390044,0.0307878414466,0.0315796535706,0.0302561284289,0.0310037229568,0.0294316475516,0.0305244715365,0.0310213598203,0.0317998225601,0.0290569696971,0.0307081204205,0.0298625794615,0.0299585137948,0.0318982180957,0.0315864556666,0.0301196045651,0.0315333371795,0.0298539002282,0.0299331680664,0.0317187209179,0.0300509596342,0.0315098266571,0.0302036543084,0.0289282082694,0.0310956719125,0.030220154128,0.028631660003,0.0362327530196,0.0292309971705,0.030327431934,0.0295290340108,0.030852334661,0.029162731607,0.0309210964491,0.0310809249519,0.0302558775191,0.0308360409944,0.0311435721574,0.0303166325831,0.0306422912407,0.0295869804444,0.0297213858306,0.0317589796641,0.0312282754206,0.0310160578024,0.0310517379724,0.029765275103,0.0315166675688,0.0300934575307,0.0298321656549,0.0294149519979,0.0322128408144,0.0293060949493,0.0309099154567,0.0303071328887,0.0294991792814,0.0315871440393,0.0303780832523,0.0302445763883,0.030846907202,0.0309176055113,0.0311104505302,0.0302080288306,0.031145593049,0.030316578581,0.0314758520407,0.0311292945133,0.0304988808147,0.0309548730729,0.0304143310228,0.0295977924873,0.0315857518118,0.0296928972381,0.0314958394983,0.031716920616,0.0300696857084,0.0303309583233,0.0303121284687,0.0312810114906,0.0315982596429,0.0308405763402,0.0300214065963,0.0318272065916,0.0316762774121,0.0298907050404,0.0297776567928,0.029740321963,0.0314617719273,0.0313560539584,0.0286992805296,0.0313396541203,0.0308761220603,0.0310023500675,0.0303950501978,0.0297332552768,0.031305875983,0.0310950726996,0.0305543074724,0.0308583861412,0.0303963961715,0.0296806831435,0.0296144496653,0.030064767368,0.0298234603482,0.0297687222342,0.0349891118046,0.0291406322241,0.0330612047124,0.032101109251,0.0292492977166
};
const double PHI410[NST410] = {
2.86032076088,2.33372649195,2.39270650727,2.17095880499,2.09986127386,1.02546867271,1.31024657447,2.43342238627,1.79173846398,1.67890464929,1.75969664006,1.79066124912,1.91494110116,0.940336286455,2.71633997831,3.01004070729,2.45121661339,2.17449420354,1.52170772702,1.44658789936,1.43989679015,1.28039580316,1.60664897957,1.52788360362,1.56677129665,1.67129742604,1.61871858361,1.3686354429,1.54549369364,0.159865658595,0.313580782093,1.06012197017,0.901333984109,1.87878751841,1.90522748918,1.78942225291,1.65150105672,1.4468275287,1.47514798151,1.62088384372,1.73274664103,2.04048637281,2.02272377701,2.12668505097,2.15905869536,2.04180505934,2.39886561389,2.05047036351,2.31502816775,2.30842062779,2.17078754355,2.17976891404,2.05159221692,2.18253866454,2.05645186456,1.91929834065,1.92167664196,1.92719541175,1.98682771428,1.30542245346,1.1965294465,0.990888512766,1.02335571649,1.28305430709,1.34361701782,1.04199312027,1.12329549588,1.1075895259,1.24880738526,1.04164891818,1.01047609631,1.11303874269,2.13683172728,2.18119778581,2.24122454453,1.08939577757,1.08442051042,1.21503939567,1.21302939772,0.868688364089,1.78025211423,1.35851471797,1.49560277147,1.65113822451,1.64189595405,0.815755771957,0.775321193943,0.62250022047,0.505908519742,0.591882436589,0.511871970109,2.96908501772,2.86029685699,3.12233937018,2.58524880699,2.82968904342,2.29771051721,2.30970730926,2.57846828059,2.60264656895,2.42183801432,2.04579608098,1.76407021605,1.53051429101,1.61007600946,1.98549794995,1.95106622016,2.20124737343,2.06416156303,2.82424636905,2.87758578499,2.73642511102,2.66202131483,2.58864950348,2.55813856605,2.30405760619,2.44321254244,2.30294925327,2.46938397395,2.33851918771,2.33250364119,2.27371148644,2.30356110305,2.16788779118,1.34725854119,1.48620501891,1.52254367021,1.6840409908,1.69219249659,1.76865422593,1.49125774717,1.35784639397,1.53459223248,1.44833327653,1.05927565021,1.20141289931,1.21528406666,1.28694545706,1.750910695,2.02548566745,0.938702270104,1.51745693156,1.49838904852,1.75574775773,1.67878755971,1.6521757848,1.87996186966,1.74156396616,1.70810159259,1.94252021576,1.85949302424,1.17640623434,1.47052483641,0.692359418911,0.416952937705,0.558595939514,1.07248614926,1.20333748758,0.587623466462,0.438231935823,0.437977567753,0.711778020402,0.344752303086,0.115929713487,0.277764026521,0.352624656664,0.32910431125,0.26732464865,0.171614199479,0.115784841481,0.700331743091,0.853359054507,0.954043719559,0.97701118931,0.573109797194,0.638162615434,0.819487646631,0.689858184402,0.868451285806,0.79870585411,0.187170842199,0.435804837495,0.19287283202,0.338741970375,2.05947195081,2.19567519982,2.08142021113,2.19669779558,1.90736238483,1.89936524079,1.7698278445,1.64429462509,1.52070765204,1.55843375738,1.69814029353,1.81053256344,1.27183824824,1.37124557466,1.11847555078,1.33272717142,1.4436417391,1.51835388626,1.25182248952,1.37232578074,1.24033621456,1.16486146607,1.27271356475,1.45843964241,0.571738791938,0.40757593493,0.415501128845,1.77586403461,1.9056628229,1.62274614611,1.6283154483,1.74752758687,1.8823656108,2.71475360797,2.86886594386,2.97805015447,2.86426663926,2.68685634736,2.57816515396,2.58185138086,2.43835753015,2.43560274084,2.57776380917,2.70821935241,2.64988247059,2.42199369959,2.17494561374,2.33142270802,2.39281631121,2.16984404889,2.13485673842,2.23886007895,2.25789834379,2.61588181369,2.84837345076,2.69682958716,2.90518625826,2.07239273483,2.1183641812,1.81970842796,1.91929346215,1.86006245857,2.00496526063,1.24434125022,1.1053338667,0.99838662459,1.05224344179,1.20574955441,1.29221263235,1.51508007184,1.45274210653,1.42205653022,1.28605069723,1.30071504872,1.22674830347,1.0434215701,0.971027628111,0.819912727133,0.737554522105,0.966851885093,0.815721143614,0.831662049988,1.03608503295,0.913827687826,0.985553506438,1.06877780185,1.20789112877,1.09160233489,1.41027209908,1.36584087325,0.883036264924,0.803075042113,0.843906749739,0.701121062774,0.426625739452,0.335214366591,0.438416497734,0.58539159372,0.643598563992,0.576329712452,1.16537399472,1.12898260656,1.31310233373,1.41109599521,1.37081490686,1.23648894642,1.07085281343,1.18646701952,0.910652799269,0.869993236248,1.41606550702,1.64844716705,1.78191231395,1.52089109507,1.53329872144,1.58140856926,1.62046635907,1.8710972439,1.77008084311,1.3967733419,1.65401137452,1.5222646758,1.88623183657,1.98914959028,1.58909886389,1.73091366924,1.48698678609,1.5462871771,0.557980728209,0.598721761386,0.852512473315,0.753025665938,1.96630264159,2.10354115251,1.90359995656,2.43919181086,2.31774348015,2.32697875859,2.58920210037,2.00976605618,2.15946094387,2.18856206256,2.0551523511,1.88930233392,1.87127353752,2.77209248523,2.64466499815,2.70386153142,2.55246513174,2.45530368961,2.48833698897,0.684572258814,0.580040026572,0.419923108273,0.395615811816,0.893912057552,0.783783426547,0.531938716315,0.658400460486,0.57929318602,0.743935139391,0.823540196158,1.83390183046,1.69443023228,1.67337979615,1.79451062183,1.95724805639,1.93892667581,1.63063917333,1.73934106297,1.68395976576,1.52575120389,1.41571472184,1.46631404084,1.93144906618,2.02083275799,1.94579115163,1.77443313635,1.78623096889,1.70297033884,0.692973286945,0.685539930114,0.953129174065,0.834007320236,0.949800272898,0.824351613896,2.20172683575,2.46103018463,2.34899988027,2.59562178478,2.65512258381,2.71775677311,2.45312997451,2.49591691427,2.41137277295,0.809827908358,0.646774873439,0.586382804607,0.708095373932,1.00828756864,1.16314895266,1.28199249991,1.34663421161,1.29742609087,1.13758170663,1.04461891843,2.14953935689,2.00532184898,1.9211780992,1.98922021007,2.23015294664,2.3858308471,2.16701864746,2.24487050544,2.48845378061,2.40713436997,0.850596996327,0.895690384084,0.992532055449,1.06150034358,1.2687454915,1.12762840857,1.37909861426,1.37803186572,1.25560947976,1.12094523251
};
const double THETA410[NST410] = {
2.9837431682,2.40619034425,2.22899884976,2.42010341856,2.58663159374,0.546173902807,0.459303944287,-1.19926142814,4.64525696982,3.22218314742,3.35305779021,-1.47924550431,-1.37335227363,-1.16364269032,3.16628180938,1.47113485741,1.80737706364,1.59779274007,3.23667428927,3.11894734528,3.38156741894,3.41466447476,1.9775203127,2.97236961748,2.12504050577,2.23972689492,2.38800577825,-0.313903964523,-0.0613687240967,-1.20979759425,-1.37534818035,-0.257667629864,-0.234262057121,0.223223666592,0.0464667477931,-0.0253571411146,0.0525034027599,0.408708052318,0.251725550113,0.201840848801,0.2981795423,1.49382565854,0.770526172409,3.83138885464,4.01737549118,4.14334492753,-0.989347477331,-1.42773274503,-1.56645728587,-1.35098156629,-1.29804197514,4.40225995612,4.32212963588,4.5979970417,4.67724606112,4.41350389169,4.57610792061,3.63191851812,3.7934796215,-0.874486432958,-1.00534131185,-0.843684635847,-0.991982900044,-0.436195981689,-0.58553107827,-0.551467000488,-0.415787464308,-0.711174017051,-0.725138765228,-1.33323413534,-1.5267506627,4.62649777664,-1.11695032666,-0.802933252336,-0.967712082397,4.44825450759,4.09313513269,4.35386783935,4.18987890142,4.70595950785,4.33715603018,4.42574715021,4.34519376357,4.56181022241,4.41412932318,-1.19811506142,-1.41843667112,-1.4409217119,3.03751118982,3.30025202345,3.55530838217,3.49385280963,3.94967078424,4.11284020147,-1.28218775526,4.48663284158,4.07079843171,4.2828233929,2.67104042966,2.97703121514,2.6066668063,-0.0408785400594,-0.188738661302,-0.330484620367,-0.208569590762,0.31295858409,0.485780597538,0.557752786762,0.603360611145,2.46875287155,1.99307981006,1.77978504681,2.43767879992,1.94154791133,2.19771331714,1.26627760785,1.57126676712,1.4921811997,0.529636514932,0.675516037982,0.847251990341,2.0751022269,1.89169324847,1.77310490149,4.12135280356,4.20199639138,3.49370496065,3.47978886769,3.73608980021,3.61474420429,3.90203038447,3.95912420423,3.74822461155,3.64088062052,3.00935967827,3.29410868677,3.01665108375,3.14330243889,1.9366117951,1.83489976472,2.24523534636,1.71333493716,1.86838302354,3.08309368249,2.95089072321,2.66541832444,2.77132245975,2.79821111015,2.51117037093,2.61151713934,2.48424339177,2.46344329912,2.40753120408,-1.03993378389,-1.07380052783,-1.18414254499,0.370454929481,0.332537105597,0.930381105672,1.36484088638,1.00444268735,1.09408375646,3.06125645611,4.02570699056,3.90362657227,3.51911835928,1.63579231562,2.64974253733,1.4802757776,2.48976391893,0.00631890973032,-0.0621313854439,0.241665333323,0.0715307907066,0.434533727164,0.692519882795,0.340149737001,0.25209458791,0.546832003581,0.704541395524,-0.269847296575,0.336281223415,0.609758088592,0.664797667101,1.32246797858,1.20407739687,0.941611890906,0.975090244391,1.55376957215,1.72278039353,1.77464628131,1.66205129429,0.673000437169,0.515266180308,0.455888623009,0.552226272664,0.621699470701,0.72804810764,0.6707670527,0.886911433177,0.990529283631,4.63827621666,4.6763928616,4.57320052346,-1.13417972566,-1.29326944021,-1.43581421169,-0.874630115274,4.60090507231,4.19074055572,4.54105766048,4.18976706276,4.09079395475,3.98574711964,4.12579830656,3.88536730907,3.92400185883,-1.08144023816,-0.290511882345,-0.820827123749,-1.25936770734,4.49180226533,4.25526114653,-1.5481600191,4.61910718462,4.37594720296,3.99595388968,3.79139365232,3.50180177545,3.92089988917,2.72917891691,2.75725059561,0.326836490266,0.061637847864,0.241113156561,0.367719237259,-0.630930341958,0.561325108482,0.240508187947,0.270014844351,0.83323044637,2.29057986339,2.12058634389,2.20814767838,2.32842389524,2.05097937878,2.00376003751,3.85301652415,3.91564952066,3.79515277094,3.61687850876,3.573473061,3.68692532452,2.69400297011,2.84849752905,2.55992787647,2.58566650989,2.8688869731,2.73991197203,3.31130679346,3.1510325754,3.12367006737,3.30873979215,3.4751653386,3.50083746244,2.1066233498,2.53625440167,2.44033623093,2.83761504966,2.71841340211,2.31182510476,2.19542843845,2.14820743173,2.28367382195,-0.562700309747,-0.404974781129,-0.761281514658,-0.826055078013,-0.688424454078,-0.342849972729,-0.0398856530142,-0.149918692181,-0.402056482521,-0.631052468897,-0.131060922325,0.029177567406,-0.165234928549,-0.0353736418988,0.12970143971,0.158367140469,0.836655818508,0.944414062797,0.871238230225,1.03500255277,1.15531628835,1.50112584152,1.44657557236,1.40683892637,1.25430429326,0.934130871011,0.774161214433,0.81308151595,0.714173791146,-1.39369572818,-1.41777913391,-1.49788245662,-1.20964706014,-1.08623975124,-0.470461819171,-0.492603095082,-0.602579754255,-0.743167604197,4.04843620241,3.7727978306,3.85912253365,3.70959373106,2.91636491195,2.89795367643,3.07599725811,0.113013014077,-0.019508304982,-0.227601017478,0.0319228052722,-0.511166801204,-0.485264935045,-0.303035638948,-0.205522373214,-0.27826556799,-0.407280971984,1.06079234054,0.864916590209,1.43570405353,1.3943511884,1.16922809852,0.976403114042,2.15221008327,1.95174820299,1.99047191255,2.34933827555,1.91695489667,2.54376658603,2.52610927858,2.40556807116,2.83236219908,2.91367901679,2.76978973616,0.974456114832,1.03468809016,1.19146959722,1.28776983139,1.06656874791,1.22518423123,-1.26724795699,-1.16716523887,-1.01728743961,-1.00356833879,-1.13046658536,-1.24573257005,-0.93020441913,-0.798053957018,-0.654608654186,-0.90493450921,-0.641110061501,-0.759141559473,4.42083903302,4.18022981895,4.37294003615,4.49584265768,4.17705155655,4.06963370333,3.04705239164,3.10730372207,2.97901981667,-0.259553798775,-0.777883808031,-0.456091642304,-0.365173237141,-0.789733181177,-0.595945756372,1.74538133682,1.72889404508,1.47935483665,1.32201064106,1.15854682783,1.10539210198,1.21074709542,1.89000281801,2.02331941304,2.03993631294,1.90344784004,3.20965884447,3.50017530502,3.35615913998,3.21759067844,3.68799735986,3.71814115311,3.51566298287,3.36291510277,3.52223961718,3.33994765108,1.40522714442,1.59189348192,1.3143232722,1.59242212643,1.73821907671,1.73373541572,1.62661719098,1.47892946459,1.38349580531,1.43165172092
};
const int NST596 = 596;
const double AREA596[NST596] = {
0.0207418467233,0.021201950136,0.0218438654825,0.0217732927175,0.0221207973113,0.0201131008696,0.0203860530267,0.0209902556852,0.020508597112,0.0218105913961,0.0204798331283,0.0210479448125,0.02036959506,0.0211322163962,0.0213817298685,0.0212982959931,0.0211217750273,0.0213850109292,0.020441456647,0.0205447429056,0.0219673609047,0.020860910778,0.021640949461,0.0214113338626,0.0211028499496,0.0212318416095,0.0212735269132,0.0207806229143,0.0211703877243,0.0212552478533,0.0214813169977,0.0208663003006,0.0202065805811,0.0206930988773,0.0214787050283,0.0213728115806,0.0218785045406,0.0214461603282,0.020130378224,0.0221161865295,0.0206987692975,0.0215051539397,0.0217491700731,0.0218951799977,0.0202090651616,0.0212423274931,0.0212391153069,0.0210388860234,0.0250662157312,0.0213480891419,0.0209255316251,0.0218232953501,0.0198289127188,0.0211601384457,0.0211627300811,0.021664693345,0.0213748932633,0.0215525188781,0.0211633010486,0.0206516372086,0.0219123000519,0.0208046258256,0.021658860122,0.0207221290126,0.0202920103278,0.020156315849,0.0202087370285,0.0214632032687,0.0213915763145,0.0211147062941,0.0210158042314,0.0216834294434,0.021338371248,0.0201909128189,0.0199554707913,0.0208187807307,0.0211547302151,0.0220061689785,0.0203837657494,0.0219940685475,0.0202900844403,0.0201199840093,0.0208795601221,0.0203938627049,0.021844015416,0.0206600737104,0.021817609096,0.0216010885642,0.0205298903038,0.0206330582633,0.0206093977008,0.021830366254,0.0206959033684,0.0216138154863,0.0206170192284,0.0212564080689,0.0201126658455,0.0200899196234,0.0226014849418,0.0217698984954,0.0205815538055,0.0211516633538,0.0210243457752,0.0214192369633,0.0216518618548,0.0207378311901,0.0209453332386,0.0214574934937,0.0208411742325,0.0207048053762,0.021078135076,0.02133997033,0.0204749535507,0.0201349976221,0.0218844023492,0.0209210009207,0.0208031238994,0.0217649794521,0.0212197605595,0.021199123532,0.0211494931332,0.0211906041195,0.0209108484973,0.0220244088015,0.0205549852569,0.0210821893261,0.0216330502495,0.0211959439981,0.020785633518,0.0212415104961,0.0210603219935,0.0204974688762,0.0217780214715,0.0210977116444,0.0209727440926,0.0206269628012,0.0213499633192,0.0209569096193,0.020883064314,0.021359164437,0.0211564392895,0.0210635684069,0.0214502824725,0.0205188699007,0.0207409241181,0.020862684862,0.0209327555545,0.0214778383725,0.021133414418,0.0215579482905,0.0205679573015,0.0213455797792,0.0210311442513,0.02176870169,0.0212796765678,0.020648454705,0.0212926480985,0.0214391372035,0.0210703172497,0.0212942298901,0.0216945918486,0.0214948855878,0.0215030640078,0.0206321077822,0.020672778477,0.020863357779,0.0205406948095,0.0218141607065,0.0206741354147,0.0215479350273,0.0204634808851,0.0210982262792,0.0218407679983,0.0204241267557,0.0201218967815,0.0209788822376,0.0214824040415,0.0205377664873,0.0210534639703,0.0210424842152,0.0208641443671,0.0209028667192,0.0210234407763,0.021312051589,0.0213605961855,0.0207039405113,0.0206243579197,0.0216704010074,0.0206150023132,0.0218558898549,0.020540428959,0.0202912538541,0.0197941548104,0.0211369718065,0.0210663427603,0.0214144861662,0.021762901545,0.0212048291399,0.020967545314,0.0211800934732,0.021295652311,0.0211299021758,0.0212704070806,0.0208869366673,0.0208667709585,0.020874990895,0.0208121331011,0.0216065995881,0.0205298406802,0.0204564447156,0.0217263149416,0.0212079768379,0.0212815653793,0.0210296140663,0.0207588696376,0.0209189556201,0.0216919732292,0.0207489553815,0.0204067954922,0.0199048115822,0.0222200350448,0.0210116854451,0.0206142499328,0.021480588325,0.0203331983656,0.0211010497958,0.0212957771598,0.0214545984486,0.0205081747172,0.020670705248,0.0218712109857,0.0202615956576,0.0210518589325,0.0215918127593,0.0208831652388,0.0214032432461,0.0204362182033,0.0204195855663,0.0204010500316,0.0203964802398,0.0203040067456,0.0208515000933,0.0216447433341,0.0206809532901,0.0207117940677,0.0217202290861,0.0207456385724,0.0206832131156,0.0211327509732,0.0213444473463,0.0203826996685,0.0207446529033,0.0215719389215,0.0208455729093,0.0214196866494,0.0216189994907,0.0206235925823,0.0210709321712,0.0213027052198,0.0205450346838,0.0217910718146,0.0219793032797,0.0199174139448,0.0206709073495,0.0206684633531,0.0212291318808,0.0209276238288,0.0209354947881,0.021401773734,0.0209562085105,0.0213820518862,0.0198772489766,0.0201865613677,0.0211656011542,0.0205032043417,0.0217070724081,0.0206238555889,0.0202134266703,0.0205688950833,0.0202517515533,0.0218209443672,0.0220253297558,0.0210282218702,0.0206997322882,0.0214847205408,0.0212776280569,0.0205355355379,0.0209160355809,0.0215674019675,0.0217692509908,0.0207424517256,0.020740239109,0.0217252031075,0.0217418184476,0.0207665444631,0.0214117606414,0.02076082615,0.0205668539531,0.0215773968024,0.0209563309619,0.0205222521903,0.0201094680781,0.0218945397651,0.020584560879,0.0215784303212,0.0204219732554,0.0217308761006,0.0210510947189,0.0211640791235,0.0210409537721,0.0211551008733,0.0207725436465,0.0212373659923,0.0207093437287,0.0215964723895,0.0206731039481,0.0212773129352,0.0209609086336,0.0207617080963,0.0215332578891,0.0204779698338,0.0221042642324,0.0203987454758,0.0211364550564,0.0208446299976,0.0214744723703,0.0211509771786,0.0206179633594,0.0206993067091,0.0217122546902,0.0213212831945,0.0213697630531,0.021160343545,0.0210859865135,0.0206737055882,0.0217485837519,0.0206492129257,0.0212086430471,0.0205661733939,0.0215401377881,0.0214003879581,0.0210941656594,0.0208482702189,0.0216781914942,0.0206135596337,0.0216214773855,0.020869202357,0.0216294182743,0.0210187622978,0.0214810750615,0.0202470277924,0.0203811679926,0.0206755235836,0.0200916795275,0.0205826106231,0.020647435137,0.0206270464162,0.0218247330784,0.0217406686409,0.0215379691107,0.020860560772,0.0215121206001,0.0207946391322,0.0210453083964,0.0199256756289,0.0205552689397,0.0207019061094,0.0205886031534,0.0216287631875,0.0218554154658,0.020914289404,0.0216577990755,0.0205827174499,0.0212875586897,0.0206481886434,0.0211711164459,0.0206416626521,0.0212780780056,0.0211721532959,0.0204958396871,0.0213795364774,0.0211044660566,0.0213737313942,0.0207482169846,0.021701924445,0.0218169045909,0.020519433254,0.0210417146416,0.021255816412,0.0207879312156,0.0213590407103,0.0207862458441,0.0211916453854,0.0208614177589,0.0216200644277,0.0209331523072,0.0213862200112,0.0210703024863,0.0208984280014,0.0208539361922,0.02147103059,0.0210185131117,0.0217308340556,0.0204100607272,0.0209035696298,0.0214267373132,0.0209170840114,0.0214929970712,0.0209165052665,0.021489043737,0.0210776649502,0.0206077855555,0.0218748449885,0.021420458558,0.0206790512642,0.0216794836784,0.0204290372996,0.0208208103773,0.0214789786871,0.0201466637669,0.020527888285,0.0241279987666,0.0201251888742,0.0223808542966,0.0203139167625,0.0209070284843,0.0210048080616,0.0198959841946,0.0217151707294,0.0216703558263,0.021132682549,0.0214869327192,0.0209047883715,0.0208992090286,0.0215024570862,0.0213456085762,0.02120245456,0.0211521498078,0.0212664669032,0.0212673630774,0.0211473536224,0.0209310071578,0.0215314716255,0.020753158517,0.0215357423812,0.0209789941711,0.02017676779,0.0214919485027,0.0206327062931,0.0216306666663,0.0206718581538,0.0206151395307,0.0217901117801,0.0213205767553,0.0208663776861,0.021520928087,0.0213464402254,0.0208890226034,0.0210999226799,0.0216172510852,0.0209980682253,0.0207048819924,0.0212552281529,0.021165862964,0.0210737448675,0.0219084479488,0.0222956338005,0.0207931697646,0.0212921134531,0.021574366499,0.0208468067836,0.0211513337799,0.0212569683059,0.0211979854134,0.0210773674546,0.0214227319763,0.0207131737504,0.0211462614827,0.0208396563777,0.0215929241589,0.0216281397662,0.0209438335553,0.0215317096111,0.0208612502321,0.0205627836141,0.0212451178947,0.021280055632,0.0212040622042,0.0207005302963,0.0211010354682,0.0208747133587,0.0213915039848,0.0215225967828,0.0208716893193,0.0209662750115,0.021436759915,0.021616190962,0.0204829080489,0.0206325737659,0.0209525565733,0.0214752511621,0.0215969292876,0.0206669558721,0.0214264086728,0.0210032192543,0.0211784562129,0.0212406854986,0.0210578282687,0.021259471401,0.0212096364106,0.020943567449,0.0214757926981,0.0212620737992,0.0212156499948,0.0212091701733,0.0210762892179,0.0213121779658,0.0213363160825,0.0211912982648,0.021478587737,0.0212518441258,0.0212314183645,0.0207420380776,0.0208971452902,0.0202564170097,0.0219377043065,0.0205765195728,0.0215231820683,0.0215188711339,0.0204393938766,0.0211922412605,0.0211131528247,0.0218709385654,0.0204602810333,0.0214750338543,0.0199850603361,0.0197490609137,0.0214542663378,0.0246783417771,0.0203614225401,0.0207453662452,0.0214009013249,0.0216755866297,0.0210389380799,0.0207319113075,0.0215000425062,0.0209189149183,0.0207654187421,0.0210151048441,0.0212658558966,0.0204502502357,0.0217864672063,0.0200870459681,0.0221297305001,0.0203834747527,0.0212064121188,0.0207772099139,0.0215381842121,0.0207661215139,0.0217436159641,0.0205544653071,0.0208710508032,0.0219432935451,0.0199727946134,0.021250582563,0.0208922263608,0.0212567810996,0.0206732708887,0.0218831289338,0.0205911140836,0.0218271630055,0.0202705368956,0.0216144684835,0.0203731334772,0.0239316064948,0.0201628944461,0.0212399528354,0.0204454294346,0.0217395388934,0.0202848437942,0.0220188291106,0.0205863305868,0.0202972819792,0.0198929738779,0.0222577525772,0.0214443509464,0.0210664386242,0.0210282946161,0.0215184330406,0.0215768636781,0.0209416712853,0.0206067920161,0.0204333384524,0.0203415871417,0.0207553169186,0.0202440030227
};
const double PHI596[NST596] = {
0.927308635196,1.17223773007,0.135468336317,1.05741612615,1.32038937752,1.66465784303,1.70893057935,1.43484509412,1.10079756977,1.22453630263,1.24813462008,1.5040410818,1.84697176124,2.12338680198,2.0959145497,2.12155649852,2.00647264025,1.99410637066,0.0592679544769,0.645809940063,0.546640132369,0.940838509277,0.86640676925,1.3510551601,1.22025803915,0.71876568094,0.664046356302,0.259510715902,0.848612419087,0.737360561062,0.472236816019,0.362100208226,0.180112497766,0.203064714574,0.676824085613,1.03923054871,0.18136951243,1.00725138174,0.590034517691,1.9615370692,1.80993384082,1.93706261575,1.71490381639,1.7859090614,1.69918284462,1.65481719744,1.77369837351,1.87672263031,1.39030098694,1.61458696233,1.64169591944,1.29203276599,1.39711493172,1.52191109952,1.5085672189,2.05913661908,1.91735250152,1.69024135211,2.02831580199,2.10416965819,1.56878344253,1.26015528606,1.07078022662,1.1279816039,1.12319889009,1.25304567614,1.28844466466,1.91723785972,2.44859873794,2.51544060603,2.04528324352,2.2968738542,3.02440464313,2.47625996875,2.41774510566,2.49928626914,1.52749296368,1.54873639593,1.46572178021,1.34557017459,1.76389107753,1.83737409868,2.06925833522,1.87407934867,1.97713324676,1.8302091547,1.90064796121,2.09066605858,2.02837384034,1.69816110091,1.51245708636,1.63937577753,1.61502367188,1.56735324783,1.7458676255,2.08765877503,2.07282830467,2.28278281406,2.17881325602,1.99371099554,1.90621961779,1.99593876559,1.916057961,2.01294117197,2.17567078045,2.21654769162,2.26208969778,2.3739694296,1.33255726362,1.45474805378,1.5484378779,1.5606235702,1.57965121719,1.36872216743,1.46786435639,1.72231032269,1.98220834893,2.62960529741,1.90065428686,1.68451475109,1.78537136755,1.67853617063,2.15030842727,1.94393119961,2.07073953137,2.15481460982,2.10164707067,2.01129772785,1.9976032002,1.90358656384,1.79429693692,1.78018750433,1.87617044682,2.21890609597,2.23307670705,2.67699173078,2.79992603144,2.22824394655,1.29315403939,1.27109025853,1.08889500987,1.20200283323,1.06195451183,1.153678577,1.3416054499,1.58891940604,1.36868451877,1.49092887314,0.0915570524386,0.183685651144,0.314278725683,0.86250102226,0.766886262642,0.635281537212,1.04735371308,1.14997950096,0.828579374829,0.898688928243,1.00977523724,0.887131555667,1.0867516822,1.06885110658,0.309632103689,0.280623246416,0.936894493636,0.708333096157,0.708602141411,0.590882748024,0.577216284341,0.69024249463,0.505799832108,0.55177228335,0.381800803117,0.309300759968,0.334314613661,0.567212414488,0.493703883805,0.379424985415,0.871125400772,0.76097525697,0.969596893893,0.959549972968,0.77055977096,0.833212337179,0.848353525934,0.973500403043,0.963089169481,1.02670386135,0.498660937099,0.396927778779,0.251105325216,0.80319268738,0.724561555135,0.513771658459,0.437733491888,0.638734942099,0.685428993658,0.504696601397,0.623981422711,0.776990047826,0.648024044681,0.71349701883,0.614190864826,0.808226626016,0.893732771338,0.951069140178,0.921063345107,0.863573946135,0.752991618773,0.717574310992,0.798625692952,1.87152712719,1.84057587097,1.72643037545,1.78108929644,1.98490345145,2.06567329338,2.17485670278,2.02197491382,2.22372014866,2.15140202226,1.51450018464,1.43720095925,1.41398636196,1.85890401228,1.73983041751,1.63713219457,1.87893572386,1.50544839222,1.39693946407,1.5278401354,1.57252876163,1.28790976641,1.27202198481,1.16438368818,1.0625299342,1.37107290288,1.51674190521,1.38821643748,1.57653923399,1.48777933343,2.06382267622,2.12027372582,2.24586202725,2.127534978,2.25452285575,2.31747854678,1.93891349473,1.76037222829,1.87277721304,1.69813461545,2.64659497544,2.68921075902,1.48833030877,1.33372225324,1.30761952766,1.14845325913,1.35624818055,1.27827149779,1.18331083378,1.10122085243,1.17900030943,1.18223489488,1.06386544641,1.07993699312,1.96388429039,1.86306528826,1.73314142841,1.74712027079,1.83096343245,1.94540941618,1.59356842917,1.48119361528,2.43681603994,2.25938164518,2.22621998999,2.3087867954,2.61063815049,2.83217224202,2.62441435305,2.70927335394,1.75417728012,1.62452658688,1.63370577942,1.73552241815,1.85946156249,1.86896496533,2.20450397756,2.27731802934,1.62358778232,1.65122072865,1.67887049206,1.59962223143,1.8304803862,1.9572855618,2.04151702545,1.78287623278,1.70919066936,1.80544405322,1.78508350375,1.66260997017,1.58931624217,1.56287101683,2.29298738408,2.20345366651,2.41323358595,2.43616208289,2.39475972512,2.4563135312,2.57335492589,2.46056950691,2.40297387107,2.59043714506,2.65292818691,1.31558836848,1.19406283579,1.41229915935,1.42590822501,1.29395646087,1.18582083611,1.69382081414,1.68097411628,1.56920004898,3.02306558142,2.88875378642,2.29640293316,2.26603818426,2.50483379707,2.30983077504,2.43011800431,2.26949879514,2.33370569881,2.44734398658,1.4187098469,1.40431725281,1.31946264485,1.21409023653,0.998648065889,1.16590426587,1.05279617395,1.66107064409,1.57003104711,1.26943832907,1.28885271189,1.1977819672,1.15263567897,2.0585474887,1.92864987689,1.81832943508,1.83592113691,1.91059272127,1.98583088928,1.7861040286,1.78051859097,1.90313848071,2.45875819903,2.58224185956,2.57868102125,2.45938562487,2.35147937695,2.34810732359,2.21182457675,2.0929817858,2.07617921272,2.50788786657,2.43428761752,2.30817721804,1.41029500107,1.43776097866,1.51118927056,1.56253889767,1.65999726543,1.63582141825,0.895105707717,0.978956034709,0.770253416156,0.748606419684,0.853455881001,0.958335449058,0.42068463239,0.192232486986,0.35289862603,0.245257764633,0.528044001432,0.358330989486,0.409711353116,0.306576926712,0.560789281633,0.680785241521,0.488286779265,0.559429891057,0.739098872622,0.68685450233,0.952798569047,0.96655238022,0.878171852936,0.761383044363,0.738793047334,0.743088023164,0.844061433185,0.842497165714,1.14041413183,1.05402917481,1.07904562028,0.921238014851,0.805393871357,0.800522251408,0.916674088641,1.0262154135,1.0259082706,0.569718570206,0.438401018781,0.375116925638,0.638434251958,0.546103808353,0.444733100574,0.462187790223,0.588943772343,0.682556245357,0.657730781891,0.943211767684,0.859753483586,0.894707631511,1.11221890117,1.00994973787,0.861887313178,0.992981754241,0.924353402862,0.830801834637,1.39213622076,1.162433267,1.21225043124,1.32770289771,1.3498598414,1.23610150381,1.1920716809,1.1278394493,1.21850067255,1.00672223449,0.979335549077,1.07450284114,1.86369982167,1.93628159398,1.87896862188,1.75120777298,2.5875014552,2.37459254074,2.47002458641,2.35278858261,2.98812894527,2.80869673361,3.02261482888,2.90147461501,1.54384195569,1.67678194846,1.73268012225,1.46664458702,2.08920706635,2.00534918278,2.21385017428,2.03682332389,1.84200293396,1.88682979339,1.80340649409,1.68496040635,2.62535542863,2.6850292006,2.67970959725,2.79636516836,2.88611626364,2.82167490488,2.16874242596,2.25325476065,2.38185148281,2.4190760753,1.38809649486,1.46954053667,1.25691203598,1.81167175945,1.86474524605,1.88917127666,1.99581172906,2.07535013989,2.02084211958,2.33029015352,2.32294556125,2.12066990547,2.21962536552,2.11074552484,2.20220723443,2.85666578985,2.79099146919,2.60110334416,2.50328145448,2.18948942708,2.29644183791,2.08807274775,2.3048767833,2.98588711506,2.85286150862,2.78300760919,3.02711897235,2.55239219611,2.54303199278,2.63796799064,2.76380204277,2.76691686901,2.65198793939,1.46431119668,1.24695213502,1.59821314193,1.58700514664,1.49072494038,1.37177926276,1.36144813171,1.46931736771,1.51293764122,1.48595822776,1.57779130712,1.69502860809,1.72341563414,1.6328566329,1.05390777585,0.932667055512,0.993842529601,1.0797271028,0.869979961476,0.833353813385,2.07646794907,2.19687320273,1.97414417676,1.96363899339,2.19991760484,2.08975480348,2.17555821767,2.2882120739,2.24742814291,2.15426784757,2.38790790046,2.40639227873,0.538077008797,0.631225402822,0.422228872601,0.628222082825,0.416209440876,0.528550831863,1.13864813018,1.15161823658,1.35486689724,1.24539169369,1.36818621353,1.27137000654,1.23845806969,1.20402774578,1.29959644404,1.42276056265,1.36229246333,1.4519442854,1.65735288484,1.71380525508,1.63957082912,1.52488266536,1.45170184657,1.51060882605,1.2127048809,1.04443055156,1.08244313242,1.49432777388,1.41897362257,1.29385003972,1.44145787585,2.48881784416,2.60685680106,2.40161133997,2.43821633847,2.57685003169,2.66292409342,2.68404775747,2.81271423494,1.12706303651,1.24584686201,1.31877252054,1.2691968498,1.07235716226,1.14192911622,2.49158242461,2.60141674888,2.40571833322,2.61738875048,2.41269786557,2.51233223378,2.71863379079,2.71099725468,2.81569399097,2.91819854702,2.83164819419
};
const double THETA596[NST596] = {
0.942166650706,3.38270065383,-1.38324398335,0.95126396881,0.924889777421,4.20768646732,4.08253296898,3.36332080138,-0.147165166233,-0.183287958206,-0.305129582509,4.62709647551,-0.682661821125,-0.311362009689,-0.602972544308,-0.161453305656,-0.0835551115401,0.0585071118829,3.66532822379,1.88279984208,2.03282129726,1.21491764993,1.08086842032,3.25943847034,3.26479344633,-0.401699704169,-0.604266455985,4.6631874612,-0.748743757699,-0.782473117505,-1.44708461237,-1.33931209036,-0.661667753935,0.0398201680366,-0.193540568921,3.39249004666,3.4418055836,2.7155949106,2.24042140875,2.38885030346,2.21018271106,2.25221407652,2.29424011849,3.0861253808,3.00408438604,0.108633471278,0.0499597187199,0.121564349669,0.625399919123,0.482806843248,0.233655909523,0.41168224511,0.472673210181,0.286608965454,0.409207651665,1.48074284619,1.73053666346,1.69573482814,1.74696907144,1.62101324052,1.45383811552,1.05256313408,1.19661012197,1.07133678341,0.83658440182,0.828056186922,0.693164970837,0.992859142747,1.22631704653,1.4108147285,0.97347655481,0.925180812847,0.353156641877,0.710735317192,0.894834289538,1.05064747986,4.37277236102,4.24151590502,4.14605255542,4.1810943955,4.28855722984,4.07684782235,4.13176331483,4.20923559538,4.24774537283,3.85579019302,3.97083980735,3.86593046879,3.98527283293,3.86768624601,4.01749689159,3.98801993379,3.23924325853,3.35013886625,3.21386856361,2.601432199,2.44828765381,2.41650772218,2.35231569017,3.1309939598,3.03781274312,2.67791773611,2.89357337115,2.83022504949,4.17231610174,3.87922302005,4.04174297366,4.0850487193,-0.0985988918593,-0.148550524925,0.0417873601359,-0.082425574488,-0.338572477038,-0.348922809732,-0.277950187959,-1.51415959024,4.39718222935,-0.797717723181,-0.14844903619,-0.271778441176,-0.079590853584,-0.143980215312,-1.15511144846,-0.772731071124,-0.741332362732,-0.863469394927,-1.00970208933,-0.368176516371,-0.508431680263,-0.285338543159,-0.34288195808,-0.47421758381,-0.555201038914,-0.558739338552,-0.404533841776,-0.540502672583,-0.416867852903,-0.0892498711617,2.51533710068,2.3860739948,2.5920087106,2.61983956211,2.43966642072,2.33976620406,2.17224028451,2.25438588996,2.29838795862,2.33823888897,1.43579507908,0.617248909072,0.769242425713,1.88263340251,1.96964624733,1.67479561292,2.86736761948,3.14338246202,-0.407179256243,-0.246141195771,-0.264697498435,-0.574619615943,-0.00890028630505,0.274693162423,4.26488042193,3.82390996429,-0.877512031451,4.71034500711,-0.981405554344,-1.05161775702,-1.28724620687,-1.38121936263,-0.879947494733,-0.626290844289,-0.970831010681,-0.701191065661,-0.0133436557362,-0.153313779763,-0.38078166915,-0.362547335015,-0.0746059394592,-0.0307915942779,0.0424641397471,0.193120486923,3.13365233496,3.27790093015,2.98480490999,2.99749883472,3.2682427248,3.13692038268,3.82805169583,3.66172002489,2.9547003915,4.36203421266,4.01346201736,4.09594122771,4.3090981507,4.15202420972,4.3509423384,4.56230129378,4.54556535167,3.44198754955,3.49316835416,3.81932762169,3.7092842598,2.82654211243,2.68953353891,2.39264827747,2.22658479093,2.5169270199,2.46902106701,2.27582156265,2.15837895665,1.98543227109,1.84919293271,1.82663673728,2.08416034649,2.0181480119,1.89923967717,1.92781238402,2.15950551995,2.08338708356,2.19678525244,2.46061541763,2.6707438166,2.54900083387,2.46750602828,2.4166782628,2.49817037254,2.60434325838,2.91778803413,3.1466702388,3.14017114237,3.03184583678,1.90986884607,1.76952936461,1.68245789259,1.74227223403,1.71148331965,1.55706505787,1.57686509425,1.67628871643,1.77046034866,1.22378194836,1.09225714179,1.08169806947,1.35473328817,1.36590720088,1.22400283947,1.46807623342,1.57925898556,1.59103272554,1.45664221266,1.43459033093,1.69069357955,1.34482533777,1.14652712841,1.49260608941,1.304453633,1.36281557837,1.27326116994,1.53817361764,1.44031728909,0.482164634099,0.611451886891,0.414423196331,0.70011060315,0.341108715152,0.25522673031,0.435180587961,0.307539472121,0.523035717125,0.482618890432,0.603794799959,0.681879235106,1.55905710599,1.80324262839,1.64671480641,1.51919421152,0.727253857829,1.08257422191,0.988837180355,1.17635954512,4.40750806623,4.57783902848,4.45686411073,4.6505248455,4.59898007193,4.47567004021,3.60115359216,3.73982693563,3.77294922402,3.44644848509,3.65623057528,3.56060527402,3.30318010658,3.26971434631,3.37097634581,3.42561653785,2.8715962836,2.81117111754,2.67271293814,2.61848713648,2.81768647603,2.7017377705,2.59510816009,2.68341685697,2.66288977063,2.84994310311,4.2797891496,3.92836032411,3.96639207036,3.56875497964,3.74242709182,3.54467551237,3.76040593277,0.0228471244221,0.0745335954451,0.216880328481,0.0959639686318,0.277124805812,0.209491022372,-1.27431341349,-1.14504671959,-1.08460999022,-0.640258235264,-0.689652309689,-1.34543319613,-1.17152782385,-0.817151897286,-0.681809183062,-0.648722092328,-0.85008267055,-1.01294950807,-1.01394599418,4.41336759874,4.54768522907,4.31827980526,4.36357271727,-0.563729085371,-0.418270152025,-0.415355455772,-0.537139635537,-0.473615790368,-1.5510970432,4.59595223251,4.50752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};
const int NST610 = 610;
const double AREA610[NST610] = {
0.0207677809853,0.0210747716537,0.0206091699039,0.0202578252173,0.0205397776616,0.0208527439447,0.0204630724571,0.0202294860657,0.0211561416615,0.0208033913821,0.0203323388747,0.0207810350004,0.0201480008343,0.0207052864878,0.0201120589415,0.0209451480664,0.0210908208621,0.0202013109455,0.0202710790103,0.0198777876135,0.0204812884273,0.0207593996023,0.0200147292643,0.0212932341567,0.021096945645,0.0214408282899,0.0200136973805,0.0210245443352,0.0198200285058,0.0212877706111,0.0200790222703,0.021452264645,0.0199379861363,0.020167979164,0.0205696499718,0.0206985368707,0.0211151411668,0.0205850863504,0.0207789836225,0.0205298880571,0.0208127736778,0.0209681371254,0.0199979928524,0.0209388128051,0.0202202916767,0.0209872541622,0.0208005760986,0.020230019936,0.0215132975506,0.0217323457722,0.0197455743928,0.0212135724651,0.0207577934218,0.0216187682097,0.0206784467359,0.0207860186924,0.0206847693345,0.0205780056078,0.0197579690832,0.0205719089737,0.0202199839176,0.021021302343,0.021120411638,0.0202225190974,0.0211576908584,0.0201075424013,0.0207103506101,0.0201087631136,0.0197949082029,0.0209709982348,0.0209827957181,0.02036733974,0.0209037230934,0.0205685450034,0.0203517263263,0.0207273507237,0.0195916055915,0.0199571313253,0.0203819402201,0.0208645285704,0.0205965025775,0.0202542528056,0.0205370861334,0.0203596738013,0.02094749365,0.0217125525441,0.0213846782792,0.02052319795,0.0211185788681,0.0198649415453,0.0201815815903,0.0199398488516,0.0211138073257,0.0204495676098,0.0211191185607,0.0205033575853,0.0205200332826,0.020833532471,0.020246286595,0.0203979433534,0.0203659189971,0.020606632014,0.0214317616603,0.0201989686938,0.0200817179531,0.0212298675508,0.0201136179691,0.0201317506146,0.0206914254676,0.0208415969594,0.0202063651925,0.020833201621,0.0205263726401,0.0205747221332,0.0206394111703,0.0208350460189,0.0212321643216,0.0202240365946,0.0206545582027,0.020190716284,0.0200094273577,0.0212074245061,0.0197691968293,0.0205565414405,0.0197055424117,0.020711956953,0.0206797087767,0.0206186442765,0.0208007818629,0.0205247106702,0.0207111392458,0.020725284602,0.020480552254,0.0211625893784,0.0195386286093,0.0211519863253,0.0197128047629,0.0202273835674,0.0202047579594,0.0203208795583,0.019739467431,0.0215982191363,0.0196654034222,0.0201485881531,0.0211445386391,0.0200442622492,0.0211734950505,0.0205832043275,0.020836785601,0.0213581327057,0.0204323620222,0.0208987179756,0.0204790674308,0.020130410291,0.0206673443003,0.0207877083504,0.0200989093916,0.0216079560069,0.0214773474932,0.0197501114136,0.0202233666005,0.0202013166838,0.0197383368064,0.0211840570267,0.0205136246519,0.0206972855286,0.0207736490056,0.0204176477329,0.0210434561922,0.0204711977185,0.020114074343,0.0208471539924,0.020978753829,0.0205369020701,0.0207725199346,0.0205444065391,0.0207589815213,0.0202307966568,0.0195419632385,0.0204204345962,0.0206656335852,0.0209527818157,0.0208177003511,0.0199573864588,0.0202978202047,0.0207628403831,0.0202639721097,0.0209540914584,0.0202714140192,0.0210754239368,0.0212469427623,0.0203570200233,0.019857533814,0.0209830145473,0.0207637042707,0.0196728979126,0.0198073962493,0.02006660405,0.0197416120091,0.0195740297756,0.0196261494201,0.020229727592,0.0212181812832,0.0201752239799,0.0211803704674,0.0208838417914,0.0205445549365,0.0207762080046,0.0202533913974,0.0202140646281,0.021265597738,0.0203788595481,0.0205917287887,0.0206907921961,0.0208154282249,0.020945747319,0.0204887060478,0.019871419065,0.0198605125801,0.0217273408472,0.0216211102463,0.0210504837365,0.0210501781573,0.0197270939691,0.0195250695634,0.0200162680775,0.0204510478465,0.0243187525108,0.0209255229038,0.0210403494687,0.0214424283582,0.0206763495356,0.0204510167464,0.020978691857,0.020583768876,0.0206669512471,0.0203851399995,0.0209917316227,0.0207516610839,0.0207834772767,0.0208166730208,0.0205525482725,0.0198088365618,0.0199580969325,0.0210805094521,0.0192013758928,0.0213602017428,0.0210412335808,0.0207105460142,0.0203677967355,0.0210124223874,0.0209302435051,0.0212493077573,0.0203492770895,0.0202396271736,0.021123862135,0.0202305903818,0.021360940537,0.0200575836881,0.0208285591074,0.0208306019255,0.0206716299851,0.0201077964663,0.0198585799525,0.0213834297647,0.0207628160738,0.020743833842,0.0203987724037,0.0199648900088,0.0194389621524,0.0208250415798,0.020316055762,0.0206017642622,0.0206598789725,0.0209051329652,0.0208935023614,0.0205449602764,0.0206467371462,0.0207422468755,0.0208339222749,0.0209085188037,0.0204773037695,0.021306590143,0.0199808186429,0.0200091422145,0.0209172772676,0.0207283057056,0.0207602102717,0.0205278657199,0.0200383700445,0.0212220882174,0.0206905498621,0.0199379671655,0.0207559707219,0.0201280511878,0.0205533097965,0.0209000200442,0.0206762022234,0.0206588402945,0.0210463945502,0.021170589322,0.0209693590827,0.0204521176925,0.0197846162293,0.0216484684536,0.019903595555,0.0212136781588,0.0210708338398,0.0202580551751,0.0202691283126,0.0208748044818,0.0204232801379,0.0211161579187,0.0201373209773,0.020281696002,0.0211509484449,0.0202601497503,0.0208567909441,0.0204836964306,0.0198263322801,0.0204558719385,0.0197410675109,0.0205151695693,0.0202712751334,0.0208597901564,0.0207495297018,0.0205422959797,0.0201979951866,0.0209923246393,0.0202599855663,0.0203830865515,0.0211059848123,0.0200303803447,0.0208695149119,0.0205340823972,0.0198878896049,0.0215134500697,0.0206537543955,0.0205975833692,0.0208799837687,0.0198227119369,0.0207569142564,0.0208393598745,0.0209755078832,0.0209406795577,0.0197347754326,0.0206593556303,0.0200904858568,0.0212562508914,0.0209104137449,0.0205867015422,0.020473204272,0.0204571859174,0.0210939654758,0.0200602341252,0.0214342366515,0.0200757331095,0.0204358112019,0.0210200350047,0.0201748988299,0.0209688577725,0.0204457555492,0.0208974388539,0.0201563592242,0.0207627718587,0.0204538611723,0.0205631100086,0.0208730265267,0.0209614725605,0.0204111679549,0.0209755083781,0.0211594383275,0.0199089196407,0.021084943424,0.0206378682675,0.0208398933831,0.0206776458511,0.0207972426889,0.0202841542237,0.0204068395292,0.0209401485954,0.0202360991787,0.0210297831909,0.0208576762501,0.0203298993587,0.0203563918648,0.0207833075771,0.020548436593,0.0206704279946,0.0205484390304,0.0205880833422,0.0212276435483,0.020059184785,0.0207613323509,0.020031427011,0.0211267695341,0.020603962477,0.0205308698238,0.0203819774943,0.0202053594794,0.0213270609766,0.0214505643033,0.0198948634082,0.0200325145314,0.019829840412,0.0217554219822,0.0195834220421,0.0207659617522,0.0205662601955,0.0203999052423,0.0210043914624,0.0204489909096,0.020480794405,0.0203432777588,0.0209652242638,0.0198875060224,0.0200355383978,0.0209435877185,0.0206432298678,0.0199368834822,0.0204768324409,0.0217483101761,0.0213372062138,0.0209666539851,0.020342554713,0.019701060683,0.0235601257866,0.0192260138993,0.0212639225113,0.0211697715548,0.019478636594,0.0205406138861,0.0202444087725,0.0206478365624,0.0198250249118,0.0204185486423,0.0193123478314,0.0196666072187,0.0207062564945,0.019839372865,0.0204684687973,0.0210628000022,0.0217206918316,0.0199853945992,0.0208940582496,0.019667086008,0.0214693595792,0.0198803469916,0.0218769240936,0.0197369493672,0.021884165128,0.0195495716083,0.0206848062904,0.021133764553,0.0199957320606,0.0206724076389,0.0205042704551,0.0202670421371,0.020767808742,0.0205654833093,0.0204498976664,0.020487701463,0.0206559225101,0.0207699350036,0.0202156621039,0.0206961699766,0.0205359575984,0.01986758743,0.0208874222736,0.0199452352383,0.0210503615528,0.0201479712523,0.0207813477425,0.0198789827323,0.0215166257097,0.021347645334,0.0201265113859,0.0203563446896,0.0203001359391,0.0210678407563,0.0208210535571,0.0202868249086,0.0207593827972,0.0197371019207,0.0235967689255,0.0197761981649,0.0195295395137,0.0211507385832,0.020368764299,0.0208947369053,0.0206677598262,0.0207717397921,0.0205953314611,0.0198766419811,0.0199480440754,0.0198525122671,0.0200256565752,0.0203788271989,0.0213684182668,0.0199075587116,0.0208316081808,0.0200142595241,0.0203203552612,0.0212417459695,0.0206954341639,0.0206292664443,0.0204977186702,0.0208965571213,0.0204902433428,0.0208052573214,0.0204973194858,0.0210297361066,0.0210884626248,0.020258359635,0.0208779052136,0.0205639358696,0.021300896362,0.0202022720987,0.021337731307,0.0214280813621,0.0198553549236,0.0200765741969,0.0204233967932,0.0209063319843,0.0209989902649,0.0208428296366,0.0207910711173,0.0207791107456,0.0208936929356,0.0206430697669,0.0204225917445,0.0209360436975,0.0206412913202,0.0205810864582,0.0200491941537,0.0204246077246,0.0208931457016,0.0206446279579,0.0206979299649,0.0207686197975,0.0199156126268,0.0202003031917,0.0201460395894,0.0212866527455,0.0208687331107,0.0203629400377,0.0197238512867,0.0198248659962,0.0216122032373,0.0196667346172,0.0216351835577,0.0198751176212,0.0236738971628,0.0235865030156,0.0197483021216,0.0212928698826,0.0192627614097,0.0210165027523,0.0199527187486,0.0198792651072,0.0195232541811,0.0210632950245,0.0210985221489,0.0202050852748,0.0212557881969,0.0202189558768,0.0214966055934,0.020056678105,0.0203376598271,0.0200853842472,0.0212835381204,0.0202334733981,0.021226234922,0.0212365558467,0.0202479012644,0.0210561103714,0.0207954644707,0.0203630700312,0.020947033514,0.0203204821206,0.02036514406,0.0211067339343,0.0201329214731,0.0206659972286,0.0202804154226,0.0209609935376,0.0198134447597,0.0210206585773,0.0210325104228,0.0203062909512,0.0203715860388,0.0210913303159,0.0203295814304,0.0211895079005,0.0197921873649,0.0239928221003,0.0211639097295,0.0200065452928,0.0204551572947,0.0204125202809,0.0209083314026,0.0209348966447,0.0205305141602,0.0207815422081,0.0191459534476,0.0202138831417,0.0202082915799,0.0212284811819,0.0207502192498,0.0206348163171
};
const double PHI610[NST610] = {
2.21952532407,3.01343352775,0.897630559855,1.61520420282,1.74522092105,2.00987728528,2.1412421905,1.16778397103,1.09892627514,2.18348606156,2.26959697265,2.34841052678,2.52267386018,2.3978365385,2.96014849684,2.76643039601,2.51414653526,2.45196927347,2.31904263708,2.54038563976,2.41183100409,2.18803441764,2.05669682601,1.98982830951,2.25127582425,1.98689332948,1.86163286982,1.333631015,1.12670860208,1.13421745806,1.24912288031,1.237116683,1.07173207786,1.67315825307,1.535310841,2.06216853637,1.70541531647,1.76269253276,1.58422529833,0.99969922401,0.954700618919,0.684607003294,0.963944176724,1.79917136044,1.92931886261,1.52962185376,1.39316068331,1.30490518751,2.11416633378,2.24509046249,2.29738856006,1.15697005621,0.746797447024,0.894675686221,1.04002837904,1.31111109075,1.39242030643,1.36178164394,1.29416342476,1.52566847469,1.53708541517,1.29198541372,1.47405514638,1.35046557406,0.619015169665,0.548281707905,0.970694009713,0.722269069445,0.930274379874,0.813348608119,1.86604906283,1.83700869954,2.26397354458,2.26515365905,1.92514892447,2.0450042799,2.78639553561,2.66002681956,2.58723035955,2.46946480895,2.41324989154,2.21375589151,2.20625149702,2.32481899214,2.32274396605,2.98369591557,2.85539083338,2.95964325123,2.85400946644,3.08809113343,2.96619450932,3.04155763263,2.87021295344,2.75861862588,2.0526547544,2.15493888218,2.21587990227,2.13439241671,2.0195491859,2.16180625351,1.77762052557,2.584861623,2.63274406668,2.77756910218,2.75306560625,2.84057808096,1.90189348015,2.06299399409,2.25513496116,2.36770118671,2.04604271481,1.96762600055,2.01481499242,2.14426138403,2.23095235261,2.17910923435,1.80313095455,1.86196528819,1.83503684705,1.94586925011,1.82143297313,1.93298957076,1.72324080101,1.72426803643,1.50180010752,1.59973765658,1.78765981452,1.82482532746,1.67898429649,1.69866352423,1.35340015315,1.43113681663,1.61840565328,1.52137145657,1.65071881673,1.17160293048,1.10949242969,1.04046719457,0.937282477855,1.55981063051,1.33985242759,1.45350813828,1.54937232913,1.6787241884,1.66175511431,1.47398023417,1.37196584957,1.60165902645,1.63038718581,0.310707511686,0.56320192588,0.652996937474,0.542709780149,1.39087347169,1.54526054717,1.52125985553,1.13121973764,1.38287443074,1.18082457156,1.3049641751,0.726775223232,0.862991649823,0.911696221279,0.855595166164,0.769249226377,0.781798705614,0.886805326661,0.90350507267,1.01167034781,1.00702847161,0.612329829059,0.958394404278,0.828767988201,0.751459892857,1.10649403105,1.18186547999,1.13332889683,1.00605564839,1.47021528485,0.656247564457,1.57201890194,1.75307213095,1.71091016104,1.66973043128,1.91388374556,2.04477526603,2.05455832832,2.11886373766,1.92293184519,1.85548873426,1.6630813559,1.72629794071,2.2440461889,2.1833249823,2.30952283853,2.33373054585,1.17218771761,1.10288963942,1.09491546547,0.975513075498,0.96887643967,1.28395934001,1.35698907357,1.48708419617,1.54314978721,1.53887548637,1.35494576923,1.47591620625,1.47732487222,1.28892945951,1.34875032787,1.1698073104,1.21611431103,1.3453279259,1.42938528534,1.6588971491,1.53314328107,1.28015533789,1.1538262014,1.14465967779,1.07809011398,0.563067549599,0.609639912712,0.543130089441,0.415775817181,0.411651378782,0.614977577376,0.854336364956,0.52946699754,0.595602828191,0.788657760086,0.791220826608,2.39655289129,2.28132544013,1.91482691302,1.93254110181,2.04956446316,2.15311642083,2.22704409648,2.29522925469,2.11635542719,2.2342963493,1.68782401841,1.75623679648,1.87590477894,1.69891804009,1.81424861058,2.06147169262,2.18783645933,2.1035547222,2.02061511016,2.42887497073,2.59551550273,2.42293759079,2.46853052796,2.39180494735,2.64333740923,2.71379651224,2.84018476156,2.68182013699,2.79827202255,2.89441455582,2.63807547842,2.42811572022,2.51059945936,2.65945680497,2.54906560292,2.44743704221,2.76957172508,2.63690928887,2.33409678415,2.41059040592,2.36254649334,2.47466580177,1.84137847248,2.03304246082,1.97105986261,1.95820366442,1.82440971322,1.76873764156,2.24245456058,2.36577710417,2.65220916985,2.58632206066,2.57177305093,2.44772783929,2.38995590508,2.45241598187,1.55763887655,2.2631804396,2.14310239519,2.31657309377,2.35174130684,2.18678465612,2.10145610297,1.84044507433,1.79048269896,1.63799052709,1.76264149954,1.63374249052,1.85920532744,1.68481380178,1.79957151876,1.46137523684,1.58360941228,1.63846751123,1.39085549194,1.56355792932,1.43866545729,1.12515126247,1.21927007451,0.954954432838,0.880781299832,0.949486009553,1.09018231836,1.15107339984,1.08330505489,1.24488543514,1.14456949292,1.27243639391,1.18585745337,1.04395002587,1.05738820359,0.835720372086,0.902023593689,0.956880694613,0.991834034483,0.939978248373,0.832802805409,0.741023768606,0.788814855301,0.919617768842,0.980895955717,1.8176720056,1.69538726379,1.65406272263,1.73591592493,1.62327825901,1.60039010086,1.51807920159,1.48151583554,1.52446718669,1.44641979286,1.47767781896,1.35354531645,1.79571094037,1.98103232936,1.77272698083,1.8529127317,1.74886321291,1.7703672803,1.97019807832,1.84864608296,2.11151892819,2.00540426264,1.90011723171,1.89154820941,2.10625430623,1.99200527873,0.412227370278,0.629627327279,0.544732677449,0.42783966912,0.197943720333,0.484529082218,0.663247605226,0.821733902716,0.789693097142,0.73397499556,0.60467040689,0.563313322844,1.21745742845,1.34462386812,1.44838373848,1.42881574196,0.751679540216,0.741401790404,0.639284808011,0.532358269131,0.668733428268,0.552791419602,0.739207381778,0.928299112848,0.734376281313,0.804555509082,0.981278150476,0.917620440348,0.79621534409,1.28895466849,1.34850795007,1.16369807121,1.22302021179,1.43744176907,1.32208719263,0.854805263589,0.964478343097,1.0853723733,1.09720355942,1.65934759998,1.72282410334,1.72488732408,1.85297612127,2.03775832413,1.84420591256,1.90910083918,1.02907893259,1.137473864,1.59004461992,1.66520709296,1.21538983682,1.2551563112,1.38503941201,1.46578606924,1.71395394193,1.83926387302,1.88395158569,1.64801004592,1.69901366446,1.80939145739,1.46773340745,1.27801581569,1.33873661696,1.52795284164,1.35001605925,1.47051388846,0.231654642865,0.348834996557,0.442345129032,0.425934500519,0.766124599661,0.731126294658,0.684853656659,0.612574757495,0.774372786005,0.729069416562,0.904304146395,0.957694076649,0.851811071157,0.564829705878,0.66842389588,0.574566857925,0.670860647568,0.35375893517,0.448573133939,0.440416045803,0.0191838562154,0.105171124273,0.151539059523,0.225980790345,0.885897004888,1.00858497506,1.09863866461,0.885168939797,1.0035141187,1.09388100297,2.08391393569,2.20102885455,1.99222437206,2.01647335172,2.2310959758,2.13741994046,2.02903849075,2.10871886194,1.90660470814,1.86555953149,2.05766936044,1.93794517461,2.39843033838,2.27018200903,2.3062619488,2.22604606615,2.61869011616,2.66757037761,2.43546351344,2.48577581516,2.56344266497,2.4705178441,2.54503648121,2.6392495522,2.54176797903,2.65035788522,2.76457332316,2.7733021529,2.92869989187,2.81219546012,2.90288421776,2.69776148655,2.55633833611,2.43501429751,2.34871804385,2.36774328285,2.47896067389,2.58225810628,2.03886646849,2.16249044725,1.97310853225,2.1710144602,2.09651149359,2.00972537077,2.04894731313,2.4683296591,2.37462074724,2.43343338801,2.25983045304,2.30585801808,2.22440630726,1.52103165662,1.60270040944,1.93392974257,1.80944528919,1.72935321058,1.97873817299,0.739132314825,0.559224373235,0.688387692354,0.771189964139,0.525234035571,0.624824605802,1.38379597919,1.17580433451,1.27327104924,1.39774534326,1.1883187146,1.29925545895,1.11426513263,1.24249620892,1.31833042099,1.27179288854,1.14779312828,1.0653713946,0.438923369322,0.426899108782,0.356522948793,0.235041390253,1.18434376603,1.14469299508,1.27822349075,1.29239897447,1.0278569061,1.05406422383,1.29808244756,1.24257883294,1.14555081669,1.18196696898,0.98671361282,1.10641119874,1.64114716106,1.58402672335,1.469392808,1.3932295097,1.37341081467,1.50130725274,1.60573940538,2.13848486065,2.05126179979,1.97965694635,2.10143579593,1.89077696229,1.92697481152,1.22824736418,1.29651614707,1.416706291,0.515658945242,0.35474578614,0.483384283585,0.554518880167,0.349820441174,0.237282395564,0.416765919829,0.198636409592,0.306870215424,0.403234692323,2.78379662078,2.69277489213,2.7228110432,2.60090714106,2.53494232903,2.5721551665,1.77430587952,1.89859299635,1.86335546414,1.94206705517,0.325528678543,0.367695542536,0.124999495654,0.208552508491,0.217216362387,0.323402603372,0.873533354297,0.940486035267,0.994766146661,1.02428011001,0.777312820686,0.815377585252,1.25173447314,1.29519960809,1.45616189105,1.34525948313,1.6944852406,1.48985697151,1.56835421726,1.53932604556,1.66348230551,1.74060456345,1.43663411869,1.68094353437,1.62434584298,1.5041488292,1.61404439502,1.49028188634
};
const double THETA610[NST610] = {
3.00171533486,-1.51117382415,1.93952130626,3.15768192007,3.15351167662,3.13237969827,3.13152494603,4.7104685808,4.61239594785,0.876367372945,0.993357516514,2.99683230823,3.18870117641,3.15449576157,-0.7442240367,-0.276533438966,4.21169381737,4.0365796956,4.02174833729,-0.619629220133,-0.68245386358,-1.21218665501,-1.19602402981,-1.07970035288,4.14086939619,-1.31523021497,-1.31752169683,2.64480633801,1.51685896095,1.77818504783,1.70546762395,1.57703351823,0.910494451192,1.52813456869,0.596949353496,0.914786182609,1.63659091341,1.86040572573,2.23474885148,2.34012723917,2.21446064149,1.41191035076,0.829626589487,3.25594714729,3.24968437187,3.25733822414,3.24724119597,3.34594605907,3.87898766097,3.86864479159,3.74100807729,3.78321796614,3.55702149035,3.83114450832,-0.772513459317,-0.372055737915,-0.474685686676,-0.25976366254,4.68988018701,4.6995882346,4.01691407275,4.01346921962,4.1278901026,4.12973854426,-0.675735703034,-0.516374720434,4.64656489931,4.70587857947,-1.48352865462,-1.4405082396,1.77380920473,1.65745006704,2.3946434288,2.22540091415,1.55288887448,1.56528285518,1.32575099481,1.27078691717,1.48598935664,1.46877209947,1.28632523038,0.4049868702,0.723975283866,0.489241461064,0.660764018837,0.881670449079,1.0303373342,0.0152976699607,0.072552128006,3.60729081984,3.22657781153,1.60665986709,3.55835957598,3.36296680289,2.35965468766,2.45495036602,2.72584339894,2.61014899628,2.65346922385,2.87503511449,2.72398499101,4.65671602601,-0.756689491506,-1.2379559156,-0.638525341651,-0.889909418581,-0.0277595225412,-0.214431634368,-1.09729511138,-0.833132513859,-0.958881574049,-0.848003148966,-0.724555336462,-0.71125380324,-0.83450361475,-0.959220475724,-1.20442498974,-1.08598857869,2.33647337337,2.4132584487,2.59552372666,2.55412145179,2.51591253923,2.3959598921,2.42947334487,2.3447020852,1.97476735318,2.21240004315,2.05179906824,2.16342000941,3.13816341337,2.67755112207,2.59874492082,2.56446127431,2.72867770152,3.33439749463,2.58746159983,1.05993309828,1.3461958142,1.35841365261,1.50049334696,1.55756435389,1.48869046894,0.449972526728,0.562594127918,1.68427661715,1.75443939239,1.72288691696,1.83148547347,3.17337541646,1.45611685347,1.8045768629,1.6886042969,1.874738216,2.01913828449,1.91197380364,2.35474084008,2.40584145088,2.4837250859,2.50792881085,1.23454688046,0.935203317387,1.08713532578,1.22437514184,1.71471192246,1.54353868026,1.79323835878,1.49220444124,1.58369400192,1.71875604029,-0.313349187243,-0.679119333363,-0.735692756837,-0.619636217275,-0.268048293834,-0.382483265679,-0.504898615817,-0.532778319189,-0.0299165475294,0.405604560329,3.3610948911,3.46432032219,3.36346167897,3.57010879234,4.24823139191,4.2519879622,4.0164502476,4.12779306713,4.02498860371,4.13298428423,4.01868157582,4.12909985941,3.58389985785,3.26634007391,3.29189014061,3.45141286739,4.01429078064,3.89959806408,4.13041006014,3.93281487132,4.08908933146,3.56256240708,3.45719731373,3.46161424584,3.57034778916,3.79109500794,3.89762705813,3.902883158,3.6775985065,3.78281157737,3.6743913251,-0.730128226921,-0.607314546949,-0.588261380443,-0.686938272848,4.23776478314,4.23840906368,4.2412867859,4.47795591834,4.24200071409,4.36682433045,0.273714047996,0.0552796822129,-0.122033474476,-0.500504189741,-0.179379898887,4.32861209022,4.14800011911,4.50895847554,-1.55487774855,-1.27124451567,-0.911464368429,1.63578433074,1.60653749043,2.0179621474,2.14560861874,2.21393881041,2.14328751295,1.15045777746,1.29459957609,1.43910750171,1.44639891878,1.31986739607,1.42621593414,1.42942108223,0.0194251263892,0.0588453207619,0.171371379474,0.241332315031,-0.0676073319215,0.0246196402968,0.386010041681,1.0673535572,0.769797032828,1.10222327394,0.954812512747,4.24994855386,4.01942420925,4.00440966816,4.51624285625,4.67789081624,4.43703894054,3.80114464745,3.71868166183,3.85498366662,3.53040433208,3.4092066661,3.52413963817,1.69678389683,1.71580003727,2.68864505489,2.83126905338,2.50876684762,2.44348970425,2.81996498516,2.89660285666,2.79218479495,3.02330103021,3.03884735276,2.93991197523,-1.3646136616,-1.43133000472,-1.20156606955,-0.989101634628,-1.38680715303,-1.31548700916,-1.12966789665,-0.989960403451,-0.670334019421,-0.282922407883,-0.320700806789,-0.553864314213,-0.399331257505,-0.578439175048,-0.463991155056,-0.860184441703,-0.977783520801,-0.769752990772,-0.755638660451,4.7082911958,-1.56188427505,-1.44680594971,-1.44044704518,2.81281362434,2.82920971562,2.94417781954,2.91868470596,3.04711588394,3.03836397564,3.21558594133,3.11912608734,3.43144596607,3.56133102044,3.68161478467,3.43992048527,3.55733099508,3.66973917269,2.76160585678,2.72796204258,2.90125723649,3.00083015156,2.82669557981,2.96196597604,2.98157154954,3.29858107386,3.05190203848,3.1896342093,2.74253852333,2.80168400248,2.67584865726,2.49449834048,2.47206441543,2.58913783688,0.972816390267,0.998900557201,1.11563335907,1.20981680335,0.79407799089,0.911002945484,0.713000337254,0.956909505393,1.15808102135,1.08782730711,1.29130393956,1.36319990211,0.398345916183,0.251215007396,0.268726833632,0.191801694952,0.760633426747,0.644092193681,0.817103260177,0.850525012268,0.476969275195,0.39670936455,0.464598703561,0.599421645247,0.62849289513,0.680838484369,2.96171468902,2.74277017761,2.57397618153,2.64203280938,2.96321777007,1.24229567767,1.99976873949,2.20083451449,2.04774344853,2.34772485602,2.35382453224,2.15197798796,2.25921795209,2.28528193949,2.19993860544,2.0946342793,0.895856304048,0.701337512712,0.621559312739,0.766546946061,1.05413200368,1.01677712846,0.0284616057007,-0.418775392587,-0.300538418926,-0.44794775134,-0.27528801077,-0.139907656337,-0.135483545708,-0.14940286099,-0.0372534923761,-0.146961390149,0.448346831406,0.507592458504,0.537386852704,0.605293218995,0.687505496406,0.625132174663,0.492997981491,3.79682325765,3.91028460542,3.68316528068,3.91266241995,3.78105006429,3.68874477117,3.80445482437,-1.37939165461,-1.43170779425,-0.886141419809,-0.989219444904,-0.947552123386,-0.824288713059,-0.800946285074,-0.900220502674,4.34955851219,4.35576379339,4.4752030814,4.46184060049,4.58519834235,4.59178086517,4.34898345088,4.46312879005,4.35032685579,4.46081179644,4.57612466788,4.57543643674,0.102453386085,0.0784002942238,0.352355925993,0.647225433232,3.86490221431,4.02943818346,3.71056185442,4.10231932241,4.54209798279,4.37703272274,4.52814457627,4.38324839175,4.2819622885,-1.34861317084,-1.20871330065,-0.894848491161,-1.00639087201,-0.759715750829,-0.991961677134,-1.26560631321,-0.246684951344,3.6100213675,-0.457480356592,-0.892449948844,-1.16796891621,-1.23098668266,-1.14778095673,-1.00143648273,-0.922880830847,-1.00115617505,1.70378617349,1.73619628357,1.80634615447,1.93773310205,1.89546904647,1.99222580682,1.05081911089,1.16795409151,1.07409013834,1.19508333273,1.30510990554,1.30819033803,0.205847427992,0.149962841966,-0.12159043913,-0.0133693853433,0.078867164747,-0.181496054958,-0.100812024638,0.0625476517276,-0.379730295577,-0.300744472215,0.463310659293,0.825926390122,0.686260639882,0.311424945398,0.732861665401,0.409579777564,2.10676146896,1.99170163932,2.67507166534,2.22663716715,1.88619070054,1.82657919557,1.95389492615,2.13711935987,2.23405687129,2.12019820183,-1.43538462773,-1.46555450173,-1.55839347032,4.65664948378,4.37134448566,4.48647513287,4.60735698506,4.55165454803,4.66081228761,4.35857839943,4.57448106849,4.30312814405,4.40548030239,-0.45914998693,-0.555615151775,-0.618007022929,-0.63625072661,-0.536147316102,-0.489217218189,3.07121110767,3.33170560978,3.3810272355,3.25674669903,3.09338427197,2.96768689935,0.883620678876,0.857152559021,0.94224082776,0.75557303566,0.712108357188,0.670513831067,1.14764217243,1.08252888961,1.15462530549,1.29763130588,1.37254328074,1.29551622082,2.10095272289,1.80942304823,2.36947077901,2.37790687331,2.13454271678,1.89657580242,1.94264563383,2.05690061808,1.97958521283,2.10516566219,0.0842348594316,0.32792565044,0.232162961375,0.0998182481623,-0.00452951333123,-0.0186502041565,0.244254496494,0.357447288576,0.379746972031,0.177676511589,0.290148084585,0.103385336881,0.127051748803,3.54299066428,3.63709198538,3.36702444761,3.3825727201,3.47334732835,3.58573151777,-1.16523616731,-1.04225512313,-1.01919175167,3.97324152621,3.53481448071,3.53036615293,3.7320217605,-1.51934046717,-1.50155291138,4.45390548105,4.17478022961,3.91353080241,4.11677132664,2.74075733826,2.50583200739,3.03848072104,3.00810532988,2.80517278468,2.59009638662,-0.416179895026,-0.388177510704,-0.162379464262,-0.255827373333,1.60768461694,1.24655004854,1.24529499866,1.79989950977,0.699528347622,0.872182563868,0.446037166971,0.139906594502,0.399535269385,0.25711181834,0.33463617986,0.167608763617,-1.37243281719,-1.25696033176,-1.4632520374,-1.47379226978,-0.320568425102,-0.247166058464,-0.343558322924,-0.129471437774,-0.104149275659,-0.19842373178,-1.23587641147,-1.21269250983,-1.33196882893,-1.33948016771,-1.1058630531,-1.12143197334
};
const int NST796 = 796;
const double AREA796[NST796] = {
0.0159234609509,0.0163249587318,0.0160387337561,0.0151771900476,0.0152544541949,0.0157020354637,0.0157384164576,0.015847268734,0.0159226136745,0.0157914819581,0.0159468024879,0.0158947097968,0.0154574034904,0.0155680496508,0.0160995428217,0.0156516968255,0.0160601387404,0.0147568329141,0.0154352856389,0.0161730583588,0.0161618907849,0.0151312711975,0.0160300409708,0.0160563588532,0.0155332993719,0.0150003942028,0.0158189940377,0.015250998753,0.0154608430018,0.0162468207922,0.0154546623078,0.016152897284,0.0154074544035,0.0162560130167,0.016371694212,0.0154510414099,0.0158376525602,0.0159225409796,0.0157152303099,0.0151612342092,0.0154487352597,0.0151403300345,0.0167301961814,0.0150678715112,0.015552329899,0.0162005261775,0.015204850866,0.0154275994658,0.0150043328449,0.0153992293873,0.01598312999,0.015633608828,0.0159751219931,0.0155138837941,0.0162135804799,0.0155940804807,0.0160686924959,0.0154312949822,0.0156151704764,0.0154991326603,0.0153580721352,0.0162726039644,0.0162755104821,0.0157320947351,0.01575576399,0.0180831054267,0.0151194711095,0.016210370554,0.0156324826234,0.0158395248188,0.0163462529353,0.0156015316207,0.0153774351721,0.0161830202039,0.0156239521013,0.0158180233905,0.0162683830997,0.0161576378689,0.0156529362532,0.0157679615108,0.0159406489418,0.0149928658331,0.0148500445133,0.0153744397303,0.0181185880899,0.0156119402426,0.0154723185742,0.0159019238676,0.0157216075415,0.0161296619114,0.0155839402702,0.015247712917,0.0161370493803,0.0154358184859,0.0162759048164,0.0154415584359,0.0156049301862,0.0161247657627,0.0158535601651,0.0158197399483,0.0154745453798,0.0162504818172,0.0161884061265,0.016012035472,0.0155628449635,0.0159974262137,0.0158140548983,0.0157179325214,0.015934291778,0.0158425799752,0.0154704206227,0.0158749783461,0.0155687062804,0.0159921776154,0.0156782441193,0.0158876642939,0.0157752472423,0.0161819468612,0.0163908301643,0.01533768081,0.0156493009414,0.0155720743707,0.0155672254575,0.016012654376,0.0149344138372,0.0165187311131,0.0152687031188,0.0181962035553,0.0152416603898,0.0161790286195,0.0155201824214,0.0155036928113,0.0161858238715,0.0157512724339,0.0159829992807,0.0154817731473,0.0160174542155,0.0155904185503,0.0161161347456,0.0154882773128,0.0156977925575,0.0156833131359,0.0160483677892,0.0151624411724,0.0168420340772,0.0149270647404,0.0155084443012,0.0152289664927,0.0163039116243,0.0149691694011,0.0156095688915,0.0160355802786,0.0158530092058,0.0157295841067,0.015988388595,0.0157408775052,0.0154967518775,0.016144363945,0.0154491308622,0.0158407268798,0.0152337003001,0.0158732852654,0.0156508934928,0.0160867392834,0.0156449699033,0.0160357550591,0.0156794157438,0.0160554543961,0.0157520656802,0.0155385279907,0.0163224085989,0.0156749577741,0.0154788650097,0.0157976585719,0.016169747729,0.0156326164708,0.015681809074,0.0160314471688,0.0158128795637,0.0154483594146,0.0159530895864,0.0158483938194,0.0159328718034,0.015841931074,0.0158847885181,0.0159339302735,0.0157864556676,0.0159030459932,0.0158662047548,0.0160916940911,0.0155636882211,0.0155638040342,0.0162034469142,0.0154903508296,0.0161212489425,0.0155805377459,0.0155399931552,0.016258567265,0.0149213267565,0.0162135698137,0.0154796135392,0.0162432403425,0.015482682062,0.0155322460565,0.0162086655182,0.0150895483331,0.0156972581259,0.0159750748336,0.0160299535167,0.0166361818504,0.0165511458529,0.0156421901596,0.0158986511764,0.0159306863312,0.0155605521762,0.0160766456858,0.0161373657617,0.0156297790631,0.0154047731508,0.0162624669689,0.0158447513277,0.01549659947,0.0162618348173,0.0153599915769,0.0161030565437,0.0149935156132,0.0153451177304,0.0163539561747,0.0160038786282,0.0157452680288,0.0152600369064,0.0154142943105,0.0157358768454,0.0160847782608,0.0158080711931,0.0160901714575,0.015729799299,0.0158025320574,0.0157073260431,0.0157919348343,0.015932102188,0.0159108836242,0.0157732680514,0.0156625127745,0.0155908617279,0.0160813742345,0.0161034353321,0.0148823661726,0.0160375535676,0.0179638468386,0.0148593028342,0.0153038598466,0.0160208131799,0.0159895476149,0.015727187846,0.0154498706614,0.0161923493497,0.0154944463147,0.0156657286216,0.0153749113639,0.0161509526851,0.0155655813532,0.0161150394836,0.0155722227087,0.0155738528899,0.016017834562,0.0157819714045,0.0159186680253,0.0160670979316,0.0148374055255,0.0160344101473,0.0157524347383,0.0161347821173,0.0156410711192,0.0160738363131,0.015275982892,0.01496753902,0.0151610878774,0.0149166960716,0.0156251579002,0.0160146159806,0.015456853748,0.0157590901386,0.0156436643919,0.0160994025892,0.0158000145706,0.0157910790214,0.0161835678409,0.0162979273173,0.0155725486198,0.0154312869132,0.0161956057985,0.0162000370691,0.0157164776597,0.016094466538,0.0156065970461,0.015924713285,0.0154422712524,0.0161489139374,0.0154294501519,0.0160125033988,0.0154405214685,0.0160239756083,0.0155779539843,0.0159510406241,0.0158551635617,0.0158013185976,0.0153716293398,0.015672910499,0.0156343259019,0.0160891125104,0.0157720824188,0.0160100243752,0.0155129961721,0.0159718091092,0.0155424365008,0.0161833306674,0.0157766960841,0.0159354720238,0.0157834899367,0.0159082371419,0.0156834903396,0.0159836756783,0.0158674972567,0.0157927340636,0.0152185578784,0.0154859732311,0.0151909304805,0.0163280871094,0.015418728645,0.0154987969584,0.01611155377,0.0155999446722,0.0165793526732,0.0148896235163,0.0148859423617,0.0167316343106,0.015124411439,0.0151858461193,0.0185958397213,0.0161310540471,0.0154676070339,0.0153676053175,0.0162452519654,0.0159665972994,0.0157110364711,0.0155258673658,0.0158738112769,0.0158610926665,0.0155257706214,0.0160298986466,0.0158019266636,0.0157767593523,0.0155266685238,0.0156984670317,0.0160303831632,0.0153935163476,0.0156637115749,0.0151440658374,0.0162997466167,0.0152238194773,0.0161925979302,0.0161566192096,0.0156084019398,0.0160191980263,0.0157660226256,0.016128649029,0.0155474031664,0.0157693494239,0.0158080356686,0.0159660465423,0.0156076451513,0.015795501245,0.0159427057678,0.0158316270802,0.0158443038426,0.0161291763744,0.0159987820998,0.0159265689126,0.0159147268503,0.0158382804309,0.015930916249,0.0152509346707,0.0161908167117,0.0156385015996,0.0159709944629,0.0160282518761,0.0158996432038,0.0157851136728,0.0159248719266,0.0160563153865,0.0159902206977,0.0157224281721,0.0158224272834,0.0158686343687,0.0157177733359,0.0155639431617,0.0154712530698,0.0160798588183,0.0160742283009,0.0155482781857,0.0150677774367,0.0160630662526,0.0159978566521,0.0157003867471,0.0160272457359,0.015800013197,0.0155417724501,0.0161585112182,0.0151995481331,0.0163303923807,0.015218334413,0.015780556695,0.0154623738099,0.016118140045,0.0152646254978,0.0155350926349,0.0149895997827,0.0152817288925,0.0160141630436,0.0158988029082,0.0149114516276,0.0154758010801,0.0160467472156,0.015445705793,0.0154614479463,0.0161380152288,0.0158390099646,0.015475027209,0.0158761915425,0.0155526659933,0.0160726290914,0.0150972282769,0.0149027098674,0.0165008527779,0.0150311875508,0.0165371755855,0.0148021914416,0.0159949098892,0.0159059999093,0.0155781583551,0.0157656349096,0.0158666365022,0.0155066899423,0.0161865066907,0.0157663920336,0.0156563530335,0.015966345434,0.0159266557573,0.0158830639942,0.0157211528562,0.0153109373096,0.0150056701238,0.0164212039047,0.0157244995588,0.0147313148177,0.0160805666518,0.0151193698,0.0186884092301,0.0150726312946,0.0159083577536,0.0157577298973,0.0155746936307,0.0161467387505,0.0154828606989,0.0153898722844,0.0155344448618,0.0163279758774,0.0154504031049,0.0158623575203,0.015735385887,0.0161708739772,0.0157660610449,0.0156079588299,0.0160182786904,0.0151981156528,0.0153015656212,0.0152553084839,0.0150809623765,0.0156174536146,0.0165296445014,0.0159327027486,0.0172625356852,0.0155910792469,0.0160256244139,0.0160638008913,0.0158896485685,0.0158637167459,0.0158940903861,0.0158178367047,0.0158266167856,0.015899529065,0.0159604582895,0.0155264647067,0.0156001830234,0.0158195235049,0.0154248339942,0.0160953282042,0.0156448154452,0.016148209455,0.0155440058761,0.0162768938457,0.0155769490093,0.0161180591492,0.0154154087998,0.0157795016721,0.0159068299108,0.0155490054581,0.0158271592023,0.0157691686243,0.0159828750001,0.0162180841797,0.0154811177043,0.0154433836814,0.0162180787949,0.0156420629183,0.0161570056979,0.015397486933,0.0151680207687,0.0151993656069,0.015423020733,0.0154836796452,0.0149922489109,0.016225284945,0.0155442723434,0.0161339188724,0.0154238032779,0.0160818878914,0.0157014330583,0.0160643248738,0.0163914216728,0.0158680781785,0.015830764253,0.0154260641137,0.0162016954203,0.0152436353218,0.0164592246214,0.0161331599147,0.0159265508144,0.0156640555255,0.0160288056339,0.0158446852041,0.015417868476,0.0163011313371,0.0153367545766,0.0155110320994,0.016324103687,0.0168114291222,0.015971980298,0.0156799419369,0.0154125802461,0.0161395232567,0.0156160579237,0.0151690787305,0.0162827907235,0.0154875879326,0.0151753083667,0.0163157617063,0.0155816240819,0.0161288151358,0.0161147354718,0.0156448149167,0.0156082132962,0.0160432592684,0.0157180343892,0.0160042263498,0.0157154985408,0.0157141169715,0.0160051340205,0.0157877071657,0.0159727391139,0.0160365029693,0.0156908273401,0.0162691019971,0.0152963602776,0.015438899119,0.0157051194469,0.0160292002126,0.0155118705674,0.0154397685962,0.0161588037508,0.0155752148347,0.0161728003506,0.0160713731898,0.0156095365079,0.0161489847291,0.0155261526922,0.0158890901496,0.0159422289676,0.0156644591313,0.0157471701213,0.0161484951969,0.0155145046706,0.018535965342,0.0152063038987,0.0148952965958,0.0165856343219,0.0158718569985,0.0154423750815,0.0162908237927,0.0154535643305,0.0161707139139,0.0155614758281,0.0158941397884,0.0157263783003,0.0155200916122,0.0161030280946,0.0155715804644,0.0154674172207,0.0150557650158,0.0159375296198,0.015449714876,0.0157652755505,0.0158142737055,0.0158823973233,0.015669158998,0.0162636022646,0.0159086609836,0.0160305449415,0.0157875304593,0.0161802820173,0.0156637587952,0.0157195104588,0.015572153847,0.0160465191964,0.0156689451397,0.015740841241,0.016246236347,0.0151941939696,0.0161556927225,0.0152554338702,0.0157817186918,0.0157723905682,0.0155926664477,0.0161729550683,0.0155232771617,0.0160490575534,0.0152118521637,0.015326436827,0.0153928707374,0.0150934396472,0.0153168006884,0.0155494908057,0.0154594772764,0.016188766086,0.016110846746,0.016023790248,0.0156738847726,0.0154205049175,0.0162718219165,0.0162716964012,0.0155032507167,0.0156360066526,0.0160200952209,0.0148443369078,0.0159881184802,0.0159576368048,0.0156601028763,0.0156549685601,0.0156870420148,0.0156725280009,0.0161265879303,0.0156224378392,0.0155600434109,0.0160953599866,0.0156390732273,0.0160971914491,0.0154557025034,0.016196601127,0.0155530849263,0.0155913778283,0.016037871956,0.015696074668,0.0155292763647,0.0160943606307,0.0157807981773,0.0156509943887,0.0154717114823,0.0155209506264,0.0161960110097,0.0156340504373,0.0161398382939,0.0161020465777,0.0156737509478,0.0157215691184,0.0157206225335,0.015709075163,0.015902663816,0.0160964738285,0.0157262716719,0.0157996865242,0.0160438158695,0.0157811034304,0.0156766902556,0.0156668654672,0.0159750499105,0.01603265127,0.0156729933596,0.0157820906661,0.0160486513328,0.0156955191965,0.0159819573589,0.0157064368791,0.0159685536518,0.0154611678187,0.0162081561493,0.0162824790663,0.0155530184969,0.015627493332,0.0159231944876,0.0148767251278,0.0164642552633,0.0166307976187,0.0185191423006,0.0152498871408,0.0155354374448,0.0158756733163,0.0152292242891,0.0155582328011,0.0154562012856,0.0165043222515,0.015057576819,0.0158611702726,0.0153980191459,0.016150246917,0.0152981994741,0.0164069593285,0.0160154461799,0.0159647165216,0.0158154924606,0.0155866466185,0.0159884663011,0.015561699255,0.0156149721976,0.0159270255695,0.0157425174161,0.016040804639,0.0161162654513,0.0152187972754,0.0149259513664,0.0167424285812,0.0158529300714,0.0154727450508,0.0160587986785,0.0150847463998,0.0151186047041,0.015141970249,0.0149953128318,0.0155230558489,0.0157212890892,0.0158586393992,0.0159938746383,0.0157045519065,0.0163416286033,0.0155341605964,0.0160832179766,0.0154892007259,0.0162188138257,0.0162653853968,0.0155277670196,0.0160475151569,0.0155600626954,0.0154477870093,0.016244687873,0.0161110549667,0.0156171286425,0.015950540949,0.0162793356338,0.0162927269194,0.0155001795436,0.0157970368634,0.0158204600176,0.0158740974098,0.0157630224598,0.0155762234499,0.0161522567281,0.0159252619428,0.0158554546471,0.0154222847744,0.0158344335083,0.0154861174423,0.0162413732075,0.0161386813129,0.0155264133266,0.015823668196,0.0158220980699,0.015535632844,0.0158912933049,0.0155778694649,0.0158634259589,0.0155181108091,0.0161443098924,0.0157425035877,0.016117646071,0.0154494236506,0.0162024786467
};
const double PHI796[NST796] = {
1.50502206474,1.77037834345,1.60855157565,1.24942939558,1.22019678582,2.8611680822,0.561928575835,0.660436796879,0.733722933387,0.830460379455,0.857743324482,1.69105024214,1.64303696248,1.39622816391,1.29646897024,1.193661306,1.19449212828,1.74633285535,1.71805862414,1.87768165073,1.51622980026,1.5959319518,1.98806334681,1.7692503344,1.94714652737,1.83839314157,1.59731770107,1.58303622452,1.68681955003,1.6994873269,1.80859852444,1.99385724471,1.89608336148,2.4178583568,2.07884820436,2.1829785661,0.491502225487,0.416221146137,1.0083672724,1.10491419855,1.15511739327,0.955494195856,0.965504060792,1.06109438698,0.884093830605,0.784068862851,0.697360738052,0.0845002719227,0.0746914349686,0.182750021623,1.19141903646,0.992910158481,0.996619465718,1.37299416276,1.24987410977,1.13725172989,1.11717146962,1.33942919409,2.44691125976,2.47342252155,1.14773089879,1.24520422447,1.27475843668,2.76879424352,2.56285071911,1.83045966226,1.73817394934,0.258177417662,0.359319072724,0.948114556124,0.114716024457,0.310792293216,0.142256090827,0.248267539207,1.09769197862,0.995612252134,1.29149859351,1.26461750805,1.35071598894,1.41034707918,1.33103799311,0.968391956527,1.16601212929,0.985163636046,1.07633608798,1.79543376312,1.4976915053,1.62086518118,1.60504021187,1.88054216572,1.98451937081,1.27630615005,1.39280834173,1.49045484859,1.48869578536,1.39560312312,1.29393159952,1.29847973984,1.61292096053,1.60696809967,0.961342595843,1.06782004325,1.71829756098,1.81611862936,1.72157281934,1.02603563061,0.955811904279,1.09865048852,0.997000674252,0.993122393127,0.899049636422,1.09436509649,1.09757251105,0.910198096652,1.0070646277,1.51114506154,1.41804523794,1.47693234627,1.35086569451,1.3698399445,1.8018247932,1.85756438322,1.91130924774,1.94031064702,1.76901307289,1.86879897568,1.70978961359,1.72999834221,1.82267501522,1.81486200325,1.81795897383,1.71684072079,1.72029144161,2.19046599842,2.29359258119,2.45712212229,2.56529876704,2.39050827696,2.37525196307,2.31005763395,2.09720080586,2.16055952733,2.26342186684,2.05962489633,1.94752421589,1.92335301641,2.13964992054,2.00037935823,2.10370176006,2.82150684291,0.594126077524,0.629758808866,0.465354786421,0.573433477743,0.638373907734,0.609837941422,0.611945461427,0.596299891756,1.06001438551,0.792557871123,0.588407960407,0.481674818201,0.669805407134,0.678646290404,0.71928269884,0.621736209977,0.558232002773,0.615275710272,0.406034596729,0.451304986991,0.597163922185,0.540940836586,0.57162771745,0.474316112511,0.119794149495,0.137709553464,0.232192475317,0.299402273953,0.541302307222,0.392991053448,0.494073186358,0.643341620373,0.696659506377,0.796188322182,0.846444553905,1.00271004626,1.1051732229,1.37782430314,1.29176691898,1.08860396446,1.09200696485,1.18459065461,1.28008132013,1.48160573029,1.47022717541,1.56219405603,1.5863310428,1.67495850036,1.66201977363,1.31816866695,1.40883409297,1.39160985591,1.28749731508,1.20895893353,1.19521852213,1.85767551025,1.77824150399,2.27441117646,2.37658089554,2.12638352091,2.12323874561,2.62349543706,1.93393035212,2.13626194805,2.03838500863,2.04054810075,2.09673807066,2.83636316081,2.45458335792,2.4156846293,2.36482108733,2.43489813506,2.40614029147,2.29835376358,1.60722960099,2.12248042227,1.25432500981,0.922711945659,1.42223691016,1.5212758545,2.02028151298,2.01986221013,1.65932877048,1.56314665551,1.55843051443,2.47817806027,2.49041056185,2.58356512006,2.63871485053,2.74724861776,2.64564203914,2.54181748984,2.55001916004,2.91764373487,3.04286116665,2.95713501392,2.93847446364,1.5951165255,1.49359323848,1.69226642413,1.67759867753,1.56665957856,1.47951868161,0.898769111041,0.912719449136,0.714778576631,0.800635986705,0.797867417223,0.269774458352,0.219879152639,0.297818617571,1.01409960114,1.10700024181,1.01852899961,1.20831353327,1.04084087777,1.22631137837,1.14704352466,1.65946540414,1.63587959667,1.53638655294,1.45000238879,1.73280937263,1.72253800852,1.8113041136,2.19625944528,2.20903414263,2.32306055397,2.37858802133,2.29288617711,1.10439178256,1.15619400361,1.33328204732,1.25928223005,1.34452007618,2.00392200459,1.90895048048,1.68007770002,1.27214858815,1.20000040557,1.15924135349,1.12253622385,2.19294430745,2.19240839711,1.15681736751,1.12467910241,1.51590832935,1.62279009478,1.62594337924,1.53122218314,1.6228364501,1.51965278794,1.64211950064,1.56256820047,1.72371557668,1.66911613944,1.75083659723,1.4333843627,1.58547213321,1.61739821277,1.53774146491,1.40303842733,1.47572597512,1.91532076202,2.10347335205,2.00818094583,1.91508525914,2.00718163041,2.1019838988,2.13055361409,2.17844139455,2.26649612273,2.23965982971,2.07139156091,2.04981843538,2.38702205623,2.29093301632,2.37768971856,2.28901969831,2.55829480561,2.47557112532,2.5866775718,2.63123511299,2.58416783544,2.67903111997,2.48245485975,2.49112218354,2.54818392283,2.70850252354,2.64427636581,2.96558633037,2.86680489587,2.76832677268,2.74526053536,0.970154051297,0.989754647785,0.320795238266,0.424787079492,0.506804097796,0.4981374343,0.794087450254,0.892564642583,0.892226251507,0.692280141754,0.799167831823,0.6971592771,1.05445315648,1.12957669314,1.20681543624,1.10395835655,1.27491296091,1.24632043808,0.955826125097,0.923440081184,0.819007947094,0.744533469572,0.948778847422,0.908336156968,0.802550280298,0.735982021798,0.787545553982,0.893466625605,1.20041588373,1.40214246855,1.05696936885,1.06805472835,1.16060342698,1.18322157936,1.27401623512,1.28567627403,1.06476266851,0.891574656217,0.780883984108,0.776498251917,0.884370570379,0.974499035457,0.500931642276,0.439202943941,0.312952352803,0.408352622809,0.236755641315,0.3945342664,0.296662139934,0.806441544852,0.704376410537,0.91530635714,0.807919837986,0.752823655619,0.720553190589,0.964882331072,0.877665078408,0.860210769915,0.936623235635,1.30616505044,1.40619672652,1.95636700716,2.16667943777,1.51552197967,1.6032454988,1.38460039037,1.46773051747,1.38455389721,1.83396605076,2.0172674415,1.93494810598,2.18261678543,2.27734399464,2.20203683846,2.48036890782,2.67227852403,2.57770181214,2.4699975086,2.37242264861,2.84720164101,2.51617359842,2.53705676206,1.81761961998,1.92853157048,2.23345735057,2.32808767731,2.42874832595,2.43492407033,2.1935802673,2.32886741193,2.23975772748,2.12556679728,2.13983698809,2.65824280896,2.74677824429,2.92809632939,3.01154978145,2.94327860735,2.89976752655,3.03865571908,3.12224153049,2.82994497967,2.6892782514,2.7957596761,2.62229047182,2.73559186195,2.63874709699,2.30658680632,2.1510691381,2.25554874365,1.78828165622,2.3269498111,2.43056333119,2.35365496092,2.29354559167,2.46849252007,2.5128022372,0.809683765517,0.727723574576,0.769755010071,0.87238084176,1.37260724251,1.55942988667,1.72946771152,1.83433631656,1.65015899292,1.65025075999,1.93202948718,1.75041429829,1.83521136834,1.74603417589,1.47153041733,1.29638296386,1.36407014931,1.45981778157,1.37287113125,1.46085286995,1.27503671044,1.35682844473,1.25992320411,2.82709099004,2.6782680261,2.73457318128,2.63691772182,2.58434457496,2.62573163701,2.80724372206,2.74624813284,0.480512340942,0.394266169686,1.82981323983,1.83890618837,2.02306297886,1.93770507336,1.91092735641,1.99935482892,2.09809293171,2.10432852755,2.01371159219,1.91934652643,2.01738179681,1.90756342834,1.83151902845,1.80591030731,1.90196334257,1.78647925125,1.86226644554,1.49775059963,1.60615921674,1.62509928195,1.53365888872,1.46110824489,1.31183195125,1.34790586277,1.31370372616,1.2581202701,1.42554481756,1.33853077104,1.44266172504,1.32261930158,1.30173470693,1.20198192769,1.2107870613,1.41227725389,1.42458291461,2.45621799073,2.37613861305,2.31316518468,2.41666061117,2.27012555516,2.24535354083,0.864033221398,0.860254339757,0.676039172824,0.776870694211,1.3397479058,1.31853010212,1.41807538417,1.52927049721,1.54129294832,1.45103054826,1.17646023925,1.08512436153,1.20724507081,1.00295197102,0.759085375014,0.297595053993,0.403120597107,0.40068993436,0.233084011171,0.33485415004,0.379537931999,0.194303364029,0.280777985278,1.23352541028,1.14129002653,0.946523772397,0.84533401122,1.03867056991,1.03418433085,0.938761170516,0.841745921507,1.13099775904,1.32322423208,1.22750674973,0.946347800693,0.85891963999,0.984366604076,0.879541826178,1.14303194006,1.05116563106,1.23268799848,1.22209071555,1.12158247338,1.04011985475,1.4477031622,1.53343173634,1.63542734217,1.46688201767,1.79296812384,1.70641811592,1.72084755092,1.81960086642,1.75069295978,1.6510665289,1.56811671125,1.75290309114,1.65415906813,1.56900688191,2.37448387184,2.31496861112,2.36562286845,2.46556887992,1.98931748992,2.15599050923,2.04834277091,1.9687101779,2.28016670633,2.18869328584,2.09548509003,2.08771533273,2.27421572873,2.17530093604,1.8068283419,1.70151136648,1.7089279294,2.11906957796,2.01850117434,2.7203565012,2.71454173193,2.78468827215,2.36536118959,2.46958485537,2.56169457522,2.03966288357,2.15120386054,2.24736481041,2.22657561078,2.21591990653,1.93903213414,1.8466139067,1.44926619055,1.47037359908,1.35703280329,1.36898405342,1.70671364778,1.79059919082,1.51737198305,1.52906603963,1.41797832933,1.32842877758,1.33650945188,1.43762861233,1.19335130729,1.08695644741,1.19336359946,1.09019823481,1.02110004627,1.55614764901,1.63538327174,1.64651194512,1.4572857279,1.53249311796,1.44465454407,1.93685709949,1.83927919506,1.93233203499,1.74540364326,1.83508778035,1.74581043193,2.50238913157,2.54490606354,2.5533192765,2.658448107,2.65365875283,2.72075958822,2.77211150061,2.75005633017,2.81601464843,2.93203666383,2.96379001964,2.86388763291,1.53640174254,1.69111007383,1.72260392087,1.64667074688,1.5571263579,1.58238943918,1.50330699754,1.39238670472,0.76476963866,0.585354251025,0.574292376199,0.667015734797,1.15335332808,1.13267864322,1.01909599788,1.06137555886,0.924347401776,0.946593965153,0.748571092072,0.7584191279,0.576634482379,0.675753546605,0.467927838535,0.563230572731,0.653134688992,0.660562828548,0.580471680679,0.478594187468,1.32908640243,1.36476766558,1.43235033011,1.45073446903,1.13707970879,1.17227446995,1.25692106957,1.23937889868,1.06573692114,1.04773164887,2.00257371606,1.90605672599,2.08931596497,1.89361373125,2.07667425789,1.97792857737,1.88960300422,1.98985027029,2.07085373972,1.84351128659,1.82484627911,2.60771472388,2.53588344583,2.01365594546,1.9031619634,2.07908529728,2.10496095524,1.96887315201,1.8835323955,2.0792321828,2.10245145625,1.97131412041,1.88839601542,2.23164604725,2.3461192773,2.34178884147,2.13500385389,1.63019559078,1.7180526439,0.862520228393,0.828172913594,0.417466054597,0.512853068145,0.36446446573,0.769456691584,0.888938952816,0.875318952251,0.68143266283,0.80918466618,0.709786794515,1.94212365619,2.04629376097,2.12180662829,1.95229884081,2.06093670524,2.42877098523,2.3491889028,2.23907645743,2.21011727097,2.22621464034,2.27985349671,2.38709548777,2.60173322982,2.55550648813,2.52032106262,2.44346205827,2.02811270474,2.01084316545,1.90520654704,1.81874557147,2.1436108043,2.04056758248,2.04401721528,2.13679094289,2.24113041732,2.24442667508,1.55126845605,1.640880578,1.56062585109,1.65793861218,0.722956117749,0.705574674071,0.655499614862,0.557432113821,2.26867028097,2.31918602691,2.40977810708,2.3777887448,2.2072219183,2.18762855745,1.94139022237,1.9338181366,1.84566299088,1.74814217066,1.83041263752,1.74037444513,0.609750807144,0.435649417536,0.433756323085,0.526024611525,0.535640057623,0.615673111603
};
const double THETA796[NST796] = {
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};
const int NST810 = 810;
const double AREA810[NST810] = {
0.0155399449398,0.0161688300168,0.0152359394744,0.015635052276,0.0153558882534,0.0159236110923,0.0154529053544,0.0153777231596,0.0158747930543,0.0174902452703,0.0163646282334,0.0157136301376,0.0156947663925,0.0145642782173,0.0157282224595,0.0154152162751,0.015779657788,0.0159386383424,0.0152711411302,0.0153143450106,0.0159087696578,0.0155769700931,0.015613521867,0.0156582629643,0.0186824678569,0.0156193418111,0.0156050348831,0.0156960244849,0.0153404024449,0.0154906822447,0.0154632406866,0.0152584092614,0.015599537725,0.0155817342077,0.0158350555085,0.0153990220042,0.0156023182605,0.0158195731828,0.0156548519196,0.0146961693208,0.0155412355947,0.0155752599902,0.0150223780388,0.015313336346,0.0158349272788,0.0160724348125,0.0155368260347,0.0149373140279,0.0157730889448,0.0157028213385,0.015159446115,0.0154160767054,0.0153732314094,0.0156760858905,0.0157690076316,0.0155355294589,0.0156848525259,0.015460908645,0.0152319716482,0.0158303383026,0.0154092622719,0.0155088656775,0.0150326993552,0.0147998287839,0.0156010446847,0.0155443426125,0.0154889660265,0.0154580631902,0.0156977203383,0.0149563878115,0.0152884062191,0.0156386129204,0.0154984108545,0.0156925427389,0.0157854031038,0.0154469109323,0.015500800021,0.0154345776176,0.0153468597298,0.0152057365421,0.0157084125364,0.0154844579875,0.0145010125618,0.0153402715544,0.014976082705,0.0162568861633,0.0152803898975,0.0154015794122,0.017710361432,0.0160664318192,0.0146953871472,0.0161405834856,0.014902931141,0.0155670857324,0.0147319773892,0.0161980065045,0.016155481072,0.0148801007133,0.0149737524107,0.0149600137977,0.0159481144975,0.0154579258458,0.0151676044853,0.0149665356148,0.0146198102419,0.0180849835452,0.0144245195022,0.0160017031572,0.0154600143893,0.0157503270276,0.0153229506396,0.0154319022186,0.0157477237024,0.0157672725891,0.0155156095423,0.0153749381926,0.0156847813367,0.0157283502291,0.0154099653366,0.0148154835412,0.0164561590436,0.014841434964,0.0151020895547,0.0152537318006,0.0153632410112,0.0157432915211,0.0156431268058,0.0154477718599,0.0154290916632,0.0155501416761,0.0156861945732,0.0153664452299,0.0157170657907,0.0154759251235,0.01554689155,0.015522451902,0.0157212733489,0.0153171612847,0.0152876405088,0.015872643788,0.0153631474043,0.0157305583241,0.0162098987446,0.0152735357551,0.0156391329427,0.0155053972569,0.0152576065813,0.0157120977976,0.0157281904876,0.0154568986031,0.0155336319987,0.016047960057,0.0151064878971,0.0159589669405,0.0151741779739,0.015869857075,0.0153159508664,0.0158481199992,0.0152373510461,0.0159498165727,0.0152287094446,0.0161735119254,0.0150975071303,0.0155146149029,0.015815491883,0.0153824439585,0.0151242477404,0.0158710078242,0.0157886224041,0.0152794757919,0.0158226018691,0.0152143719559,0.0156739183651,0.0154831545336,0.0156813246914,0.0157554029423,0.0154131377166,0.0156452036988,0.0153045024865,0.014590539258,0.0161237805596,0.0163084272534,0.0145803135472,0.0163599773157,0.0158004623144,0.0154566950715,0.0154390507417,0.015769724491,0.0155141702916,0.015565748242,0.0156235024824,0.0145857930979,0.0148226055962,0.0187275797572,0.0152589204403,0.0154136514979,0.0188383697097,0.0162366870957,0.0159652812986,0.014604989175,0.0154299624986,0.0156195182983,0.0156205300061,0.0154968188677,0.0161028502029,0.0164354677854,0.0147009664917,0.0151136630909,0.0149786485471,0.0159951008312,0.0152642358339,0.0151457476976,0.0158332118753,0.0157245038702,0.0154457120771,0.0156729414993,0.0155431843474,0.0155637134586,0.0155135342162,0.0152519980458,0.0158033566085,0.0156029898167,0.0155093862206,0.0154472085807,0.0154486843824,0.0155858795215,0.0154236925269,0.0156844148136,0.0156703679453,0.0154246791842,0.0145281989467,0.0155531540567,0.0154667115486,0.0156770726485,0.0154395269551,0.0154665333667,0.0156705935873,0.016051801765,0.01525396156,0.0152897022652,0.0159027962616,0.0152124824979,0.0154658000877,0.0152622666542,0.0145668436324,0.0154259147017,0.015520003151,0.0153165109989,0.0157497234302,0.0154607412251,0.0157411526229,0.0151472026079,0.0158822798847,0.0157607498885,0.0154272978643,0.0152921971868,0.0158973490236,0.0153633521162,0.0154233367756,0.0147483700824,0.0153360435566,0.0155460555431,0.0155255976301,0.0157103848373,0.0156514828116,0.0154394537501,0.0152042485027,0.0150729621588,0.0158180729598,0.0155989613565,0.0156461586305,0.0154417401625,0.0150778509989,0.0152248086163,0.015059077409,0.0151894285875,0.0161083824718,0.0148238857638,0.0151609341507,0.0155418903944,0.0158175559437,0.0153657364129,0.0155454385132,0.0156120338461,0.0152148534702,0.015257262332,0.0158558949509,0.0156911396872,0.0156151835111,0.0155743994118,0.015160463759,0.0155182329696,0.0152040897519,0.0161731387997,0.0150166689044,0.0152783457005,0.0160057585954,0.0152909294022,0.0157363616502,0.0153376531741,0.0145669274091,0.0158161050679,0.0157834094686,0.0152522023849,0.0159467115873,0.0151489750456,0.0156110820062,0.0155171814289,0.0156417373362,0.0155410581671,0.0154291996009,0.015773852633,0.0157910853035,0.015360019029,0.0157471759147,0.0160225602049,0.0148506229406,0.015219881556,0.0147717471355,0.0151886607936,0.014774510378,0.0148257652767,0.0159150775923,0.015927558412,0.0158348795006,0.0152443180483,0.0144689559696,0.0160226385721,0.0156921580201,0.015507155179,0.014465359073,0.0181352761708,0.0151438021758,0.0151042732684,0.0160379451752,0.0160440063384,0.0151393784557,0.0156796699989,0.0158287632208,0.0147558460765,0.0162405112836,0.015125478759,0.015012727976,0.0150398112594,0.0148479485204,0.0150714218599,0.0149083671623,0.0155065774988,0.0151670032767,0.0158508224094,0.0149888400162,0.015777268001,0.0152869741177,0.0156554866071,0.0151728953281,0.0160379019337,0.0149479824402,0.0160392668355,0.0149681767776,0.0160231265194,0.0150402066735,0.0164241380732,0.0164394988868,0.0155087685326,0.0157426094769,0.0153531417364,0.0157856486038,0.0148897693126,0.0147463525739,0.0153597406237,0.0157431931311,0.0152944977655,0.0146302836822,0.0158444189001,0.0155046754714,0.015932673263,0.0154131977854,0.0145394933565,0.0162226798271,0.0152154809821,0.0152180732821,0.0158329878039,0.015232071224,0.0157874687918,0.0158045735371,0.0153777232787,0.0154292479589,0.0155751729109,0.0157230412015,0.0155033389394,0.0155813074162,0.0150214165745,0.015539165494,0.0156178908509,0.0144291833142,0.0162306071262,0.0154755448052,0.0153252114028,0.0152683257684,0.015875441194,0.0160672129996,0.0154734774257,0.0157165834775,0.0154474046194,0.0155215422069,0.0155830115374,0.0153475455913,0.0156296083195,0.0155015351418,0.0156140231664,0.0156018769504,0.0152743415252,0.0157989211998,0.0160613858664,0.0150870166583,0.015251950858,0.015981171476,0.0155502121309,0.0156533693019,0.0156069314817,0.0155283120956,0.0158202720738,0.0153550589678,0.0156177789714,0.0154955910007,0.0155548720626,0.0155184971987,0.0154461587371,0.0152973209231,0.0156626694744,0.0156926264625,0.015419938785,0.0146024801815,0.0157737590324,0.015532485276,0.0156417485879,0.0155003576053,0.0156169670064,0.0153153142485,0.0158030221745,0.0153434264132,0.0152168452157,0.0148578214715,0.01524747918,0.0147067375346,0.0151846769821,0.0145585410226,0.0156589439081,0.0155005132633,0.0156277422476,0.0155614743451,0.0154851197868,0.0156314026664,0.0148666311924,0.0149779309099,0.0147105087631,0.0153149747398,0.0145277010658,0.0147016535814,0.0161676647174,0.0164110350719,0.0147140883999,0.0155060204557,0.0156761507655,0.0151326604914,0.0152104587388,0.0159606734803,0.01579631224,0.0153949285732,0.0157879427039,0.015094875273,0.014787246892,0.0159363552828,0.015030572553,0.0151760048777,0.0158777790783,0.0158724844994,0.0150246130998,0.0147812832773,0.0162737603629,0.0153238141489,0.0158640020727,0.0157085229603,0.0154874754355,0.015733368645,0.0153545034547,0.0156021732374,0.0156494388971,0.0152603609219,0.0159662233062,0.0158689543631,0.0150107902162,0.0153851719763,0.015205227914,0.0162222053406,0.0146980856372,0.0189891577647,0.01482031712,0.0160435649705,0.0145577564127,0.0147920019171,0.0185750216189,0.014674775146,0.014516162197,0.0156290382337,0.0148649263663,0.0158350026962,0.0154987637488,0.0156386766585,0.0159727808907,0.0147210156805,0.0163367469573,0.0148072941544,0.014478141671,0.0162702205567,0.0148523604368,0.0186473978612,0.0153755181868,0.0146412082976,0.015881494549,0.0152173313823,0.0157808665253,0.0152586903818,0.0155487480958,0.0156965835095,0.0152870395786,0.0152761824983,0.01603938378,0.0144313455141,0.0155620676932,0.0156977038632,0.0155175646661,0.0154812265644,0.0154605325685,0.0154351390741,0.0156512633931,0.0151361973453,0.0159373811297,0.0156289129506,0.0153115425739,0.0157331767809,0.0152253982681,0.0155492495123,0.0145984557019,0.0147893916555,0.0151494823247,0.0175015000777,0.0165454665136,0.0150333006837,0.0162039970294,0.0148161232967,0.0149909813969,0.0153097558434,0.0153792477188,0.0157481760648,0.0158105251486,0.0153547722764,0.0153760713784,0.0158545528697,0.0156327036004,0.0154104165734,0.015554327854,0.0153671554,0.0156436776286,0.0154808236972,0.0159742467573,0.0152835902576,0.0144585578932,0.0155636303186,0.0147634787954,0.015091166156,0.0181420583019,0.0162755711076,0.0144693423654,0.0165211687598,0.01486044244,0.015021245315,0.0153755611214,0.0165815228193,0.0147439629769,0.0159792998114,0.0149589472055,0.0153100797616,0.0156420815553,0.0155361702902,0.0152444469392,0.0155739061481,0.0154995100714,0.0147442790055,0.0151735693801,0.0151472669633,0.0157616779427,0.015115592321,0.0147793239021,0.0148002092789,0.0154573456078,0.0153286350668,0.0154619035739,0.0154791879461,0.0152394611225,0.0154341450801,0.0158924793705,0.0148451364993,0.0153777690168,0.0152807197667,0.0159861602165,0.0150351328122,0.0158959638723,0.0150768299248,0.0151599585485,0.0159246199323,0.0155063427108,0.0155947200148,0.015148146497,0.0148419864635,0.0145433300534,0.0158051780706,0.0153246050351,0.0157877084822,0.0153858280826,0.0156888379358,0.0155032095526,0.0152028634685,0.015761802524,0.0154634674429,0.015157404781,0.0155159839232,0.0151496535391,0.0158557952489,0.0159899411052,0.0152054480183,0.0156526252257,0.0154882125311,0.0153513384175,0.0157674884118,0.015448180335,0.0156811980801,0.0156524497701,0.0153074230961,0.0152235677661,0.0159324439868,0.0157025302662,0.0152220591218,0.0158861731822,0.0152179419289,0.0158215695303,0.0153239582366,0.0158602805066,0.0152877963309,0.0154997509467,0.014514280969,0.0157678232221,0.0154349864531,0.0156563688998,0.0154720540475,0.0155140131297,0.0155912356862,0.0156539204443,0.0153893596498,0.0152429968179,0.0151473023816,0.0149507176569,0.0160486792047,0.0162984128772,0.0147684498732,0.0152771777726,0.0159584345444,0.0157487304349,0.0154704670357,0.0157880643931,0.0153116047098,0.0146351247135,0.0154598881482,0.0145867790988,0.0161231304247,0.0156631372775,0.0155061899621,0.0152304235393,0.0152241853971,0.0158712373182,0.0150811701488,0.015033900187,0.0155220647055,0.0156203161384,0.01531504288,0.0156895835308,0.0159741609657,0.0157913424458,0.0156471173995,0.0155994659912,0.0155860925976,0.0155340850339,0.0155244732276,0.0155466199557,0.0156468877236,0.0153846629968,0.0159032237097,0.015402504729,0.0158473579641,0.0153948476701,0.0159461459629,0.0152408607568,0.0157715693305,0.0155167702081,0.0154616350936,0.0157017946822,0.0154363983174,0.0156816947393,0.0158375971598,0.0153393600483,0.0153738696339,0.0157989845461,0.0157353206739,0.0153182296937,0.0158874865229,0.0156524358726,0.0156278613191,0.0154993633034,0.0153769862723,0.0158722536773,0.0152432185031,0.01427368713,0.0192511719647,0.0148282019053,0.0159861577235,0.015441016981,0.0147719061745,0.0160086273712,0.0156653806232,0.0155421538643,0.0153878935102,0.0153151297628,0.0155935486758,0.0153476082771,0.0158123476985,0.0154552740884,0.0156002047103,0.0160236714549,0.0150662692568,0.0159734331235,0.0146978229999,0.0153001202366,0.0153695540603,0.0157371084867,0.0150849376796,0.0154910764744,0.0153877926528,0.0156387335706,0.0158990378835,0.0157865553146,0.0152814912493,0.015581374229,0.0153704244969,0.0150380829671,0.015687118104,0.0152981040938,0.0155938424177,0.0155894088768,0.0155861630986,0.0154956967967,0.0156323092487,0.0154122507495,0.0157820702192,0.0153705593272,0.0162488762348,0.0144549978701,0.0150556490171,0.0155289710384,0.0157284997044,0.0153678789915,0.0151495734602,0.018051197456,0.0145395729207,0.0161551594732,0.0145433355263,0.0163338450793,0.015671684427,0.0153780403049,0.0158321635723,0.0151945976907,0.0157700458657,0.0154111662754,0.015717265893,0.0155275674272,0.0155812621153,0.0153875806968,0.0158126608221,0.0153645862231,0.0153681289065,0.0157403394458,0.0152658092655,0.0158480596713,0.0154204706004,0.0155676078012,0.0159183974371,0.015280121391,0.0153067924223,0.0157698679913,0.0153938736211,0.0153395926754,0.0150860390945,0.0159344494194,0.0157041634983,0.0153745109373,0.0154497487242,0.0156910669375,0.0155871013938,0.0153820275619,0.0155434819478,0.0154167577349
};
const double PHI810[NST810] = {
0.761235344749,1.9907799862,1.74308537818,1.13285973652,0.744807762039,0.811390672278,0.573663673569,0.569665610298,0.640925058905,0.9957509979,1.11270146186,0.630470744584,0.589255334008,0.920113481925,0.805195233172,0.74391745672,0.810484495401,0.971499566487,0.922290070985,1.08675169932,0.984215227207,0.0870089156405,0.0958438678254,0.207026230325,1.04078533853,1.24830456458,0.601952840767,1.04269914654,1.10794614876,1.61937281881,1.58810902227,1.79957224546,1.8905438517,1.75062234696,1.71321038578,1.78322606962,1.88855495981,2.50271096916,2.04562810142,2.17867676852,2.03103836227,1.72194297069,1.768993322,1.9428548956,1.88227813805,1.62426805604,1.65753917056,2.64362387222,2.22579491025,1.78549664562,1.89282020333,1.19173221259,1.91221837231,1.96031686134,1.85306352834,1.92997716653,2.0429054046,2.0776893509,2.13929090427,2.08831215823,2.14026955009,2.24916060599,2.18601947379,1.21671903564,1.06340108596,1.14665166373,1.5503286032,1.68342590504,1.57443477542,1.51212888609,1.45503166399,1.57635198489,1.40623883952,1.46388995556,1.53212710438,0.579320648763,0.638964151663,0.64130386856,0.959686713583,0.914218077724,1.07134559116,0.961338189494,0.499135509519,0.606622708643,0.45534991895,0.41619839458,0.937915784805,0.832324015254,1.29800295306,1.08724009648,1.24072568412,1.1407130129,1.38519269718,1.54142317499,1.43805992803,1.19529714845,1.37566316099,0.963732479879,1.01905306723,0.94501242548,0.869173489878,0.779849646216,0.85100401437,0.797078357418,0.752927925321,0.76840566515,0.860920476383,0.841102424689,0.266213938853,0.116283372765,0.130140992182,0.501054229489,0.606039994718,0.311572400161,0.422922843712,0.243852870199,0.315500241749,0.468557058092,0.422356879861,1.1125086502,0.958748913594,0.913799713065,0.941044597428,0.924999397948,1.00270926956,0.912709009241,1.02722050137,1.09404968668,0.78357326541,0.711991117078,0.536955208067,0.426898283816,0.451272569239,0.375473271083,1.10921998997,1.00908091061,0.927656043726,0.956555063956,1.13726573271,1.06536991884,0.827624058967,0.818616383403,2.15539957762,2.1403741015,1.86012246577,1.9283034318,1.14854140389,1.60383098679,1.79552867592,1.19664753957,1.11885711677,1.00756830744,0.981687573214,1.48478633662,1.41666153694,1.73587400916,1.62588905099,1.56190790224,1.7792105407,1.70832765324,1.60129221719,1.6613854048,1.58944176445,1.63407881306,1.74698125396,1.88415264793,2.0213429251,1.99549976797,2.43699812943,2.51916283657,2.59309681952,2.54613388987,2.6809298597,2.58493516932,2.32760015267,2.22008432684,2.37182127517,2.40931294402,2.34807882283,2.25901156872,2.25485222679,2.30703169493,2.12304978353,2.20585158199,2.10548920302,2.03909189616,2.0793906011,2.21636658833,2.26020272486,2.18904743545,1.95830579974,2.063928047,2.09554119589,2.13842824883,1.83935987014,2.05233891192,2.08809017173,1.87176685935,1.91242094697,2.01472364361,1.92861784421,1.90615738372,1.72317685214,1.80104203654,1.61211596431,1.70390379549,1.74431141196,1.85193293142,2.02975158073,1.92518412209,1.88180696856,2.06110277897,1.98604643907,1.55404275661,1.52987019677,1.42789966929,1.34940356161,1.87575529744,1.90772921527,2.09841150585,2.18647389927,1.99841202159,1.98296057586,2.17129976075,2.06807946683,1.85465226337,1.72161476483,1.7449411259,1.73504620377,1.65586165643,1.691485677,1.67776767111,1.59112108022,1.78605145703,1.80271466271,1.7147579086,1.61157348209,2.55196279129,2.53747164325,2.2814816511,2.36941198838,2.46212150949,2.46262957702,1.80398427186,1.76278250033,1.74090911529,1.8011195722,1.64657482782,1.75063373083,1.90544833727,1.96632133075,2.0556773744,1.95304003835,2.11819749327,2.07603952148,1.98040776707,1.81012264443,1.9211660422,1.32054317013,1.29168309148,1.432122476,2.11648572723,2.07279619927,2.13597358068,2.24984061811,2.3084602767,2.61900257942,2.74190477644,2.43142977934,2.68341846674,2.13881140785,1.98525512936,2.76491113589,2.071182341,2.05876376738,2.1442111516,2.14870372926,2.23696643608,1.31400899627,1.50990642761,1.48320492746,1.38895645961,1.0106585044,1.0877175052,1.24998252947,1.43509702019,1.33343450404,1.64651627031,1.76914753576,1.67349462766,1.7175096093,1.57324290943,1.61022874877,1.53839023139,1.43906811211,1.42540636833,1.2949766947,1.40378509114,1.4663397518,1.94166673214,1.98022678848,1.91611481127,1.35045673255,1.27782577676,1.31692267162,1.24878589762,1.1655776961,1.13581414134,1.09125239974,0.798500581598,0.752925465842,0.909315995352,0.826883330142,0.977309848855,0.93941936385,0.988683017589,1.23583012017,1.125710774,1.08764097972,0.298027375329,0.394450857336,0.397706548678,0.577632827417,0.482653128545,0.601359100092,0.498023556822,1.0455630863,0.964902713256,1.03669385481,0.94831156513,0.588360757581,0.495362315118,0.530219673813,0.48173169098,0.404882241764,0.294465231641,0.286235171523,0.472771369844,0.387859214398,1.46408682957,1.4675255329,1.55955809957,1.09750493429,1.18819119665,1.13823193672,1.2491920515,1.28007049181,0.666576992307,0.842814659306,0.773226288802,0.85070686781,0.757796962509,0.659018652583,0.814460303351,0.929120828633,0.969519077838,0.90482517778,0.58837531789,0.670107165548,0.478438162865,0.462232674571,0.6614035053,0.564950728973,0.189676826278,0.268492634117,0.365792941815,0.255358789581,0.670556342233,0.573130451746,1.42945424501,1.39146601864,1.28676191153,1.21693065272,1.08277468093,1.15410767869,1.3075253357,1.26643048847,1.12556913585,1.06910960119,1.12898987205,1.2408594782,1.29270067265,1.23652582317,0.990035269927,0.963857954751,1.04717651041,1.24774783706,1.04320198271,1.16911699065,1.06555613937,1.10990175907,1.2128931931,1.18607268548,1.09730020896,1.28482221611,1.29881705528,1.37288771837,1.04201843387,0.891984278131,0.93291989753,0.968820826365,0.745814955874,0.641194617662,0.558884389265,0.59651914183,0.930133874494,0.871596371957,0.885789234657,0.775868891543,0.760024452906,0.707415568795,2.03476729468,2.00447654229,1.95123697549,1.84544633866,1.89642025794,1.82074328912,1.76988172319,1.66101235127,1.69601665493,1.62407778358,1.73358272121,1.65993722498,1.55172483682,1.51370923836,1.47713591028,1.33701354061,1.30210594544,1.51379355431,1.44595976224,1.37652230524,1.47897628293,3.08526437873,3.05408264657,3.00565537548,2.8549592743,2.75364843275,2.90659222468,2.7001533501,2.72750520894,2.82437692601,2.35162324132,2.23625296492,2.38074452727,2.27308387779,2.41004043507,2.31647991215,1.98619390466,2.02653854458,1.95309279767,1.84313335998,1.87589919196,1.80589611739,2.04484614355,1.97171810104,2.07022771324,1.8924522865,1.93237683552,2.11195033611,2.05914681992,2.10391407489,2.2040554211,1.29083019783,1.22179921781,1.56598714765,1.58736130143,1.63156170933,1.47532873838,1.40590781075,1.45271176912,1.54852866531,1.53037371794,1.5935291728,1.42294305436,1.79895063997,1.9253740348,1.6108688359,1.58608319819,1.48253511331,1.40099156115,2.40125995986,2.43415687932,2.29344258196,2.22269544053,2.25225234578,2.3547493948,2.28446346793,2.37276766669,2.35769560787,2.2557620089,1.97259890286,1.91640936054,2.08315775274,2.12544003192,2.04864293497,1.9509141289,1.81933065372,1.85349274589,1.59090309326,1.48876373957,1.49298742076,1.3974627667,1.39908938876,2.22191153784,2.29097902194,2.22077440235,2.5831435419,2.46999631477,2.42029630967,2.638849835,2.74196473723,2.73246072674,2.81409891073,2.90779480634,2.80526447542,2.9691530062,2.90934560297,2.60905803108,2.73486036523,2.71941324691,2.53320826245,2.55055473455,2.64190826269,2.29355793346,2.39631509724,2.24494482977,2.73244205791,2.7919587046,2.8974895648,2.76620731607,2.94825901964,2.86738859263,2.28694367534,2.17444814987,2.11743948516,2.09388214032,2.94479004375,2.8587492184,2.83820661455,3.04408446235,2.51074342233,2.61718878556,2.73812156979,2.52953141545,2.35986453892,2.34906947584,2.40941531455,2.17428386871,2.25044289154,2.16845459997,2.23757200147,2.41323281544,2.33283803505,1.00391583579,1.11135709714,0.968476644987,1.04235118587,1.1944875694,1.27365381004,1.74387335272,1.8073677623,1.63714322217,1.49536986464,1.67018750759,1.56648846637,0.990144320077,1.0170529947,1.06819108967,1.12864332525,1.17945725188,1.2355712295,1.16012662607,1.40189452203,1.3457533592,1.3644884234,1.27013577134,0.230063242881,0.116262370347,0.309185889405,0.302219934738,0.120703439101,0.221625251809,0.669819346728,0.764594763208,0.853591450139,0.861973205963,0.782418546985,0.679604330175,0.647109750253,0.862586213066,0.686538743328,0.791438660236,1.88925207248,1.54905702432,1.44959067588,0.309093225626,0.399534039715,0.228250271607,0.28685497975,0.632649201945,0.728345847975,0.738589017001,0.659996935113,0.352230912132,0.438661275709,0.394446340949,0.494336369633,0.537902827199,0.556572590688,0.624654197049,0.732545527544,0.790462720359,0.739589485765,0.796619204958,0.948382545873,0.90774863209,1.38927591559,1.35752264302,1.24974928326,1.31514915863,1.17196430715,1.20591039905,1.09722464253,1.22397068332,1.12322502373,1.07486886444,1.27514115808,1.21205910083,1.10755632246,1.24013242785,1.14448967648,1.51716303867,1.40875448423,1.37927057382,1.45736328392,1.47833565549,1.44055331589,1.40594831086,1.32971409787,1.296109366,1.25722566086,2.81099906808,2.89009478558,2.99447575482,2.98019230368,2.44877069806,2.63880293467,2.54022370944,2.45008289496,2.32383239919,2.2169793479,2.163773899,2.21047596438,1.3729997844,1.27034319395,1.3857424194,1.43580110674,1.20721946998,1.26028054111,1.8202957762,1.76380501949,1.65913234488,1.76094375528,1.64896565235,1.60324350092,1.93593611503,1.90321943664,2.04182866576,2.11602120461,2.07713267666,1.97057229076,1.88213022882,1.91800152333,1.83328108752,2.67494095714,2.56460510314,2.66453206801,2.39475184508,2.56945217445,2.46680955043,2.58440194391,2.39543967723,2.49864602871,2.58269480186,2.22776094829,2.29394673264,2.26319971782,2.37066740051,2.31356191797,2.33704481507,2.23639666772,2.22406384835,2.42234621325,2.43368631447,2.63167481287,2.53195676762,2.51127221208,2.68460196319,2.5809871131,2.7119075955,2.62416044741,2.52873928658,1.29307375131,1.22518784904,1.36770575145,1.33358156531,1.18389997706,1.14976049194,1.49356487572,1.59813785007,1.45747792119,1.52849789996,0.718433712502,0.775952287542,0.690629843936,0.877765494861,0.903161706065,0.828326457353,1.68628841604,1.58134983402,1.57427610689,1.70840413925,1.62902757045,1.79833552516,1.80141785661,1.69625662185,1.61403889589,1.43047112503,1.51529838346,1.31940454059,1.30545512289,1.39375697661,1.49245036604,0.409932373008,0.493930849548,0.589521826324,0.449091056687,0.560887884041,0.620232193893,0.882826446728,0.868041144499,0.796584483885,0.688394137383,0.67858477506,0.771591896229,1.40475525356,1.30273083534,1.48645786417,1.17444392354,1.23340471854,1.15033311206,1.27899951503,1.5894330749,1.76286777861,1.69733489352,1.55889450333,1.63068276775,1.72656436322,2.38621119334,2.49576879219,2.55039456196,2.48061364337,2.3667691305,2.32493802467,2.07420113085,1.99826738195,2.18045453148,2.19482242807,2.10394758701,2.01422209726,2.28899090371,2.29778623755,2.38563603342,2.47895365085,2.40291093684,2.48928853688,2.62423674844,2.55488277319,2.56890666542,2.4590923728,2.40414553891,2.44659576737,2.8749718521,2.81131650088,2.70836686266,2.80425424646,2.69963614368,2.66012124701,1.6326602455,1.83897308665,1.76871413131,1.66646580482,1.80725906044,1.70346804382,1.65786168276,1.66913992992,1.74368185905,1.84382279091,1.35797251007,1.46319845393,1.41813994799,1.33626993224,1.5478210017,1.52423723584,1.77890798871,1.76874196628,1.96575752744,1.87663638334,1.95692703893,1.85767738414
};
const double THETA810[NST810] = {
2.99361173966,3.75753618789,0.67105552789,2.01998695478,1.4115179321,1.53767283164,3.88917819302,3.1560996294,2.99406156847,3.4522951692,3.69913111233,3.29575799163,3.48273765675,3.33822263466,3.11431629146,3.25532805691,3.36397547356,3.22276252773,3.10987254112,2.99595633004,2.99555587343,-0.802577954985,4.13305607898,4.18883486531,0.592494997397,4.64452327901,4.08041154755,4.36777363345,4.46582359049,3.05254239333,2.94644705102,0.296399504609,0.497772335423,1.57506601931,1.46833626979,1.38193942571,1.40346167765,1.11796302101,3.3190218868,2.32873178285,3.19779018756,4.33131669075,4.23422643967,4.31071286456,4.22297537478,-0.120429699948,-0.799340981247,-0.575814653769,0.0444949819274,4.42569737802,4.41651103992,-1.41758847407,0.304975908016,0.40324214009,0.68757300987,0.599023849456,0.613267499417,0.723436033678,-1.44738505129,-1.33930739731,-1.2222793992,-1.21143438025,0.758212782068,1.95508047972,2.21375566248,2.14287751534,1.83462074949,1.65820909356,1.63997521883,1.72670732067,0.424127325784,0.256930057682,0.319617505761,0.236344686572,0.636439498029,1.2626353063,1.42790687535,1.11178019669,1.38276874033,1.51053374485,1.37339464516,2.15692982089,2.77079678403,2.84257447549,3.16058108153,2.90957740524,2.87147708102,2.86588972935,3.21905779756,3.21921097976,3.10048811181,3.10761986762,3.21661453493,3.12956844797,3.10744935847,3.61196726786,3.46708448297,3.56544508823,3.68212716265,3.79024139388,-0.297681882747,-0.202973503334,-0.425240929855,-0.654283629936,-0.506659629438,-0.785752600213,-0.900151070979,-1.03999490845,4.55425622381,0.346622495736,1.20073216359,0.853658262687,0.933171624353,1.51785887367,1.00929760615,1.19914659719,0.913535254464,1.24888893125,1.4671116433,0.522961085042,0.302785730934,-0.638921532609,-0.509187952445,-1.12180324606,-1.32246082927,-1.26166390992,-1.05651062777,4.26066367888,3.99384998601,4.11283444314,4.23927739361,4.22422170497,4.66123830742,4.4694735498,-1.49782686398,-1.45501868211,-1.54498349192,4.6050916995,4.66726917753,4.57869199333,-1.50042547909,-1.34652186524,2.02998738815,1.89319008704,1.59810453183,1.51316927909,2.88807623428,2.06508980349,2.10448691468,-0.207488132281,-0.117208896291,-0.141169688851,-0.260693952724,0.0479401642538,0.132098880014,0.380526630024,0.360413828704,0.444263839163,0.483677456348,0.568046747962,0.549029299402,-0.0156576814803,0.0696903773634,0.174610453047,0.193839536469,0.789902746741,0.918985063301,0.810656206224,1.4695508101,1.78681974353,1.63749471331,1.45855318806,1.20101832044,1.26155071409,1.85959554357,1.81397411204,1.6077731727,1.74913169726,2.00114348056,2.22227445615,2.0905010088,0.954253964962,0.968525065176,0.897600506747,1.43510880868,1.5336584825,1.64696208668,1.45236342681,1.58465817072,1.67934769891,1.31269819425,1.32395230418,1.09883581254,1.19928616283,2.52338625393,2.56300087243,2.32638557455,2.32458655413,2.43357716613,2.44971978356,3.15720335224,3.04293049926,3.08474387085,3.00849228187,4.3407038502,4.14093250551,4.04604331616,4.03154677317,4.08560129403,4.11436036094,3.92048801957,3.96402220897,3.88241441405,-0.329698806599,-0.437649884754,-0.464106088728,-0.381021199358,-0.743026892308,-0.525487061729,-0.53885171373,-0.610465191956,-0.593187769358,-0.708150836661,-0.745644771451,-0.787110716877,-0.848138630989,-0.975038380711,-0.874099834742,-0.382710264467,-0.302887911741,-0.199631502613,-0.698322141877,-0.622909829313,-0.668731123595,-0.565027240883,-0.49030936418,-0.517915160759,-0.665854176986,-0.862744952285,-0.54518877841,-0.631730517533,-0.555648615973,-0.372073822178,0.109512809623,0.00495404137551,4.52470455275,4.62398933103,-1.56230892902,-1.55903194948,4.62440917219,-1.55551120596,4.50652542807,4.51569169687,4.6132629811,-1.55689147553,-1.34842952025,-1.45828028811,-1.45488248027,-1.55303050464,-1.44870949578,-1.56279928692,0.516232415461,0.406918943347,0.297574558345,-1.45209054631,-1.33351356442,-1.00862679507,-1.43913930965,-0.0155910567153,0.94138294182,2.79319332128,2.96427930828,4.55103827409,3.70291633069,3.57097993804,3.37063670623,3.50469130416,3.57434755789,1.99896122746,2.04685365829,1.93066522061,1.91157186265,2.41919659864,2.33784583432,2.18630181376,2.1368113569,2.10851015001,1.85428402341,1.98860449603,1.96889679527,1.76490191522,1.33954621127,1.44635908659,1.53452928996,1.51380698725,1.21310207087,1.38518512145,1.40476173934,1.31885682417,1.00580816307,1.11396897398,1.20328884689,1.00295170628,1.08809363481,1.19304035692,1.27896286339,1.07234640376,1.26889788197,1.16707239582,1.26912890512,1.13403576807,1.2687467565,1.01564639085,1.15793577614,1.03901394755,1.6158920927,1.47332368221,1.47106932792,1.58721240537,1.86616995205,2.01548016894,2.31360052706,2.00783170172,1.89076769845,1.60718443621,1.65439098839,1.82850297797,1.7472492803,1.9552145698,2.01956157781,2.20096784233,2.3650838536,2.55134731759,3.56167422543,3.38291626812,3.4622430421,3.85411872985,3.79797773398,3.96029605757,3.30036371734,3.39892602629,3.23757608522,3.43404211365,3.50687087584,3.31591631673,3.32311438973,3.43513778271,3.58934907964,3.74660880605,3.51573939448,3.59955499128,3.83960160339,3.77376495759,-0.070642435343,-0.0476657595302,0.0746122736847,0.178515505843,-0.149869345202,-0.258967183586,-0.213009656173,-0.435437534541,-0.442623603997,-0.545321311967,-0.85924588124,-0.480417561276,-0.593026967011,-1.2830242631,-0.824932938928,-0.728617461815,0.619889972251,0.512102249993,0.495355044675,0.580501708835,0.0869903023192,-0.0100159427132,0.111545481033,0.00657256309772,0.396108434398,0.301062875044,0.190158927638,0.198070659385,0.302100587872,0.389983621965,-0.721598033182,-0.852943502475,-0.926473716563,-0.407944970501,-0.471140693245,-0.32043840114,-0.34836834103,-1.11837913242,-1.06309143932,-1.2967639082,-1.2462969923,-1.24111010814,-1.13374269019,3.97367771804,4.15175024356,4.01980994717,4.14360048935,3.91297176944,4.67645173245,-1.5548719427,4.59732820201,4.4130688711,4.37685948919,4.26151425985,4.50230415041,4.52644786686,4.25873298276,4.39899890904,1.84889971504,1.73537249515,1.92989548642,1.90028149552,1.70754923887,1.79067821359,2.89932927169,2.8699995385,2.68762806429,2.76560575987,2.50141690915,2.58348622779,2.56013869712,2.74175630377,2.64005947811,-0.0778466887883,-0.185304156544,-0.140024549741,-0.0573757732911,-0.270690780929,-0.246322116968,-0.539176118195,0.990700789532,1.94907517525,1.37361273922,1.41766478606,1.77420705079,1.66391995379,1.92284036774,2.04957617965,2.3009051504,1.20032060567,1.33876005397,1.34297634439,1.17752156648,1.09355121871,2.65541471788,2.76756874913,2.85136766307,2.82155306833,2.63195015687,2.71381142162,2.22041432492,2.03988474006,2.09340859275,2.12548521414,2.23491450009,4.39494977868,4.29781746055,4.18025519429,4.15133633445,4.54399307096,4.454677352,4.4393133955,4.62487860502,4.52876118868,4.6272208598,4.53699078454,4.44497209632,4.25488246903,4.06872385808,4.15212014965,4.0783460565,-1.05947338184,-1.24922383621,-1.00019610287,-1.09850899768,-1.14192363828,-1.08480748067,-1.06201985057,-0.905239329422,-1.08095893904,-0.972208886092,-0.83636045581,-0.790807584447,-0.392918136404,-0.299487880721,-0.13597295552,-0.0948080036662,0.202774468065,0.110305724173,0.191620195835,0.0694728488215,-0.0297469398502,-0.00124000916624,-0.166505358704,-0.0655265580741,-1.46372596434,-1.46674092325,-1.25495627046,-1.30449872855,-1.39296370137,4.59198893994,4.6984198017,4.44189482062,-1.19455775765,-1.20011353542,-1.34191870048,-1.39167208443,-0.692593282545,-0.946111977085,-0.43973525767,-1.17188082798,-1.1775427085,-0.684616122367,-0.317028976832,0.0973893530471,-0.209268633339,0.0450863577826,-0.0549441472477,-0.254234896002,-0.340540501533,0.163135046168,0.146191269068,0.294965273218,0.51469525919,0.268843104851,0.231942372301,0.79810631634,0.679753426886,0.966345527172,2.94360408496,2.91309068629,3.11981319411,2.9994074008,4.61414788365,4.37273564964,3.98070669477,4.25863067968,3.01845904892,3.0847156557,3.95068122159,3.91221821535,3.76597106842,4.01152297647,3.89542671709,3.78483626259,3.72245948295,3.9244242743,4.01680941063,3.61921457439,3.509477641,2.76197366764,2.77772939091,2.63806708373,2.54342970486,2.37600229552,2.29661464223,1.2742783804,1.186767652,1.25415983199,0.830715881022,0.757941810972,0.742723238854,0.820925663304,0.94481020423,0.73728348762,0.967779786031,1.66008840219,1.83065268654,1.77077738556,1.71591965098,1.80480635181,1.60796157873,1.58696819356,3.15414599124,3.12514637425,2.82128902893,2.49489555646,2.14502185143,2.18306618048,1.91439093222,2.00818919477,1.93962041636,1.79075506513,1.68841356157,1.73821890668,2.54701587354,2.61035205101,2.70784533941,2.72777231035,3.69075378494,3.95617185354,3.8943129449,0.55648086331,-0.0251070423429,0.261211300187,-0.0823072905391,-1.3756096214,-1.27914869573,-1.10841660093,-1.01099603203,-1.18260618367,-1.37319929703,-0.884657540809,-0.891003036148,-1.27368064185,-1.0735673735,0.0309850952934,0.315603189885,0.174902485947,0.0479543950222,0.426724616314,0.545258219939,0.412956069629,0.812469088022,0.707509521703,0.685263690424,0.89784628743,0.770719987331,0.878904795177,-0.679277674329,-0.523653249963,-0.55803602264,3.93167137945,3.96031539259,4.06055948309,4.04760555987,3.84202697076,3.82697047152,2.4572227105,2.43294887249,2.32670212181,2.24536515533,2.92297130616,2.82230479361,3.00661700809,2.80547038242,2.99711849126,2.89635100071,3.34301771934,3.60558472201,3.45447711106,2.71621976477,2.24265010984,2.06733794478,1.9717965657,2.06904856213,2.45098844101,2.46559576764,2.57686751494,2.69531071693,4.17001914122,4.35712936624,4.35475685259,4.26314452608,4.26152451515,4.16594527402,-1.26270336039,-1.36532274666,-1.18128257118,-1.16787735887,-1.36758591069,-1.27843116909,-0.931679374167,-1.04272399149,-0.90666550157,-0.999387204103,-1.11977902412,-1.13732434185,-0.232772230027,-0.412715988169,-0.345528413884,4.40411535176,4.0952589923,4.1580473885,4.65853079167,-1.5547420517,-1.50361541387,4.51557380121,0.854839054645,0.927388370588,0.826159759267,0.53333926445,0.422205271921,0.667136392201,0.705117183216,3.07658222511,3.36266419473,3.29592235886,3.16449296894,3.12737928349,3.28628443137,2.29690225957,2.36401764179,3.57965509197,3.70930748498,3.73912446706,3.45640064045,3.30565307017,3.38729491941,2.70279166246,2.48747162223,2.61832242913,2.5136849385,2.68382993815,2.5725562744,1.12759509782,1.14771892159,1.02202059376,0.935566594692,2.42802677853,2.16912749373,2.26317536776,2.23486229181,2.37493915325,2.47039010272,3.58956424478,3.54493364846,3.44416533905,3.93302491723,3.89295161947,3.85356483482,3.74678306326,3.69403180116,3.76015151407,3.79536427084,3.72492319681,3.75700300688,3.65401431848,3.58168816394,3.61358423043,0.452905159008,0.616293258061,0.534691777338,0.198615534252,0.187408415857,0.346000568758,0.78140875387,0.650011777398,0.880149503209,0.825358977613,0.65137889567,0.581024399166,-0.572742849387,-0.604731427839,-0.650728526473,-0.758719290635,-0.949571638609,-0.876118209241,-0.719066241042,2.3762730918,2.31020384372,2.39671282898,2.27020241745,2.18031999265,2.19965861595,2.56997712558,2.54669884392,2.701783647,2.85380969565,2.83413448547,2.7048096981,-0.152221966788,-0.23109024948,-0.191340915016,-0.329625835781,-0.408146163484,-0.351214560039,4.24357670456,4.38815738795,4.16632682466,4.22623202131,4.49274701806,4.41062960211,0.472106486431,0.624920884476,0.282281087614,0.28788849695,0.433135450426,0.583827388672,2.71115645835,2.40281099926,2.47242546108,3.00540858874,2.92927115798,2.70186611984,0.952896338947,0.986973104497,1.07855673891,1.05980343539,0.878568559639,0.863638857781,3.27036022388,3.37915312595,3.19512941394,3.23238553269,-0.791225330541,-0.755497874959,-0.969107126176,-0.905038563471,-0.828092465703,-0.928633963529,3.52678161895,3.41635028061,3.50997748414,3.57448913861,3.39053496512,3.34554796509
};
const int NST996 = 996;
const double AREA996[NST996] = {
0.0124857992829,0.0126828741137,0.0125184014875,0.0128358140002,0.0127090064398,0.0127975238237,0.0132433411671,0.0121885428733,0.0128358379244,0.0126213160783,0.0125536759372,0.0127893036403,0.0124257214309,0.0128533592399,0.0127217921705,0.0121363617427,0.012921979963,0.0126049019802,0.013857314232,0.0124487879018,0.0124816577559,0.0128317495644,0.0127367625669,0.0128679748734,0.0128333284615,0.012522238749,0.0130710565716,0.0124718988375,0.0134878024292,0.0121363226402,0.0126838839511,0.011966449436,0.012409483946,0.0124414705065,0.0126177073084,0.0127339921714,0.0125914028789,0.0126433520902,0.0128259326019,0.0124397021536,0.0126155278322,0.0127535867899,0.0125231719999,0.012665352027,0.0127757075984,0.0128307876078,0.0124209678906,0.012391998649,0.0128746083884,0.0127113638998,0.0119768789116,0.0123996772788,0.0123159574129,0.0129278842807,0.0124407148589,0.0125975461957,0.0126988734242,0.0126975935252,0.012580349257,0.0126203041624,0.0127429182115,0.0125221683108,0.012664785813,0.0130360637122,0.0132615597256,0.0128233890657,0.0123873298295,0.0127862971971,0.0132209749638,0.0123613590925,0.0124256761597,0.0129130171622,0.0129105287607,0.0124184193849,0.0121154297228,0.011968798085,0.0125504982556,0.0127264949097,0.0126420007134,0.0126929807898,0.0124765955152,0.0128612666665,0.0120711530249,0.0124865086923,0.0125518953282,0.0119379637873,0.0121466263996,0.0128806071415,0.0124079533032,0.0130013446701,0.0128537866369,0.0124191060087,0.0148178026425,0.0126041862962,0.0126019799706,0.0119471432606,0.011982641158,0.0125271676943,0.0120796155069,0.0118903493955,0.0120665508054,0.0124901005007,0.0128150973684,0.0125836195165,0.0126798514631,0.0128410020404,0.0124924164871,0.0125814946069,0.0124506189978,0.0121940312524,0.0127611894941,0.0124934071654,0.0128632860177,0.0123456845315,0.0119755982065,0.0126813726794,0.0124208174308,0.0127545902796,0.0125479248296,0.0122289369237,0.0122935805423,0.0126878122916,0.0125581116411,0.0126657482011,0.0126574068209,0.0126446415109,0.0126782643612,0.0127412093188,0.0124044027641,0.0117725376756,0.0125633911094,0.0127279115861,0.0130088328469,0.0124491566243,0.012540253171,0.0127671129094,0.0128459470403,0.0126265081445,0.0124950744629,0.0128459303594,0.0117526888362,0.0129915567285,0.014465168067,0.0125298306099,0.0143901943074,0.0125770738208,0.0127551756953,0.0127097201044,0.0126823064165,0.012480205004,0.0128988425916,0.0126295836759,0.01278501293,0.0124878292944,0.0126440332597,0.0126896177415,0.0125360853397,0.0127144339734,0.0128164814681,0.0125700489342,0.0126057507443,0.0121591429909,0.0123834120202,0.012622010642,0.0122954858709,0.0125841187748,0.01277743071,0.0128778511575,0.0124970338298,0.0127662066433,0.0126079681503,0.012290413344,0.0127142952978,0.0128555765923,0.0124249313224,0.0121192378651,0.0125529170624,0.0120261639353,0.0126919942123,0.0128460887347,0.0123603205638,0.0125918221716,0.012213462916,0.0132513206317,0.012175017712,0.0127451462065,0.0125156039562,0.0124346548174,0.0128502943217,0.012228192612,0.0126717337268,0.0126756185495,0.0126732438997,0.0124787248071,0.0126289243991,0.0123039861245,0.0123069192866,0.0123270181744,0.0120664338177,0.0124652207295,0.0120449289403,0.0131644821766,0.0124327796472,0.0129243425754,0.0126441512534,0.0126198741816,0.0132983257553,0.0128073304436,0.0129182872209,0.0127593909282,0.0123915547712,0.0127919587563,0.0123865792783,0.0132599081482,0.0121357313499,0.0120454216041,0.0126979008449,0.0125819497361,0.0125935019696,0.0127484360559,0.0125588877955,0.0125183633926,0.0125155577295,0.0127043824169,0.0127235433058,0.0126038003191,0.0128531506365,0.0124145441654,0.0128567285389,0.0126332709322,0.0131039179265,0.012091182226,0.0123817564693,0.012628124647,0.0129396178823,0.0127449036751,0.0125211429286,0.0121260405654,0.0126071569386,0.0118855637035,0.0125915481048,0.0129325565945,0.0121298800437,0.0131388503193,0.012799878241,0.0118607573697,0.012595676972,0.0120129672017,0.0142739658104,0.0141216534323,0.0119572362544,0.0127618304764,0.0125494302399,0.0125070121142,0.0127776542642,0.0119891913549,0.0127053634416,0.012528253551,0.0129016443855,0.012738753138,0.0124756964325,0.0124449489225,0.0124047034593,0.0128656341485,0.0126067606959,0.0128672424188,0.0126679978271,0.0126782887677,0.0131209770734,0.0121470365957,0.0135358279308,0.012627687001,0.0123924064067,0.0123777833641,0.0130296352464,0.0120748426963,0.0125272883613,0.0126562207575,0.0126819215779,0.0126280921901,0.0124854752583,0.0128285395366,0.0128903703256,0.0124734158803,0.0128365374397,0.01243385708,0.0124949337329,0.0126799783922,0.0126034380067,0.0120901757888,0.012741977664,0.0126324566366,0.0124685555344,0.0121899160993,0.012355796953,0.011986755724,0.0125925296022,0.0124638423508,0.0146853964355,0.0119654889542,0.011959901357,0.0123944928168,0.0127180606733,0.011837811526,0.0129063091034,0.0132022703509,0.012356311284,0.0123340695691,0.0122272343084,0.0140857806373,0.0120636468856,0.0127646080853,0.014775683477,0.0119898678286,0.0120374153477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};
const double PHI996[NST996] = {
2.54757754322,2.68876540457,1.53700968414,1.52551185934,1.50434374498,1.48623705749,1.31600045188,1.39592325428,1.38531106044,1.29886680567,1.81035649949,1.81744985068,2.39201242164,2.32577850405,3.1046406245,2.26728661193,2.35895721656,2.21032763438,2.24921201437,1.98955877927,2.15052882721,2.24641652111,1.12173988184,1.03706698392,1.55061188563,1.55511465975,2.21462762607,2.2403141289,1.38594814879,1.29607012154,0.571830943849,0.0330578500801,1.71843979671,2.02927130495,1.80393714852,1.62522071758,1.6329142785,1.72039319161,0.823733508093,0.694554690086,1.10873066182,1.00883380121,1.66589907947,1.42770834479,1.32982986905,1.52071138005,1.39652414695,1.2741146881,1.18386783811,1.3624353496,1.46253071948,1.4590839644,1.25544325903,1.33797693513,1.41712700141,1.51103132744,1.40230053652,1.30833668556,1.29752468766,1.794748648,1.7840072902,1.73909811281,1.58677297392,1.85423506543,1.84703306963,1.67857703209,1.75247273844,1.89397830293,2.4878810829,2.59140454855,2.50240199758,2.48383125645,2.59185156555,2.5015451842,2.22350020982,2.30540837341,2.54893369168,2.64597976146,1.89150324225,1.88426204485,1.96599590676,2.05882007831,1.93411118236,2.03022602746,2.10876561879,2.1907049874,1.85941975408,1.89206764621,2.06002222669,2.13266606386,2.01588397792,2.1111171708,2.47222028866,2.73996215665,2.65644744079,2.47741094693,2.38840706487,2.74503607339,2.54590343426,2.63235014007,2.55568571617,2.44231264236,2.52311548868,2.58796600613,2.54224774358,2.388268651,2.29011885953,1.86886991714,1.82145121062,2.39338260647,2.46903034785,2.47635299981,2.31389688074,2.39532718727,2.55617749003,1.12979661341,1.05092539601,1.24160989506,1.22666084564,0.989991765631,1.0571364008,1.46950044753,0.960288304065,1.11681584125,1.01988538006,1.20301350071,1.19466903023,0.538850511779,0.0649398976252,0.222367335206,0.528272592966,0.437105251468,0.895853965054,0.178354786154,0.226960153737,0.141200364292,1.66311000578,1.73863105262,1.59188642717,1.62448605776,1.26880601079,1.17060276056,1.49217642573,1.27151369218,1.31920788665,1.96006494711,1.86303395294,1.70633306341,1.79753687288,1.97885425171,2.07016641805,2.08203434472,2.04981230997,0.410133882062,0.558854768249,0.640810365559,0.54282753104,0.697093416188,0.503933770969,0.572678195222,0.666136151604,0.137127060815,0.497767151022,1.00064438694,1.00455472453,1.09322650918,1.0950268255,1.45759832397,1.46356617054,1.19855535941,1.19294489632,1.29263744842,1.28564997027,1.37963954019,1.37823328017,1.43855136513,1.41548827755,1.25574670932,1.31769339348,1.18951610223,1.19137986787,1.28406645263,1.37065649665,1.36296254309,1.27808580063,0.740341042862,0.833464527304,0.906745917173,0.91269627091,1.16314703111,1.11242536417,1.57270316772,1.49867127973,1.55028758803,1.45225506031,2.15700741631,1.37149372284,1.46154423205,1.44840031508,1.1803469901,1.55392856995,1.47158595547,1.4107373886,1.50722399325,1.36994153593,1.42440848451,1.08271721165,1.27044900852,1.28426531261,1.31234268974,1.1558845648,1.24042877332,1.341013724,1.44403629712,1.49936655164,1.46829618143,2.1582771202,2.23850881384,1.96455452785,1.88626568694,2.05461784935,2.06599039869,1.79727370422,1.78086041927,1.6870224737,1.61571555066,1.5486276047,1.63056383631,1.71817820245,2.23565854475,2.16207650626,2.24287543711,1.54995945607,1.36242295598,1.3669943123,1.27057441512,1.27225530357,1.54751359459,1.56415285045,1.23127565521,1.22459747794,1.13765687217,1.06626627782,1.28119352356,1.38001214094,1.40424078773,1.15464092068,0.96835442632,0.929002528704,1.14384377431,1.06578994297,1.61631543432,1.6940627349,1.52793399781,1.51523654378,1.3515928879,1.3814654705,1.89596529047,2.06908796259,2.16497473408,2.16311212566,2.07414568955,1.98152174253,1.98490080373,2.25518386826,2.42434930515,2.33971015477,2.42354941686,2.39184712377,2.18520255983,2.28893475372,2.91994932577,2.7039466051,2.76930794898,2.67447824991,2.65148305517,2.83564780339,2.93027631269,3.00239872031,2.93903240148,2.67190651062,2.64581428184,2.76692497285,2.70187925056,2.80041284163,2.84247662531,2.75944611636,2.67104921031,2.55152370567,2.35724014007,2.41120557934,2.50841065549,2.08278982361,2.05980710061,2.12917263495,2.07928920676,1.97982819253,2.0653553969,2.02240716698,2.08779937895,1.91860904787,1.90235355085,1.98360092759,2.06519231176,1.38445602017,1.3850944018,1.29577608453,1.29333867493,1.76131765904,1.69894254681,1.61255768076,1.71961689591,1.60504615751,1.56024688202,1.85935013337,1.77170214934,1.76109759438,1.70049653863,1.56865398699,2.58648122245,2.6333342137,2.68609607789,2.71392363466,2.39844318557,2.26459350685,2.36250455232,2.82761215766,2.97318276496,2.57179677083,2.48466340913,2.48029239221,2.53889878652,2.80538548563,2.79314999785,2.93235561751,2.84144075853,2.29208895153,2.38913770212,2.42538830228,2.23588410986,2.14296320224,1.95985175316,2.10285681626,2.00986321598,2.42497400563,2.52211232963,2.37861214501,2.35656429341,2.46700892811,2.54249232346,2.33500192518,2.33579703416,2.40998154028,2.4060662431,2.51223122293,2.20076399362,2.21892364951,2.30392756995,2.37782453457,2.3582369998,2.26626929438,2.81299260711,2.64209654171,2.64132783772,2.71897982292,1.17100809286,1.07750772172,1.00841251643,1.04283463094,1.15135400092,1.33555057037,1.14185075698,1.28510346989,1.2009712786,1.68623336265,1.76728934853,1.48623477834,1.47319733737,1.22540241969,1.31554031101,1.2155671843,1.29678079189,1.39636434475,1.38752017078,0.879260028507,1.05165818999,1.12938718386,1.21890658726,1.06725446251,1.21513186976,1.21328274295,1.13107392622,1.12624108098,0.525967515926,0.542336172356,0.634438566488,0.551275730203,0.356283391151,0.817858403511,0.764507081513,0.619968645492,0.668626030153,0.766560438568,0.693014964237,0.2716911297,0.325230442966,0.120558768948,0.189595328514,0.163259070379,0.194093900912,0.111580291561,0.166343832876,0.254804004603,0.439810656711,0.360636523763,0.450003866235,0.275911977093,0.388900105118,0.296940248148,0.906959842601,0.846236914281,0.860015647069,0.919416354832,0.934948556299,0.575986626078,0.764506576663,0.484239455869,0.307161783301,0.392139909992,0.47342743327,1.42797813257,1.29663603653,1.32833694977,1.36134211587,1.49349417381,1.45836814318,1.46109970211,1.48634011811,1.41169533489,1.57755288584,1.55895675194,2.096640777,1.99961272285,1.70521140958,1.80445428107,1.69704672914,1.77578707932,1.60452364407,1.59408335674,1.76286858918,1.67380363231,1.96987235214,1.87862880586,1.9402762212,1.86606374007,1.9949110873,1.92383090144,1.83680397068,1.82316322446,1.89471067933,1.97932354658,1.19651827992,1.16587350362,1.12975374459,1.02737489614,1.06502103246,0.893241483947,0.992966068678,0.219433898755,0.349951348112,0.255963292177,0.497369449917,0.402196254507,0.893488049002,0.667189475359,0.836734613764,0.755477783105,0.586404359029,0.666298928929,0.605703536762,0.699624106768,0.794147515435,0.857093738491,1.88915947843,1.98848479665,1.60160239225,1.62318588349,1.73909958489,1.71862904921,1.79203382411,1.94627417902,2.01575724262,1.85169691867,1.83089731519,1.29388304054,1.34423614771,1.32168434781,1.00871699469,1.09476927439,0.925187353724,1.20284622724,1.38194670667,1.28157049002,1.37082448717,1.21996048738,1.30976982748,1.56617071512,1.66532657441,1.5785609551,1.52391877333,1.67849480328,1.72330270029,1.21691582759,1.11428284531,1.73166578637,1.72535927455,1.90412838967,2.07379534687,2.13397568397,2.22518602045,2.18072030031,2.11318223756,2.28405380883,2.30941192797,1.55133886289,1.55025523699,1.64226185978,1.64042828842,1.45985035587,1.45690536493,2.04691313679,2.11419566435,1.9966647708,2.08647497059,1.98286351303,1.98712359529,2.07172427782,2.15275307962,2.14563394012,2.06056368486,1.64499916685,1.72134752103,1.81320582756,1.54912212025,1.54874782724,1.4554139827,1.45639704128,1.73273739638,1.64184107125,1.64123734526,1.81921636882,1.89548302533,1.81478248347,1.7277649449,0.954041720749,1.04234163805,1.04536726984,0.977101967064,0.91227866066,0.820921961286,0.962564491484,0.987000835503,0.931836535261,1.08338301404,0.983346532023,0.715461412187,0.80673038968,0.64801554693,0.67954731108,0.840408726147,0.780007780991,1.82329478278,1.68528855689,1.66263934423,1.73027411311,1.61499109669,1.73197175769,1.58899427303,1.56875719505,1.63843212521,1.75279634253,1.67934536098,1.94501253937,1.85024257421,1.77963075675,1.96799332791,1.89638650504,1.80308008088,1.37410479721,1.28189515294,1.44896788319,1.45722168055,1.54627554685,1.72330472528,1.62647468476,1.71489817725,1.48343723511,1.473331345,1.65237982576,1.57387146705,1.6436083845,1.55506961794,1.89343823683,2.19599623793,2.04842284861,2.10208205941,2.03131741133,2.33301664052,2.31533104039,2.24840307131,2.15424569848,2.14148721345,2.2183801152,2.05794547364,2.15819684151,2.80720938973,2.39022137071,2.48553100712,2.47730459768,2.8224386872,2.75540400989,2.66397307727,2.63203103047,2.77468391063,2.67851137228,2.01199856997,1.8617607028,1.95420351546,2.03189202632,1.91783375264,1.84516843602,1.6122400927,1.54798645132,1.45797623944,1.55922686765,1.46099765897,2.1522679865,2.24084310927,2.13549029809,2.31542193633,2.20904892459,2.30079220324,2.81257112984,2.87346887189,2.80889484905,2.71574513491,2.23709399985,2.32174954332,2.40224264832,2.61341065154,2.6070070096,2.51011241117,2.88235451855,2.98719423668,3.04736898931,2.96906555383,2.88971545989,2.84703117993,1.38801544874,1.19841127155,1.23215761143,1.32730540291,1.35208299889,1.25796650665,2.50290681001,2.55720045187,2.55041506218,2.64053073251,2.70979116866,2.6718369428,1.44012694869,1.52060064452,1.60393957657,1.59361090317,1.50138941461,1.43117809013,0.590768023236,0.680666404725,0.576457157842,0.755429224948,0.899124201007,0.995324464285,0.8673334919,0.872987300482,0.705719778663,0.795578221375,0.607155185743,0.61163878207,0.704433742639,0.694629414429,0.784976541024,0.779078891469,0.475331386222,0.380425115727,0.318438946316,0.378392749754,0.520234951479,0.481510783706,0.438097466403,0.529103463395,0.604301484445,0.589530572546,0.498931331691,0.422340846817,0.271635434834,0.418081007458,0.324490702902,0.49139020048,0.327640370265,0.412901604451,0.335131861664,0.750639123956,0.608266316085,0.703932065403,0.711505525817,0.816690764725,0.821264345776,0.729365761788,0.641758481152,0.64882914224,0.740488971955,2.06885042922,2.19033019213,2.09636220903,2.13289398745,2.26027055765,2.22994891107,1.64411315684,1.52130263639,1.54554380474,1.48474123164,1.68178449287,1.655237831,1.6195250983,1.84156303094,1.97271314053,1.93933957017,1.77971614692,0.89214737253,0.872733531951,0.783700875527,0.788597505898,1.15102137457,1.0576489558,0.990640222311,1.02775773605,1.12777718476,1.18434666147,0.829364374526,0.732043425713,0.680913142624,0.714722728846,0.739702593088,1.01066978934,1.10021052346,1.11174000447,1.03538077655,0.866271868855,0.770985262404,0.755614306227,0.838151269134,0.928309037706,0.941754661075,0.951554072803,1.11022285597,1.02008855822,0.995480491698,1.15185848456,1.10498938893,0.948059604625,0.962881042613,1.00747439153,0.859500087851,0.797435839165,0.842172146418,2.01214784164,1.93782059645,1.77092836201,1.72645389216,1.65666335549,1.67614109879,1.81836685269,1.84357044921,1.88544732982,2.06798419042,1.99417586977,1.90406669768,2.05100673479,1.95886230352,1.13122466124,1.20677860042,1.18942891292,1.10227512354,0.931485562851,0.853837190897,1.03414863066,1.02257841751,0.960490016994,0.871943711158,1.06337942669,1.1065526349,0.961762582068,1.03930667788,0.946973536123,1.81887710142,1.98584257574,1.89624608633,1.81440828442,1.99002278457,1.90490627083,1.88602604578,1.96005342284,1.93708483567,1.84495329571,1.63213901936,1.71778343817,1.60181917261,1.6691684298,1.77689656197,1.79541417237,1.07410666187,1.14550002724,1.23261704693,1.21627313327,1.11976997224,1.81091104612,1.64163104774,1.7246452697,1.81021595832,1.75409732021,1.66275475139,1.97046442758,1.89133392748,1.81013934427,1.82217440015,1.91520354325,1.982443312,1.56582692268,1.65004023864,1.72944443695,1.56152213558,1.64437463533,1.72805151827,2.0571032581,2.15464496746,2.66004303756,2.74679326866,2.72505576562,2.78455189082,2.9755518561,2.90370509531,3.06834291511,3.00726035901,2.9150864505,2.88183604332,2.22799295601,2.31846312155,2.33139414143,2.2446581274,2.15570931408,2.15160945363,2.4188657753,2.49656581592,2.4165361065,2.50158880848,2.58808626702,2.59123993653,2.32232450982,2.23790449861,2.14248420073,2.1273007496,2.18464189047,2.22549342233,2.12826653665,2.11032702967,2.31286772605,2.21475091611,2.17144538507,2.21918033065,2.5068993213,2.46409006457,2.36449389091,2.31355700458,2.35725411039,2.45053176595,2.3500314034,2.28129693421,2.30452493448,2.39669959597,1.42632327458,1.36095874811,1.35092057266,1.26271833776,1.27699120903,1.18674141668,1.18264439345,0.824762835867,0.66327016889,0.725239880369,0.711231131337,1.0189056228,1.1054371079,0.660679735918,0.667228076255,0.748720812113,0.835928561694,0.461813049729,0.557719488794,0.498051901967,0.426341091732,0.58945920296,0.615719263632,1.75184767657,1.93858212646,1.90926221066,1.81433434547,1.87419445842,1.78269351678,0.705860766293,0.560728421891,0.657773201823,0.725952409969,0.832425536482,0.872321391719,0.912473178775,0.99951719782,0.972628994523,0.418415675314,0.251776363353,0.320839855002,0.623719100888,0.541235683933,0.619099948734,2.02279398253,2.07599711667,1.92210087281,1.87681616189,1.92341303278,2.02128832963,2.30342164924,2.34722390586,2.37905396821,2.2042965791,2.24780504271,2.17950363871,2.44462004544,2.50840777313,2.60080636587,2.63041749486,2.56047841125,2.46870351221,1.47452229351,1.40572426772,0.84989252214,1.02806047467,0.923081848359,0.930461913574,1.01718332375,1.01297499794,1.10161857681,1.09859242991,0.855905572481,0.953155189874,0.959607834442,0.802522672545,0.867968516917,0.841677372616,0.878734065382,0.779956271287,0.760825524991,0.935628723251,0.95398605432,0.552917922199,0.444837049557,0.542244706416,0.586580548243,1.40215386995,1.49622971366,1.52005170302,1.44910992357,1.35361289162,1.33034655112,1.23605340974,1.16204818234,1.24252691527,1.31024116058,1.2833965147,1.18653606036,1.11523384518,1.14499144262,0.464738304275,0.457002725791,0.309619920135,0.397989693874,0.296923700398,0.378988880703
};
const double THETA996[NST996] = {
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};
const int NST1010= 1010;
const double AREA1010[NST1010] = {
0.0124299296763,0.0125351810871,0.0120562856962,0.012375946706,0.0125941480088,0.0127945223199,0.0123495231232,0.012683752365,0.0118924571799,0.0123784183386,0.0126082093541,0.0123259763507,0.0126774174972,0.0125641155111,0.0125181129023,0.0124813613113,0.0126311091378,0.0125064245984,0.0125180115164,0.0124010360858,0.0126934006505,0.0122641033471,0.0122608327765,0.012287042425,0.0126050590514,0.0122942279071,0.0124566879501,0.0125056155249,0.0121910561936,0.0127460124488,0.0127676141388,0.0124788007833,0.0125333433979,0.012261769768,0.0120537417533,0.0117212622177,0.0118754187773,0.0116809995964,0.012306268984,0.012433943302,0.012604219621,0.0122148210652,0.0131504593833,0.0128066070005,0.0122759108436,0.0127883576715,0.0123919875785,0.0118448396031,0.0128052208767,0.012209549724,0.0126229039352,0.0127365023111,0.0122961256711,0.0116854580792,0.0122461079312,0.0123162955312,0.0148520441431,0.0119075599984,0.0115935811041,0.0128832603034,0.0118153980238,0.0118080078058,0.011823930501,0.0122057046292,0.0122074480664,0.0144344693889,0.0125427825633,0.0125194952293,0.0123660849415,0.0122320402518,0.0122585979143,0.0122928733423,0.0121550900372,0.012331404555,0.0122604157905,0.0126989702943,0.0124219735533,0.0123254685575,0.012698214708,0.0122437111951,0.012284794452,0.0126213309971,0.012326210442,0.0123607062984,0.012483317499,0.0128695057445,0.0119701931493,0.0125328798671,0.0127084566048,0.01220579679,0.0125119305054,0.0121237854928,0.0123099396207,0.0130339169031,0.0124599877103,0.0117868738617,0.012214159278,0.0116334490086,0.0128695228118,0.0126273337427,0.0123348956764,0.0125841505877,0.0127066223678,0.0122704581373,0.0126152382591,0.0123115395157,0.0121456977266,0.0123284123627,0.01208598949,0.0127080066477,0.0120296087782,0.0129074399965,0.011938046968,0.0123211373904,0.0116806293432,0.0126135703844,0.0123001557254,0.012431965604,0.0123284814306,0.0126722066063,0.0120640572833,0.0128147330018,0.0124209808245,0.0127914831285,0.0122309909393,0.0126523001656,0.0128296924494,0.012741246726,0.0127261310686,0.0126452330912,0.0122710857891,0.0122724581266,0.0125069843027,0.0123420094274,0.0123346440298,0.0123206185482,0.0125651400377,0.0127620687508,0.0122098125055,0.0130717107235,0.0127224033202,0.0121157858421,0.0126925987192,0.0126806288836,0.0123770979915,0.0124339684986,0.0125439204709,0.0118542463264,0.012498444723,0.0119955405934,0.012031825529,0.0121980450429,0.0125063138499,0.0120765751929,0.0127921151006,0.0121989796224,0.012696980681,0.0122694391412,0.0126200239892,0.0125064848701,0.0124071319928,0.0126348878018,0.0122145313309,0.0122929424916,0.0122940749765,0.0127261601851,0.0121660457344,0.012730457051,0.0127733589438,0.0122558120422,0.0123276617994,0.0123027429771,0.012761742278,0.0123621831097,0.0125851236599,0.0125891664888,0.0123781876932,0.012386484152,0.0125365755006,0.0123415494781,0.012657689798,0.0126171639845,0.0123502002319,0.012255696691,0.0137894509536,0.0121932260107,0.0121379847322,0.0117901580675,0.0127038969203,0.0121743572213,0.0122020096599,0.0120930034688,0.012077609742,0.0129371819965,0.0149812108795,0.0116187856541,0.0123839245375,0.0125322033086,0.0124727076447,0.012441829285,0.0125376486075,0.0125234197054,0.0124996267073,0.0122393053272,0.0124971637563,0.0123488097593,0.0125966019809,0.0124402694885,0.0124786875251,0.0125419428982,0.0122908854477,0.0122442992348,0.0126582465425,0.0125688108554,0.0124289953845,0.0123642447917,0.0125694336307,0.0125321439743,0.0123873267315,0.0120781225301,0.0123896657393,0.0119119819063,0.0119572350701,0.0120274786019,0.0124661043354,0.011989749628,0.012678807141,0.0123927930944,0.0120523087013,0.0127838817383,0.0122802607626,0.0121507950555,0.0121187209227,0.0127262215171,0.0122648711238,0.012695004371,0.0121827074681,0.0122866978262,0.0125525705007,0.0123572189504,0.0124551707958,0.0125240654046,0.0127268745697,0.0121952620293,0.0122881959254,0.0120626148221,0.0120956823003,0.0128720805318,0.0118694418325,0.011937237375,0.0128016779121,0.0124119054631,0.0127800302406,0.0118695274309,0.0126363831874,0.0124783383506,0.0130200846724,0.0127925452952,0.0127101696931,0.0126562386375,0.0125820803334,0.0116364151515,0.0142258833357,0.0119044810759,0.0122933412071,0.0118144673888,0.0132921457402,0.0119390489914,0.0143622704449,0.0124324608983,0.0125846984756,0.0126073159886,0.0122713566842,0.0122460277394,0.0123786840784,0.0117763720008,0.0129929059604,0.0120344869074,0.0124698387146,0.0114772076788,0.0129961070054,0.0128247872028,0.011720489384,0.0125142274463,0.0117504584064,0.0118095162155,0.0149872336949,0.012583446908,0.012200035066,0.0127592295689,0.0121844934289,0.0126805546913,0.0127109337902,0.0124113091243,0.0123391354644,0.0123184974238,0.0116621802507,0.0128776423391,0.0127895926562,0.0119637358563,0.0124268149713,0.0122292999059,0.0117816755543,0.0125705829427,0.0126236190606,0.0123530740324,0.0126736882274,0.012340687405,0.0124266921223,0.0126834204108,0.0125039977164,0.0124063376089,0.0127011460992,0.0122280097939,0.0124768018499,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};
const double PHI1010[NST1010] = {
2.24639082309,2.21849567011,1.30195843331,1.84407574052,1.92209035602,2.32564078358,2.17326274065,2.08860420888,2.13671805105,2.11509715295,2.20792305752,3.11064047693,3.02468014701,3.02320506322,2.94095211194,1.89012118829,1.81130793762,1.73310489855,1.43126516321,1.44937794061,1.76831134201,1.6794232202,1.60642741149,1.57681969114,1.66212001362,1.49976128037,1.51215406198,1.333319254,1.1533155387,1.42787434794,1.64403276003,1.69729290714,1.59970755765,1.57288597517,1.61635822242,1.67460881724,1.60721751183,1.5095665445,1.51978424623,1.69283590848,1.61805746671,1.63722539876,1.44104603867,1.56507014695,1.27569597778,1.37712757937,1.46617980435,1.21823828469,1.56194354002,1.4780058009,1.43072946151,1.09858267466,1.09886974962,1.37051765888,2.01299591624,2.09779811144,2.22003364982,2.25718476956,2.2747160507,2.36899905666,2.21966647033,2.34534224694,2.25875952672,2.27822650196,2.25102580583,2.32628528601,2.04366082203,1.95247816232,1.88049536866,1.89063132511,2.22427686078,2.31674083697,2.61379138461,2.56081280986,2.66427116507,2.69199306575,2.91594252831,2.94724073213,2.85988073777,2.78161763293,2.79897968352,2.86031735443,2.95985547158,2.96952885963,2.85070817946,2.28322927297,2.29513365148,2.71253309157,2.17581069432,2.1980438639,1.85481847151,1.86590567862,1.88411325687,1.78312801126,1.79122649812,2.60267883895,1.75483357442,2.06365447401,1.61384948969,1.71783453747,1.63205204334,1.62321722179,1.56563362902,1.54690935485,1.36993206884,1.21665100112,1.4907976919,1.39283212709,1.34413366121,1.31685766753,1.60089534055,1.51099481099,1.44002774715,1.60296343244,2.0909904519,2.11873624581,1.83666966022,1.81871208317,1.99680937539,1.92759505203,1.98063738676,1.89351697008,1.32052734437,1.30544034841,1.39930046804,1.40617577169,1.13259222521,1.06079240533,1.19744396859,1.26284136086,1.34495256491,1.18263647363,1.1953691103,1.93112978174,1.86506507117,1.7423831219,1.76903310465,2.17013746921,2.09647970698,1.76504859586,1.95946291843,1.80539561363,1.89782708216,1.35149336551,1.52777127654,1.75165349396,1.73085250614,1.52605961845,1.67897260249,1.58613936247,1.40308971393,1.49972224888,1.51691448751,1.4438878269,0.741091791397,0.313547603813,1.01712097127,0.930299195795,0.769937726427,0.844607781742,0.852192261067,0.947985433838,1.02742868954,0.933374477997,0.803072624984,0.83632567515,0.704300913836,0.797516863863,0.9371265327,1.03263980927,0.191352987476,1.26582663723,1.0984453812,1.11155993471,1.19519706472,1.37356096917,1.34920627308,1.18581881143,1.25493527119,1.48500511931,1.41164177347,1.51294569075,1.42507471256,0.87001934654,1.36905740541,2.22281420841,2.24208612958,2.33599808933,2.13946151573,2.36190895013,1.49447431506,1.52846063362,1.38026009725,1.46261034936,1.61181549174,1.51694680949,1.34927241097,1.18429678944,1.26433082747,1.35995996762,1.12520948766,1.09773323563,1.1597107119,1.26981605458,1.2453562239,1.11461325156,1.20226969386,1.55065925832,1.52687686253,1.47761570519,1.38338013222,1.43151462841,1.36087680681,1.4496103859,1.31161174736,1.35653647141,1.28708227726,1.40651638666,1.4752397167,1.31404705306,1.25347097768,1.38073374136,1.33709005445,1.69751710375,1.43527443134,1.52887110202,1.01867639591,0.921333767944,1.23651317489,1.17689589225,1.07785081067,1.05475673015,1.2188813836,0.970095344136,0.895446679685,0.553793927617,0.467837194473,1.62901697644,1.77335026396,1.67501650662,1.74487492707,0.989069295727,1.05421340435,1.06560019728,0.967199973071,1.30690554369,1.13609138169,1.13363619879,1.21604842986,1.38675764959,1.29410765762,1.13366142132,1.23608817295,1.27609533836,2.07972023828,2.52354821761,2.36515678122,2.19529019958,2.02356973863,2.05880900866,2.18660298751,2.17093381574,2.25390603204,2.34126718313,1.44360908178,1.5305789621,1.60977351421,1.4306783511,1.3906358458,1.72219733523,1.64821988687,1.78858747913,1.71615188777,1.76784851652,1.67181811013,1.44572705231,1.41329283739,1.53975477348,1.70934577896,1.5400372696,1.61352046883,1.80661684189,1.72410302582,1.80491206279,1.71703324125,1.62628973017,1.6209707617,2.49200699091,2.39109330512,2.34889991762,2.3986838792,2.70193123673,2.49944423231,2.65511680183,2.55140903454,2.78362844004,2.42409850498,2.49205574609,2.39775141775,2.37469572094,2.49422740309,2.3898689198,2.21682539622,2.02411091887,2.14781777217,2.05307268895,2.18711713653,2.05760965423,2.08913667754,2.32387485099,2.22896011333,2.2345224019,1.97477363059,2.05589128951,2.06051826534,1.97594308911,2.14694540117,2.14353343967,2.66807358556,2.72411529597,2.70067303773,2.82646946916,2.65707355015,2.5627500496,2.55803606986,2.51693404866,2.82250782901,2.80308405943,2.87193360173,2.72146782097,2.704211616,2.6668197071,2.12355140541,2.05548121878,2.13640981453,2.03253110203,1.96495536932,1.95482583607,1.8293819002,1.81520854315,2.01630622832,1.92758560339,2.08519670266,1.91357466077,2.06812138358,1.98528270117,2.6655832191,2.81690109213,2.76442629014,1.96564787228,1.91024001399,2.04315468758,1.94725873206,1.68850579946,1.46125290388,2.07191294737,2.167234327,2.18762038502,2.00461975014,1.91453248637,1.844985574,1.79253899864,1.88573791609,2.13501642518,2.05774620219,2.02752527896,2.11517753096,1.88322580978,1.79322932915,1.78201559368,1.86119132078,1.95331622559,1.96417321732,1.95149015007,2.04805362066,1.19206777042,1.25098688352,1.26968424661,1.99586385892,2.07204027789,2.18728336843,2.17016706254,2.02992499412,1.94146376325,1.93330012947,2.01262383019,2.11498178261,2.10568547511,1.12685001982,1.21614051316,1.22435788983,0.59206176905,0.627422670975,1.05919738942,1.09455123711,1.02407124409,0.92773623507,0.896008291211,1.22071471226,1.34854925946,1.32462497392,1.15399468956,1.28600642975,1.19588027359,1.81887503372,1.84111093867,1.89021981391,1.98496644303,1.93364722751,2.00642929627,1.21299355198,1.25344768514,1.68312199965,1.85893698011,1.85659950713,1.77082402355,1.774579652,1.68967349871,1.68438348753,1.77447662816,1.58714698224,1.59235786746,0.521031822426,0.488786343813,0.563528153365,0.62470065738,0.660229462727,0.689770247542,0.761372993532,0.754672806272,0.679982213699,0.871610508616,1.0192607799,0.853325261904,0.932553014185,1.12620433145,1.0341825248,0.96568683018,0.994502091106,1.08847511154,1.15187063291,0.505665055404,0.397464949266,0.409483838531,0.583388429526,0.470955953991,0.28506213523,0.335534946631,0.42887960488,0.76940336783,0.59510410302,0.562800236199,0.616752643971,0.705856963768,0.619079816811,1.05302628843,0.678840736282,0.773215724082,0.757415816455,0.672852188645,0.846257314235,0.855852548832,0.510041580707,0.438040698267,0.349843697385,1.30620799552,1.32557147854,1.14870303134,1.21289935843,1.25317018418,1.16970596582,1.57349209469,1.75388813125,1.677613464,1.58810819549,1.02744876052,1.08707545885,1.19540287331,1.30203925998,1.34738341908,1.29856035559,0.75804582982,0.719273560423,0.908609220405,0.8527561047,0.994720321826,0.897682899421,0.863514891436,0.90433951557,0.850692851905,2.23703626148,2.35533848679,2.29092708484,2.30240060545,2.49885646684,2.46576026659,2.37843592055,2.12330088137,2.1726594054,2.19456669567,2.5156014027,2.56543264492,2.50314745913,2.4123053399,1.45153168297,1.52710329806,1.28551974185,1.23182465483,1.30406564038,1.13808157807,1.11950772767,1.19490719061,0.996422997149,0.93272586711,0.831230912614,0.793204711578,0.960486531736,1.04759844148,0.892487591907,1.07008556288,1.43599671365,1.47257732956,1.56117568829,1.50100148925,1.59747922864,1.62122700232,1.22648737888,1.31628893543,1.16104995988,1.1882186,1.28288698725,1.3457316628,0.566445940732,0.660615348844,0.464538277309,0.524109243737,0.491052009727,0.481394632324,1.47004712358,1.59139614986,1.49942611556,1.65370000378,1.5282862326,1.61976956002,1.60207942444,1.76609231814,1.69151170085,1.58771088954,1.66570166131,1.75453841899,1.35488695809,1.30838257825,1.15968966858,1.04609155904,1.14733863496,1.20439419118,1.00189934914,1.05902250912,0.8085535074,0.637448433391,1.67601098483,1.76813765028,1.86187837664,2.03650530524,1.9695805143,1.88391049829,0.824232082145,0.897212431399,0.732814002613,0.886440878621,0.721478550665,0.802477790825,1.27693658644,1.22207637803,2.00547439411,1.91516075537,1.8428050074,1.85505144851,1.94495561337,2.0310759366,1.94102051675,2.01917294702,2.11669075554,2.10861239168,2.72197688641,2.55003910141,2.45883264749,2.37531956261,2.44911253668,2.3525861555,2.27255779901,2.28543103856,2.1979694778,2.12855457413,2.11134209208,2.23133268395,2.27862366907,1.80184609255,1.78289636724,1.89488731565,1.96450009603,1.85796633901,1.94641296537,2.28440337085,2.2784855409,2.35040705171,2.64384039203,2.47777049598,2.44457342378,2.46617215897,2.63728769922,2.54019398499,2.48356151033,2.63590319087,2.53631394171,2.81126059089,2.83174873005,2.90931878408,2.88003465687,2.99673120214,2.9142645705,3.07520752915,2.9993311551,2.11602320743,2.07324264183,2.20907509357,2.11759974806,2.79459025895,2.96645850433,2.86974300017,2.79533644281,2.95886250681,2.86293416118,2.56831807173,2.66827107578,2.70357649628,2.62488364771,2.53171238211,2.4568638145,2.62861172299,1.72788706454,1.61726448457,1.70784665141,1.65303792872,1.5576804674,1.54178496977,2.3649073789,2.29248297019,2.31095464992,2.52170341837,2.61732959188,2.46216441801,1.96950284438,1.92093281267,1.82269954436,1.77581181064,1.76774580648,1.82181804965,1.91690456922,1.80389281747,2.10461962889,2.06376995676,1.59834747348,1.65495993224,1.45028154566,1.49734596296,1.56645982517,1.54969886524,1.67493362055,1.75241758746,1.63444693144,1.72848994605,1.90189879632,1.71686330668,1.7890865373,1.88128004016,1.15279753701,1.13882471788,1.07384013259,1.04175976131,0.955899631132,0.972180468263,1.15474623031,1.13877861392,1.29808388659,1.47272719067,1.4086154843,1.32246175443,1.45445950227,1.36620067419,0.34881874316,0.404883166008,0.398081556916,0.560508313604,0.636388317595,0.536232411535,0.491623955621,0.574766469401,0.673156187393,0.665215864768,0.593479025709,0.497767345949,0.486314667695,0.992799184525,0.894203922861,1.01721272126,0.935458156198,0.855695278581,0.853226929957,0.717768867303,0.752569213838,0.790123521544,1.08960886189,1.02078727708,1.06476262755,0.967123175016,0.890930735425,0.920320522132,0.348267760053,0.422653104111,0.731028005372,0.772351141415,1.22858427356,1.33481321495,1.24613526226,1.18803121463,1.34637697798,1.39479189922,0.777808532747,0.931089396606,0.871449333664,1.04717070808,1.14598573541,1.06510047684,1.00522660061,1.16472429104,1.20417221136,2.32861457067,2.45009595556,2.36144847928,2.3912331892,2.5187347413,2.49250705809,2.10665482544,2.20017015011,2.06443433428,2.11437795219,2.25620308765,2.21224780857,2.36051059455,2.26017086737,2.33575302192,2.402421836,2.23685462018,2.20268829782,1.69264181985,1.39733196695,1.47047377169,1.41951354048,0.965687056863,1.03267820726,0.841515149034,0.864511513496,1.00425559878,0.914317872176,0.180208645074,0.320334335483,0.276004466949,0.0103118360256,0.112545019408,0.494970178565,0.104665905392,0.164379969024,0.689635685506,0.775270197356,0.673011125182,0.627225027554,0.37759123694,0.388958471721,0.286216662103,0.188241813187,0.571419744158,1.16408219291,1.49254576725,1.47504651225,1.37262999055,1.41315576576,1.32230472203,1.36747069285,1.38119049522,1.47182523071,1.48295872974,1.52866557668,0.736509383756,0.766127879344,0.576220149988,0.646364646366,1.24057539301,1.18553244705,1.31232500099,1.28909665834,1.01262652854,1.11031582977,1.1424431482,2.62809919648,2.59349659581,2.50183228326,2.54789248206,2.44609297397,2.43217556388,2.73494713271,2.80108441953,2.82191540233,2.69784534223,2.62358063121,2.64144255191,2.28903986397,2.20457710348,2.20524782072,2.29252475809,2.38611357788,2.38176934467,2.46775309751,2.34686843452,2.36825683953,2.4141830842,2.51249938175,2.54583753554,2.72878653126,2.63532668449,2.74690488457,2.65969882922,2.57095254398,2.56315228468,2.2087758321,2.24894660995,2.34941855593,2.25803172538,2.39395819738,2.34177664339,2.38174325983,2.4642589381,2.54260323271,2.51561471099,2.35887777393,2.41574082089,2.65515249871,2.76570106949,2.75227098803,2.67562100907,2.48397648333,2.41216698905,2.40458464831,2.49943443753,2.58811475799,2.57976395459,1.89488107906,1.92463533277,2.0133508397,2.07814196287,2.04844069045,1.9540376988,1.51757237948,1.60968724519,1.45944722337,1.50630112611,1.66668536588,1.62113474349,1.8419019987,1.82707839106,1.67448349552,1.76425392159,1.65930600271,1.73436141947,1.09365357286,1.07278281425,1.04195702688,1.04573090619,0.258567867427,0.0787725599242,0.150712957154,0.229786196632,0.677783545524,0.643737968713,0.777534107933,0.806798431268,0.72860389276,0.473402291137,0.603879393621,0.512765600257,0.439757785691,0.632283574553,0.573338358331,1.82345239532,1.78834281866,1.92525142233,1.98120532204,1.61990361061,1.69053203406,1.53617708754,1.51372026172,0.467600840888,0.438680301874,0.338714043557,0.481034849242,0.295884025156,0.195969052718,0.185954152475,0.285450408752,0.368521738986,0.372853429143,0.207575183808,0.158325887828,0.23533067065,0.323340268617,0.359842398443,0.313807438993,1.23234376714,1.24901290972,1.35380202917,1.32062867512,1.42386307811,1.44046797215,0.562760328252,0.612363060357,0.711274201606,0.755782342516,0.706965261375,0.613832897999,0.946136101426,0.850073500312,0.786943577745,0.827624612573,1.08086689794,1.07549737828,1.12441515926,0.976381217754,0.926612034453,0.98262858517,1.06115758157,1.02555734095,0.932549236464,0.873668780173,1.01022076927,0.9161849355,0.959563386799,0.97105258994,0.902109857959,0.874343409215,0.875369955677,0.796650122804,0.977464891462,0.96412897376,0.90476826139,0.813302261932,1.78386957924,1.93404066263,1.84351786345,1.58574524923,1.56454076121,1.63850844573,1.62958217561,1.7389869025,1.64819813256,0.311643224822,0.413709322278,0.257070938853,0.323134832419,0.460581676979,0.42017138893,0.544468224131,0.710075772618,0.745989405454,0.723476544838,0.779209896671,0.624296261686,0.795388327733,0.632524441411,0.709433159572,0.65340255563,0.746480709458,0.811710428205,2.15394363363,2.19377391092,2.22661726128,1.81079372602,1.73580676335,1.68170365039,1.70325284156,1.75798671849,0.652799758584,0.544503209718,0.632741559209,0.585919821341,0.486370539308,0.464098396535,1.90851219416,2.09820114528,2.06370539078,1.97254843071,1.85749638152,1.9333108424,2.05473878692,2.03144487755,1.81571291739,1.79844845693,1.90850631407,1.87657280498,1.99017303578,1.97541508973
};
const double THETA1010[NST1010] = {
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};
const int NST1196 = 1196;
const double AREA1196[NST1196] = {
0.0105413280503,0.0104684519079,0.0106691150452,0.0103394603654,0.0103664994121,0.0105256950535,0.0105122734251,0.0106738694517,0.0100294481215,0.0107387747231,0.0103714552469,0.0102553599552,0.0108393971118,0.0100254841885,0.0106813192593,0.0108000767359,0.00996876674383,0.0116690910713,0.0104894586529,0.0100870699359,0.0103024258835,0.0102543865634,0.0104841027585,0.010370849411,0.0105334564756,0.0105733679033,0.0105395048446,0.0111017191903,0.00982437570698,0.0104734639299,0.01058292671,0.010761337823,0.0100814243555,0.0102489960059,0.0100766263298,0.0100708166792,0.0109961564616,0.0101003056023,0.0102030450105,0.00999864780198,0.0106810620315,0.00989274892885,0.0102105016332,0.0103985820081,0.0103397354438,0.0107401556934,0.0110557964424,0.0104527915134,0.0105768727994,0.0107396469992,0.0102084948769,0.010400693081,0.0106007057951,0.0104944960259,0.0105845336627,0.0104131811371,0.0106054613707,0.0104764313124,0.0106024853212,0.0103473693542,0.0106511463271,0.0107398702769,0.0104174349402,0.0105692941786,0.0104133143245,0.0106676889015,0.0106739545143,0.0105578510927,0.0104540566879,0.0103487721351,0.0107639906508,0.0102549418747,0.010221418405,0.0107226846025,0.0101819883419,0.0106037370125,0.0104032094461,0.0105631930731,0.0106373054183,0.0103275797804,0.0108041690475,0.0102778224321,0.0107507869777,0.0102028794199,0.0100683229828,0.0103393960485,0.0103319454066,0.0105326927412,0.0107138536692,0.0102771441278,0.010397955464,0.0103885572623,0.0104558967874,0.0103578584587,0.0108559790899,0.0107349105976,0.0105563043499,0.00996571182433,0.0104489201232,0.010450217357,0.00985655555083,0.0100949377995,0.0106590914123,0.0105325707841,0.0106435995496,0.010428294729,0.0106167297473,0.0104901182397,0.0104559364111,0.0103438008893,0.0106557354763,0.0104097313614,0.0104741261666,0.0107473613022,0.0104235775329,0.0104859044507,0.0106835082259,0.0100245402692,0.0102322530641,0.0104577375395,0.0104465599201,0.0106543315422,0.0106106531093,0.0106193985011,0.0108439513215,0.0103997046333,0.0104710557648,0.0102720391437,0.0102888217542,0.0106873263584,0.00987433435392,0.0107463142361,0.0103814359287,0.0103601233673,0.0106930550552,0.0105205752269,0.0105460779841,0.0105710474284,0.0105490914623,0.0100186299285,0.0100223136968,0.0106977558575,0.0105149625334,0.0105473287249,0.0110518157187,0.00993869851403,0.0105164054639,0.0105260357096,0.0105634334051,0.0105676410737,0.0103681048245,0.0105438919582,0.0105392784988,0.0106394395784,0.010442023957,0.0121027854162,0.0102942780059,0.0105125387183,0.0106771865372,0.0105553392779,0.0106890632829,0.0104110504342,0.0106597983192,0.0103859192589,0.0106835248333,0.010441230153,0.0106544599268,0.0103605174719,0.0107235192019,0.0127631379934,0.0105671148665,0.00998227870515,0.00990562774348,0.00997504259897,0.0113405288869,0.0105821372483,0.00993909399229,0.0104894151544,0.0104164648344,0.010046550741,0.010488139058,0.0123317484939,0.01027833154,0.0122146886712,0.0102847272445,0.0107121221424,0.0105800618209,0.0124849653291,0.0106877930344,0.00975210980363,0.0106028714768,0.0104556333156,0.0103280693403,0.010555217428,0.010546479007,0.0103500870003,0.0105118409917,0.010756676416,0.0103527546049,0.0104932588313,0.0105552903787,0.0107843175455,0.0105513405432,0.010534363238,0.0104051757541,0.0108427652908,0.0102992011662,0.0102607420711,0.0103572048254,0.0106929960984,0.0104728811771,0.0102008475302,0.0101586476057,0.0107638510766,0.010341407631,0.0103819534185,0.0106776875671,0.010109141918,0.0109197310208,0.0111719366537,0.0102386791147,0.0103383778244,0.0106354331252,0.0104506213037,0.0106225881791,0.0106805304194,0.0105871442197,0.0104886717073,0.0106561286035,0.0106966541817,0.010482341442,0.0104386145726,0.010524072449,0.0105889832514,0.0100612010769,0.0105679105271,0.0106337267556,0.0103427682942,0.010482371405,0.0104812768048,0.0105540427753,0.0105326670512,0.0104119944991,0.0104968887546,0.0106000180295,0.0103847916202,0.0106625262926,0.0104322779155,0.0106536375604,0.01044497673,0.0110863139093,0.0104827856633,0.0106537377067,0.0104844572201,0.0105846131926,0.0102513765916,0.0104360229361,0.0106668066431,0.0106662599567,0.0103706016138,0.010483471806,0.0103604901782,0.0105261507867,0.0104922550924,0.010293515267,0.0106955907242,0.0121120747249,0.0107338050864,0.00990238136536,0.0104414002977,0.0105858478239,0.01036782393,0.0102529016619,0.0106648348898,0.0101810414926,0.0111502829087,0.0100633742783,0.0105987636134,0.0104280217727,0.0106480946281,0.0104894007919,0.0106619817633,0.0103828923064,0.0106920999957,0.0105562383272,0.010539079371,0.0106802953612,0.00986251518471,0.0106528646955,0.0104567304616,0.0104606990552,0.0103891834661,0.0107519664916,0.0104078396337,0.00986313007667,0.0105740454622,0.0104551815171,0.0104360528675,0.0104387098591,0.0106226615774,0.010494138006,0.0108076122362,0.0106336326959,0.0104211189729,0.00985909965503,0.010608742492,0.0106911476268,0.0102849762304,0.0101055598053,0.0104590759743,0.0107180344541,0.0107546567125,0.0102068741647,0.010352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0962719,0.0107220117559,0.010362194416,0.0103656409005,0.0107171695681,0.0107942424079,0.0109114381706,0.0103217584572,0.0106394632545,0.0108275571859,0.0102993603503,0.0101031258984,0.01029644255,0.010194137422,0.0110847895735,0.0106056448133,0.0104447371265,0.0103108042388,0.0106835698109,0.0105484902106,0.0106420309846,0.0105739698147,0.0104450314481,0.0105665651767,0.0105267569441,0.0108582233585,0.0100157484839,0.0103287825216,0.0103580097878,0.0107676594033,0.0102350183492,0.0104200613453,0.0107943005828,0.01061001635,0.0104432231174,0.0102620458187,0.01074074281,0.0103557392302,0.0102267023788,0.0109437258763,0.00998568820048,0.0105123278531,0.0104989176643,0.010492289828,0.0106016397796,0.0107174018357,0.0104430735479,0.0105689421919,0.0105378739185,0.0104425018359,0.0103828649677,0.0104119645856,0.0106714432754,0.0104412019371,0.0106699189407,0.0104147937356,0.010437277164,0.0105880700834,0.0105217491498,0.0110562257497,0.0105563399039,0.0106241491893,0.0104876163215,0.0103810054003,0.0106984524735,0.0104021187195,0.0105692420448,0.0105019155161,0.0105418172561,0.010699466536,0.0100423266327,0.0103761360446,0.00985667890422,0.00999199598108,0.0105316282455,0.0105739456971,0.0105929522968,0.010510312118,0.0105861478761,0.0105515537672,0.0105475195892,0.0105296505571,0.0103952432968,0.0106852822386,0.0105460073128,0.0112915970621,0.0103139288665,0.010706741432,0.0103127903612,0.010715614148,0.0103470180004,0.0103877115346,0.0107079185885,0.0104348854557,0.0105735676763,0.0103480768755,0.0106606847913,0.0104756773659,0.0105942651619,0.0102539697446,0.0103924589355,0.0104840815671,0.0106563792819,0.00977996205358,0.010856977039,0.0104821689963,0.0110848608707,0.00990288979203,0.0111748762927,0.0100734300484,0.0103199973845,0.010661143181,0.0107719809971,0.0100106249864,0.0103783372224,0.0103948463042,0.0104641648236,0.0105968260736,0.0105622355168,0.0104597360585,0.0106738594487,0.0103125707824,0.0102550813313,0.0107548419136,0.0106234847672,0.0104440004807,0.010507127359,0.0105965477158,0.00986195320277,0.0105202956167,0.0105257387212,0.0116282204944,0.0103918430359,0.0123132813577,0.00989134829845,0.0104834586074,0.0107037756302,0.010118839989,0.0101238686413,0.0113031732712,0.0101294334197,0.0104912948816,0.0103622547448,0.0105276236603,0.0105470527167,0.0106348190959,0.0104596236973,0.0108818476776,0.0112111607113,0.0106873069131,0.0102588250845,0.010880432215,0.010089655822,0.0103914698952,0.0105813561989,0.0104050871835,0.0106776944698,0.0105560616852,0.0105139988658,0.0106706404518,0.0103578271632,0.0107213616644,0.0102640044167,0.0104930892839,0.0106622240966,0.010543224538,0.0102885480743,0.0105893256349,0.0104159556197,0.010828008363,0.0101687861367,0.0101203134104,0.0110675828415,0.00979829244324,0.0105211376691,0.0103741103697,0.0106648211362,0.0107029997572,0.0102861554528,0.0102883788416,0.0105147138665,0.012528715277,0.0100680295644,0.00999416623141,0.0105380554314,0.0107178789057,0.0105820525677,0.0104117149345,0.0105268474132,0.00979281685892,0.00976628410851,0.0111711657112,0.0100905885315,0.0126440839844,0.00992647126683,0.0103867776955,0.0103927894556,0.0106740220206,0.0105234269965,0.0104405808871,0.0105989080067,0.0105772285568,0.0103555507923,0.0105403800597,0.0100160601848,0.0103243282654,0.010780805974,0.0105939044194,0.0105804121349,0.0104924452737,0.0104147704275,0.0103981276532,0.0106935697245,0.0103982082259,0.0103188948232,0.0107848548425,0.0104042969134,0.0107585688659,0.0097388702479,0.0102478837781,0.0109027155225,0.010592031862,0.0104394689929,0.0106714874087,0.0104119132158,0.0103089989265,0.0108178938453,0.0102122142193,0.0107553221452,0.00982443275802,0.0107491341003,0.0099184707404,0.0122984453185,0.01023304204,0.0104431923249,0.0104513020286,0.0105386075706,0.0103492179854,0.0104942258253,0.0106246589642,0.010502577223,0.0105799625312,0.0105293990786,0.0105452535444,0.0101612150281,0.0100121148462,0.00995625993227,0.00999261975487,0.0101974763915,0.0105943331114,0.0105317119961,0.0105416015927,0.0104297027931,0.0106445010797,0.0104011583358
};
const double PHI1196[NST1196] = {
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};
const double THETA1196[NST1196] = {
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};
const int NST1210 = 1210;
const double AREA1210[NST1210] = {
0.0105815883748,0.0102644697028,0.0104742230477,0.0101228244027,0.0102778786277,0.0105767279545,0.0102115947054,0.0104148922907,0.0104393595463,0.0103726242421,0.0102692103925,0.0103217424558,0.0105131183484,0.0120667339444,0.01022560461,0.0104616103637,0.0103126447991,0.0107995393712,0.0115537350518,0.0103980021895,0.0104701261581,0.0104202677378,0.0104032617992,0.0103175669261,0.0104961212921,0.0105548146995,0.0104372123936,0.0106007132435,0.0105827946548,0.0102469637394,0.0101932987443,0.0105293486584,0.0106285571503,0.0104933508411,0.0103611740815,0.0103961454428,0.0104170163534,0.0105174286489,0.0099753028681,0.0102834549034,0.0104068022485,0.0104420427935,0.0103811507109,0.0104252593459,0.0103063172844,0.0100554913097,0.0109846527399,0.010321035523,0.0105077330421,0.0103035458075,0.0104128387912,0.0103882853077,0.0105752463397,0.0105611618263,0.0103449475104,0.0103132287976,0.0102283922993,0.0102343914771,0.0105934950677,0.0103998604332,0.0103044361257,0.00987679968378,0.0105876851044,0.0104631508568,0.0102559503428,0.0104037420954,0.0102516577104,0.0105767282596,0.0104523685296,0.0103347920941,0.0106589337092,0.00996380546814,0.010108243519,0.0103099151758,0.0102914590053,0.0109198980792,0.009964430837,0.0102963650385,0.0104925752787,0.0103666477341,0.0100911068216,0.0120841664683,0.0102857274078,0.0109600175455,0.0102958181392,0.0104432663056,0.0103189035617,0.0102832458158,0.0103560590655,0.0104748686079,0.0105863982892,0.0104943774439,0.0102965851622,0.01054290173,0.0102691459518,0.0103406991862,0.0103406962665,0.0104727307703,0.0106172361432,0.0105470190165,0.0102622973396,0.0102160239831,0.0103796467278,0.0106947182487,0.010714446147,0.0106740638035,0.010690951782,0.0106880805801,0.0105630808166,0.0104898188451,0.0103757060715,0.0102289095535,0.0104200361736,0.0102781971857,0.0105440703406,0.0101065645837,0.0104037406759,0.0104520907029,0.0097627893333,0.0100988158698,0.00988555472511,0.0099786861237,0.00965370089592,0.0125030532463,0.00988210906848,0.010299173925,0.0105361639788,0.0103899148201,0.00971535743967,0.0105957302075,0.00982670796505,0.0101792440939,0.0102284088233,0.010539932162,0.00991278333349,0.0105110118218,0.0102540782241,0.00986942374763,0.0102491043966,0.0100552612772,0.0105577024759,0.0102641956867,0.0104540626571,0.0102125829929,0.00983627521059,0.0104080262433,0.0104193734776,0.0105448821806,0.0103666311533,0.0102947016475,0.0102661842223,0.0105621394289,0.0096992980693,0.0107708638655,0.0098979620282,0.00965283760768,0.0128903307138,0.0101955664823,0.0103132466465,0.0104420204548,0.010277925134,0.0102488695992,0.0106181619889,0.0103044496208,0.0105367002053,0.0102527160946,0.0103015799929,0.0105684044325,0.0103607349557,0.0104381654239,0.0104243973608,0.010344058014,0.0105035426792,0.0104471079359,0.0103854048374,0.0103043647427,0.00980962843679,0.0112293928536,0.0101798815941,0.0105441072953,0.010540281906,0.0103908639322,0.0105214042198,0.0103117794916,0.010296991709,0.0103164857432,0.0104867610257,0.0103228916973,0.010349554102,0.0102588182716,0.0105896802269,0.0102398876233,0.0105011514741,0.010371464687,0.0108026478126,0.00984867498031,0.0100598352636,0.0103403446021,0.0101329989664,0.0101964363164,0.0108329295962,0.00981355697703,0.00993604973807,0.0116705197684,0.0101131236941,0.0102661011738,0.00993891527786,0.0105484632863,0.0100357804769,0.0103336120241,0.0103833340105,0.0100996097185,0.0107883755675,0.00976243221501,0.0103726823229,0.0102970231156,0.0103873972098,0.0101840275449,0.0105141745996,0.0103306257918,0.0105384625792,0.0102934852398,0.0104748143175,0.0105852990553,0.0102324895736,0.0104991879776,0.0103477484654,0.0103363527839,0.0100908358678,0.0121087768377,0.0100011366004,0.00990217522895,0.0105757765571,0.0104523321884,0.0105176875887,0.0101361445671,0.0104233794565,0.0104199584909,0.0103533837002,0.0104369976822,0.0101144032396,0.0100306965546,0.00979897295644,0.0109607159854,0.0103759182024,0.0102144418933,0.00995550156391,0.00983018115058,0.0105038438099,0.0102826134614,0.0107485448589,0.010133050021,0.0106006782045,0.0103215580486,0.0106308432735,0.0096580254756,0.0106480095225,0.0105660108159,0.0102722516355,0.0105645102348,0.0102211605036,0.0102680951458,0.0105453789053,0.0104209609716,0.0102708224938,0.0104504505926,0.0103722572591,0.0104885925456,0.0104430093234,0.0104373786661,0.0103979297728,0.0104552322245,0.0103678905248,0.010492343908,0.0104883486149,0.0103630832353,0.0104215618951,0.0103773136011,0.0102754466101,0.0104600754232,0.0105403200067,0.01037977422,0.0103190193238,0.0104464777031,0.0104887116206,0.0103765017187,0.0104511273858,0.0104599323375,0.0101823087867,0.00976869496094,0.0106456612029,0.0104006365873,0.0103526006817,0.0105185015193,0.0105259659,0.0102554934394,0.0105948047764,0.0102222578007,0.0106259104843,0.0104516634894,0.0104405860361,0.010714987457,0.00997604858463,0.0101797681823,0.0102044898556,0.0105375652157,0.00998694889754,0.010377928368,0.0104752946476,0.0103520998581,0.0105082117879,0.010123226609,0.010371494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};
const double PHI1210[NST1210] = {
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};
const double THETA1210[NST1210] = {
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};
const int NST1396 = 1396;
const double AREA1396[NST1396] = {
0.00894018181647,0.00898190985275,0.00867251788703,0.009150701645,0.0104968461728,0.00862231377865,0.00899449729583,0.00874033629379,0.00939149485975,0.0089838496196,0.00915268615624,0.00888460276935,0.00895829332014,0.00930653610979,0.00916509516134,0.00869548588248,0.0090927836731,0.00920653230867,0.00894923424682,0.00877493050388,0.00862584990874,0.00938537797909,0.00892078607148,0.00895601436726,0.00910987672998,0.00869419894767,0.00887666867214,0.00852025222886,0.008955792361,0.00875006747972,0.00948137642964,0.00886322073709,0.00883286011585,0.00888942520634,0.00876435588376,0.00920615704042,0.00889576969031,0.00906959060715,0.00911609496644,0.00909347632403,0.00906206640256,0.00893933260409,0.00903301369616,0.00900773209736,0.00910940711343,0.00901671738745,0.0090792278104,0.00897711388331,0.00899986164277,0.00899258008533,0.00904807765263,0.00906514807217,0.00936210103878,0.00885044011472,0.00923171643839,0.00886319687979,0.00923331589779,0.00860488679994,0.00912818438017,0.00874278990686,0.00913962603316,0.00900982188294,0.00906326719033,0.00838425474961,0.00922373818429,0.00909367346905,0.00923647741988,0.00896505294824,0.00894184748471,0.0091044387789,0.00902321938426,0.00894457250028,0.00909007240014,0.00899365313326,0.00911598896703,0.00895019283801,0.00873392073821,0.00892321649495,0.00846409591391,0.0103613825681,0.00888497231921,0.00905184190441,0.00888402796087,0.00864291898841,0.00869830639888,0.00865819211661,0.00865193417673,0.00902500548487,0.00906046964309,0.00844135827346,0.00897152433919,0.00913810205854,0.00906533853823,0.00894757504031,0.00924295025494,0.00913968227195,0.00924280132434,0.00913498483163,0.00890825050722,0.00890746735805,0.00914222135819,0.00910050149405,0.00920122492835,0.00909369190868,0.0088551461056,0.00907792990976,0.0093934017487,0.00902926994333,0.00898277861005,0.00897203791064,0.00894396204089,0.00882364984166,0.00911488345564,0.00900544304636,0.00992883719765,0.00917332784354,0.00923501554781,0.00884572732488,0.00909508217842,0.00897844078871,0.00903407444474,0.00916686465053,0.00899310737491,0.00856911261047,0.00853842047526,0.00910841198192,0.00890522813135,0.00904537220316,0.00925409163002,0.00889643040831,0.00853287128049,0.00903565645626,0.00905356580203,0.00894540542949,0.00933580198024,0.00909131760892,0.00883535243506,0.00889553647872,0.0091009262343,0.00929898531415,0.00914201018594,0.00908291042211,0.00901120453878,0.00898175967136,0.00893308867564,0.0089757609442,0.00909120569018,0.0086464595328,0.00850244487149,0.00883462919356,0.00883392735912,0.00917622937396,0.0090856997451,0.00895203607293,0.00945816734825,0.00891922709028,0.00872550437503,0.00922409676412,0.00888470265311,0.00915464296697,0.00912014612062,0.00861830269521,0.00892834983485,0.0103146683518,0.00900313419685,0.0090931174162,0.00914363004999,0.00893449289136,0.00870314797351,0.00906919086183,0.00898111702759,0.008938583441,0.00908333854578,0.00946669542072,0.00923173790308,0.00938930990817,0.008546643907,0.00968987737695,0.00857862220914,0.00868049310841,0.010242409869,0.00861546050394,0.00901034696304,0.00905532442441,0.00900366049615,0.00900692228145,0.00920806819106,0.00919500770707,0.0091967469328,0.00900116593844,0.00901983172682,0.00880412447364,0.0091274748248,0.0089516613288,0.00849865417715,0.00857509864337,0.00855543571949,0.00846543321635,0.00846135401465,0.0103933021656,0.0087659991676,0.00899563627628,0.00907759436512,0.00919360793825,0.00896520016618,0.00899971952551,0.0087584364514,0.00883967666979,0.00859647641738,0.00897713513349,0.00898663522149,0.00885838151696,0.00912774892885,0.0090431269295,0.00895457507364,0.00884806785326,0.00921567974039,0.00887317507527,0.00885168138432,0.00917457983906,0.00922013709616,0.00883920314793,0.00904150504916,0.00906409620498,0.00899747916134,0.00909656028954,0.00924999228537,0.00885109205036,0.0090499450975,0.00910771713553,0.00895731982346,0.00904093199704,0.00915300250915,0.00896471186739,0.00885313433618,0.00915171920589,0.00868930175211,0.00873203318811,0.00860903224494,0.0085515091821,0.0084449390776,0.00928186204632,0.00927564416792,0.00918185043943,0.0088933538498,0.00889800967479,0.0091520121121,0.00902062478499,0.00895194244022,0.00907623884454,0.0088494701927,0.0090476930798,0.00892398119483,0.00861820089181,0.00910747909348,0.00895294229834,0.00918154716686,0.00890454073325,0.00912893413227,0.00903848993385,0.00898167812993,0.00904162317997,0.00893204529694,0.0090945772763,0.00909102837277,0.00891780351454,0.00882159618047,0.00911040596927,0.00898389395732,0.00894234779399,0.00888559368932,0.00916186555271,0.00865995499348,0.00936180660448,0.0088982133177,0.00910979580298,0.010326554403,0.0088262436829,0.00893485203447,0.00901584018015,0.00859076074956,0.00897949759597,0.00896722255753,0.00883190464112,0.00921091324661,0.00870675673091,0.00895171403112,0.0087505250752,0.00962827977253,0.00865982569064,0.00874205988484,0.00859541912656,0.00919375583643,0.00887362524008,0.0104096312468,0.00854122003634,0.00847412301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};
const double PHI1396[NST1396] = {
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};
const double THETA1396[NST1396] = {
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};
const int NST1410 = 1410;
const double AREA1410[NST1410] = {
0.00879695591057,0.00901969149878,0.00880105390457,0.00908467662938,0.00889606258752,0.00895260183949,0.00919475003504,0.00896162037782,0.00897112300605,0.00898653693402,0.0084479989165,0.00837889825232,0.0103674467502,0.0085360562692,0.00881680587249,0.0085068376872,0.00871738935461,0.00885212317268,0.00937873782519,0.00893116007229,0.0089411373258,0.00883505549369,0.00900118020878,0.00898905475171,0.00915006142058,0.00914118874667,0.00911842831015,0.00866805724649,0.00888392142495,0.00867841256828,0.00865713997234,0.00881005313485,0.00878490581873,0.00883844457803,0.00880441328137,0.0090951626048,0.00882608886723,0.00906928513503,0.00883557733167,0.00874202088132,0.00893640771079,0.00895370784695,0.00903647978762,0.00904466967158,0.00883654829243,0.00890175622161,0.00847409056227,0.00862607946967,0.00910077472162,0.00896693376229,0.00899756322092,0.00885858873145,0.0101657247266,0.00884606832158,0.00938619006078,0.00857334292192,0.00901568746878,0.00891231546562,0.00904908764919,0.00894337745994,0.00911273371368,0.00903477579649,0.00897639688818,0.0088834479457,0.00895858042556,0.00910098238226,0.00876753107427,0.00894993485138,0.00894854259355,0.00885763923343,0.00880245954698,0.00908416948147,0.00880560251645,0.00908713043757,0.00881505870482,0.00908545783662,0.00865155005444,0.00919191592417,0.00881840533939,0.00903015328062,0.00885295152286,0.00901528218003,0.00866414386931,0.00940640900068,0.00842298775941,0.00881052114343,0.00866309483993,0.00912950498092,0.00905804687837,0.00882105005088,0.0088852610403,0.00890234411781,0.00893713116948,0.00920372744413,0.00894076088685,0.00918767303018,0.00913410699827,0.0083117355162,0.00899360065223,0.00923787261448,0.0090783946289,0.00862891857522,0.00885265171917,0.0090072250639,0.00893335163923,0.00888873850784,0.00900244584007,0.00889074198759,0.00943499713772,0.00887112524727,0.00859839097294,0.00929361923148,0.0106293460608,0.00944441849842,0.00835108489124,0.00908852058608,0.00870332001405,0.00841256128312,0.00884426443479,0.0090275263923,0.00890545244038,0.00841903759594,0.0088950259818,0.00907534110489,0.00950091487424,0.0101579857191,0.00914656304184,0.0090403743405,0.0089564094832,0.00875132228015,0.00916957609473,0.00909505361317,0.00927483257642,0.00887739665044,0.00866517402582,0.00884950707141,0.00849131897046,0.00901457200018,0.0088112353148,0.00854516404688,0.00928024060507,0.00922727102148,0.00895689795684,0.00885414427556,0.00891619236987,0.00896314768585,0.00893506396848,0.00887980958532,0.00901296888453,0.00887962419771,0.00898801459531,0.00876235975402,0.00894628765517,0.00882916566135,0.00884231080163,0.00904745368996,0.00891200147198,0.00895794640131,0.00892260993648,0.0089309936498,0.00894388341735,0.00894272149333,0.00913486525511,0.00888303621749,0.00885890784189,0.0090091417515,0.00901390566605,0.0088644262756,0.00893195415907,0.00892224228213,0.0089398714884,0.00920087726271,0.00891293350389,0.00890910914976,0.00892024894349,0.00884793811438,0.0089672682404,0.00899182000857,0.00891133514795,0.00889278215121,0.00881258741713,0.00888049629279,0.00883007407414,0.00888638466362,0.00899707609687,0.0087826103036,0.00880390332684,0.00880244254772,0.00904443911717,0.00891149297102,0.00899300559022,0.00888113404403,0.00902068897608,0.00883257804178,0.00905445775764,0.00880083433031,0.00893810030164,0.00891704199986,0.00877880729654,0.00894674323994,0.00875734781822,0.00880180148475,0.00908751213639,0.00899492275052,0.00912011814577,0.00901113196726,0.0088897905092,0.00895443344658,0.00897304698826,0.0087434804966,0.00887905207536,0.00899252730279,0.0088676907674,0.00913323428851,0.00843034769567,0.0086464677594,0.00899046061341,0.00887115846345,0.00882491298965,0.00890795259777,0.00888672157158,0.00892308135492,0.00835262722826,0.00898070647581,0.00902440814244,0.00835831799831,0.00952237163008,0.00907093765958,0.00850156564483,0.00925036196563,0.00821089198865,0.00939280516903,0.00860163837781,0.00850622352082,0.00926604449384,0.0104232041887,0.00907048800459,0.00875090127083,0.00899145726676,0.00896398436979,0.0089943720877,0.00903814952232,0.00879847350817,0.00879806266139,0.0090364869402,0.00885211582351,0.00903422226654,0.00878621124436,0.00922231024265,0.00874817864282,0.00908889741089,0.00880012379769,0.00884309082143,0.00904982955141,0.00879934868034,0.00883590680012,0.00883963705048,0.00904204819235,0.00897914667597,0.00877629526258,0.00902060559704,0.00881412885225,0.00885384068543,0.00911568997059,0.00867110228784,0.00899767808553,0.00896857821898,0.00890835976444,0.00900534141511,0.00893298792337,0.00894904703186,0.00905285933102,0.00884306809316,0.00893735181587,0.00884453807941,0.00914309974651,0.0085554293387,0.00875928412603,0.00871051437522,0.00876337109785,0.00887815807592,0.00888908450405,0.00900714810825,0.00896343406727,0.00891160657147,0.00918759016032,0.00835862835279,0.00857643424341,0.00904588886004,0.00879215464576,0.0102879969531,0.00839934945712,0.00845156825446,0.00890210530618,0.00896364747443,0.00890045226698,0.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};
const double PHI1410[NST1410] = {
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7,2.06883782595,2.02301475698,2.30177827807,2.27294065336,0.881985450392,1.07426548409,1.01793107809,0.937039009487,0.91460436878,0.959544884663,0.974031461448,1.11237821911,1.05254856964,0.885409201642,0.882637304828,0.814862887253,0.742254613516,0.835563547676,0.820673866473,0.679223893653,0.745458128743,1.24600961228,1.23452606207,1.10316291275,1.18133330869,1.48152566458,1.57761004607,1.49343104011,1.61662282307,1.55726267166,1.92742044141,1.86698576284,1.88379523035,1.96282277549,2.00768882203,2.02642400864,1.74407667482,1.67897891878,1.69482824531,1.82237501642,1.77179665626,1.83435466349,1.00311263916,0.961711890607,0.880931282941,0.970322100469,1.42871933645,1.32771730228,1.34528477878,1.39626227254,1.48042027384,1.49540219809,0.639083890886,0.766028243666,0.691868292136,0.679972327761,0.802483084187,0.767856887438,0.253600393531,0.408842419624,0.457570480309,0.461423648213,0.39121125003,0.319412435921,0.334767378911,0.400842828806,1.68760035989,1.63847051689,1.67188346643,1.75135982125,1.82421992948,1.91132532384,1.93486047838,1.7680606703,1.87822144861,1.79853745497,0.934842078649,0.906273947435,1.02067090506,0.877095277332,0.867074354638,1.44439257662,1.36933489625,1.46939961254,1.40602911541,1.49075105952,1.44486293466,1.38439205765,1.55175828279,1.52739686008,1.26071617986,1.38551074904,1.30751038452,1.24483472632,1.40295146094,1.34078062689,1.08488041645,1.16737364539,1.05394717063,1.02713536614,1.19334090845,1.13739879888,1.08712147561,0.948421131824,1.02025475796,1.08777084563,1.93012853194,1.94720147965,1.84970579795,1.88259589593,1.78783589756,1.80375665048,1.89483998241,1.82822187583,1.98118985458,1.97294612865,1.83826515489,1.9131018174,0.981154704141,1.01593427242,0.898280167759,0.853692102398,0.821653109855,0.884737277265,0.963790821066,1.21464103586,1.13371365091,0.880668388484,0.948431197285,1.01966544915,0.889181722035,1.02841862618,0.965557933907,0.885485172501,0.868823405773,0.917293762959,0.782838861951,0.664869385022,0.748388651291,0.802997111702,0.642465728576,0.655690989479,0.376868816333,0.403500341148,0.240446579126,0.296961416182,0.357184797956,0.277546475353,1.89085571974,1.82204316252,1.89634499193,1.9237319147,1.87023197608,1.7904333616,1.76940597797,2.12236952025,2.04642764287,1.99921480323,2.15150982375,2.57715223118,2.6310220783,2.52764415147,2.55151715836,2.69955900358,2.78106353181,2.65972375731,2.69083624682,2.82532084712,2.77260108293,2.640048909,2.5579977,2.56709367449,3.0738807895,3.09729570555,3.01436317359,1.63985558111,1.64258979773,1.70291782838,1.70739822634,2.05757622267,1.97203442767,2.13077227954,2.1800816549,2.19976691866,2.08905345865,2.05829252354,1.92059120251,1.99137564198,1.85231643029,1.99360894687,1.70747465691,2.07883648292,2.07354283348,2.00601334889,1.94049051168,1.99475702337,1.93440403565,1.84575781281,1.99068001599,2.07419213923,1.93052257096,1.95392609062,2.09756813453,2.03732434665,2.25207273885,2.24494434003,2.17325032287,2.06220116425,2.01258162005,2.15009805025,2.18660068858,0.980188540792,0.903441401087,1.00753179363,0.957561594029,0.868725391247,0.840946098018,0.634920757239,0.699833827035,0.769573178642,1.16216682344,1.097981599,1.02379761341,1.16010721923,1.02120549707,1.09329131916,0.892470511343,0.867819003464,0.790313586414,0.735399797377,0.764871589459,0.844047146562,1.15957744262,1.07635674916,1.21142855645,1.0007363834,0.961728423788,1.08875755361,1.42147777614,1.40085463819,1.44742812358,0.907630027573,0.843929076979,1.06840277252,1.1491204893,0.999264391447,1.0865023099,0.432039105569,0.506560545545,0.567959964041,0.43565480595,0.515400302142,0.573150674859,0.77946318879,0.70276312187,0.833120559846,0.710775279358,0.794778307655,1.99030445065,1.96971499666,2.07066788192,2.1264149744,2.10096648941,2.02481487693,2.78698872843,2.7135873544,1.85509988223,1.92535543711,1.78251612967,1.91504330136,1.83760301229,1.77516822611,1.49956411228,1.55620962212,1.63174818664,1.49707944359,1.57666614871,1.47280022682,1.526821346,1.60606434223,1.7644323385,1.84691662031,1.91205494957,1.89141460318,2.00268302295,2.04832001231,2.04521131986,2.12046187113,2.16394118023,2.13417019355,0.776587871704,0.800874847236,0.750709697752,0.69602030844,0.638679016291,0.669971789773,1.00118069596,1.05075713559,0.966629960468,0.945189875081,1.34900203333,1.3217828788,1.246473254,0.933714015791,0.986478253154,0.959620169854,1.04046290416,2.70312231363,2.64831260282,2.59669289528,2.62125742141,2.82351139239,2.88714572507,2.96405117338,3.00200058747,2.93304361485,2.86112415953,2.96198039108,1.74512189305,1.70016022271,1.7846658098,1.80702903358,1.63983939677,1.66254272303,1.07715607119,1.20305917902,1.12575107173,1.23208291587,1.18258289014,1.10517250871,1.30107020003,1.32703703264,1.27799525118,1.20089323992,2.84672342746,2.73193681794,2.76421516733,2.88762486714,2.7568476611,2.82542503965,1.06722356563,1.2259957631,1.09509450307,1.17483123813,1.11948382407,1.19859252156
};
const double THETA1410[NST1410] = {
3.15026418775,3.07710262364,3.07326826409,-0.0911346091709,-1.24130495534,-1.20992705766,4.38575066458,3.45162189132,3.66717626721,3.64338582012,3.21981026785,3.36361819701,3.34972758506,3.28377861572,4.48701675354,4.5182004306,4.45981437689,-1.45526001619,-1.50567947786,1.77488557233,2.00818447701,3.01168462934,2.85274265301,3.00065815094,2.39443767123,-0.122626403851,0.268153561099,0.262674432481,-0.0211281815933,-1.05545043246,-0.993920256401,-0.597428551996,-0.693675741637,4.58806940225,-1.19817754128,-1.38527222256,-1.35083734868,-1.07374826186,-1.12985828707,4.35123058326,4.2451089902,4.19639597009,4.42565862531,1.95361158377,1.9860644221,2.74258143974,3.48675967943,3.34680017881,3.0819272472,2.91022130309,2.90212057522,2.9907701746,3.24812118168,3.28389135856,3.16171580788,3.13988076964,2.98833899796,2.83355589231,2.7379200421,2.70375514067,-1.08894350174,-0.909374369025,0.209351506219,0.304590303252,0.298189918286,0.11273708358,0.209011363069,1.0992142254,0.406064741221,0.490946397154,4.40299924005,3.48096833608,-0.8467646265,-1.13291445507,-0.890014296509,-0.724506989473,-0.514878484161,-0.631124068167,1.61285973461,1.70151886851,3.02601675669,2.96642925074,3.21370773596,3.27552776289,3.24926249064,3.12845165594,3.16517748043,3.10643762468,3.74921519546,3.59874840193,3.75716963327,3.8841327447,3.78673832526,3.77636290045,3.70474917087,3.43893158562,4.48209665065,4.51078056732,-1.5201305049,-1.52012916447,4.67614384884,4.60837559777,4.67117788215,4.60442148893,4.63882279485,4.65873347437,4.08454515606,4.18648285064,4.50033819434,4.49079652191,4.57331740963,4.56338575022,4.2670085187,4.41587440146,4.35091337818,4.41674562026,3.8557126928,4.20747019087,4.55020713804,4.62952103342,4.69573234696,4.68188690739,-1.10710816658,-1.13979842977,-1.40993675582,-1.52636546727,-1.52969316539,-1.16002483871,-1.19871525602,-1.15755833858,-1.24302250086,-1.47839611722,-1.49814700765,-1.56075124915,-1.57060010674,4.37307089455,4.21599158017,4.12170177547,4.14048899742,-0.899329198197,-1.00577864241,-1.31201378616,4.42252793786,1.63666185258,1.70922854432,1.7006246466,1.8568473725,1.93300127959,2.01181464896,2.01147504444,1.64311509832,1.64914620425,1.86275576518,1.7189129352,1.79126568642,1.72040357974,1.78750311842,1.79060396268,1.86364201538,1.93635845307,1.93658854876,1.8607028988,1.64872622329,1.63459384789,2.23014433463,2.15410474237,2.08559147844,2.08253104159,1.92893671224,1.93262974849,2.005319698,2.40799826429,2.93789745808,2.85762563754,2.93075389913,3.08018430706,2.99709043542,2.92162311119,2.99908575317,2.9242269027,2.99870863945,2.77825615904,2.833703595,2.84325517806,2.77152087847,2.8422820233,2.87709562953,2.79248149486,2.77615762482,2.38600076214,2.46690982614,2.54023579723,2.62281564297,2.69332470862,2.58750570623,2.45320378205,1.67502395954,1.76518803142,3.60175411993,3.39145596254,3.34510122569,3.54897967694,3.49956497185,2.99164168333,3.05433014552,3.19290635793,3.19984748543,3.42383935068,3.69581096175,2.71634336134,2.94054149649,3.17314942686,3.15198222133,-0.175085270285,-0.0733636188926,-0.0986809005846,0.281379903445,0.287592283219,0.331076668345,0.91084515352,1.00215859058,0.924115355094,-0.0116744349146,0.0229546404508,0.109696308638,-0.567131799584,-1.03792128135,-1.12413536925,-1.13880427966,-1.17728298475,-0.742259327377,-0.833682676247,-0.659207567523,-0.842946813538,-0.887206556841,-0.750105836221,-0.183571122993,-0.0335603033133,-0.600576330037,-0.519616630587,-0.548302989809,4.56425337844,-1.55591180804,-1.40420278439,-1.54964303867,-1.30683907168,-1.27876255462,-0.549359391127,-0.389280573242,-0.497548882041,-0.577192659962,-0.683951632958,-0.853700370824,-0.751255461714,-0.719528175051,4.39337092271,4.46356099944,4.49031202865,4.26803959752,2.49802768675,2.7472664029,3.01505833941,2.58517391392,2.80383002497,2.98246599389,2.27580460755,2.53643371126,2.4400194156,2.4558813803,2.24137400741,2.16745263399,1.80509845332,1.81277448704,1.5805650229,1.69508703131,3.34713497327,3.46212680937,3.62890662503,3.99367425918,3.89775306263,4.0299122626,4.08163357155,4.01655772762,3.92406917622,3.8584080097,3.81151346176,3.69414441282,3.74649025082,3.85123316838,3.58581868924,3.5760727729,3.33666424839,3.47120856104,3.75070594452,3.673319598,3.71979341392,3.6212168168,2.78970356943,2.80755612826,2.87936704176,3.09945134141,3.08808338806,2.98630211986,2.86569304332,2.98514540284,2.63988813112,2.6771480286,2.6011501696,2.50518361785,-0.867925014831,-1.45184749208,-1.36853029804,-1.46002103088,-1.00663464849,-1.16607273812,-1.06128029145,0.34700873747,0.354205007709,0.638460189295,0.117002067181,0.121294741349,0.207127156112,0.206791323738,0.101607825056,0.986443120009,1.11088675819,1.16508405618,1.18650430622,1.32400156259,1.3925386975,1.45973055951,1.14850316608,1.29416935519,1.25526968115,0.688267101294,0.779564379715,0.926181066786,0.982775405542,0.911264766726,0.622232870432,0.769866737176,0.666914262543,0.593403737761,0.737681681532,0.810967091212,4.63991780536,-1.25904846849,4.3542193895,-1.3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};
const int NST1596 = 1596;
const double AREA1596[NST1596] = {
0.00898161472215,0.00793682351914,0.00783726493283,0.00782135123312,0.0074515533379,0.00795027285775,0.00754964557486,0.00754709851389,0.00789529320983,0.00779422962641,0.0079598426657,0.00781208999869,0.00782222139311,0.00793534499444,0.00785454321021,0.00787019625809,0.00789994885333,0.00790234378106,0.00789239710852,0.00794186991099,0.00902995471139,0.00740452989968,0.00771354178207,0.0077928398572,0.00790263620368,0.00792652528232,0.0079634858516,0.0079683816427,0.00785004525586,0.00788545009992,0.00786835858881,0.00834110622304,0.00760578122914,0.00817281886622,0.00798607134963,0.00867766491901,0.00811427399573,0.00752765823815,0.00732914423251,0.00805994337421,0.00763119737763,0.00798127102672,0.00786152117516,0.00776565252017,0.0077537397352,0.00753720328731,0.00772085304708,0.00752374898059,0.00748862773388,0.00780995092341,0.00795562496885,0.0078777278841,0.00800603742547,0.0077889175066,0.00784319815166,0.00801618045518,0.00777821788753,0.00797682885569,0.00782875378278,0.00768468291508,0.00810254353271,0.00772306506771,0.00795275629356,0.00772903805536,0.00797767947585,0.0081371903108,0.00786369969534,0.00789445354644,0.00786416718552,0.00797746159238,0.00786882936882,0.00756299057667,0.00814079455955,0.00784613639084,0.00780160697227,0.00792102959074,0.00745670930428,0.00748200498895,0.00782134771026,0.00795317289266,0.00767401433596,0.00801610949628,0.00784972361624,0.00780643416237,0.00786437909415,0.00783814293829,0.00780153681811,0.00783024067183,0.00800366105568,0.00780102084296,0.00795358205916,0.00786317933465,0.00787993546148,0.00797125353596,0.00791593752927,0.00781347555591,0.00785045788102,0.00796436721636,0.00782778116135,0.00791269597233,0.00784978175952,0.00750260869672,0.00756237168506,0.00774604241931,0.00754645494411,0.00804202871288,0.00791089290936,0.00774589772623,0.00798192053622,0.00782458635071,0.00765570924067,0.00795675883932,0.00774984513443,0.0081034102948,0.00792981152629,0.0080613304939,0.00771900213821,0.00765215407236,0.00828701935049,0.00754954439258,0.00794568879158,0.00788818566097,0.0078373845923,0.0077606510394,0.00801362272013,0.00774636913226,0.00781870563392,0.0076398073947,0.00799830347767,0.00762493512953,0.00786456002171,0.00845775861574,0.00750382673007,0.00858935446889,0.00748497121451,0.00868060566407,0.00753618968285,0.0075875387935,0.00778913765524,0.00797809433969,0.00797912331517,0.00787986329649,0.00793431323721,0.00783634585003,0.00800865463389,0.00775140401935,0.00777637810634,0.00932436942175,0.00802639600159,0.00776616512533,0.00802696140042,0.00774012409232,0.00800807369337,0.0078590915576,0.00791011882051,0.00786170636672,0.00828292836645,0.00777633158101,0.00800169814087,0.00753012056473,0.00745626449743,0.00763095847552,0.00768240110701,0.007882909447,0.00795223006364,0.00844685363646,0.00817073762648,0.00767568915754,0.00795096123014,0.00776221396848,0.00787829201953,0.00740190807849,0.00793489135432,0.00784633567435,0.00786262881205,0.00797874086825,0.00778118816078,0.00797728411855,0.0078716129665,0.00798654519255,0.00780531895904,0.00753596230686,0.00744429925992,0.0076607193185,0.00774911272191,0.00793339659714,0.00740683174483,0.00806700677297,0.00753235100743,0.00753077756248,0.00766197177015,0.00789339400098,0.00762443342574,0.00809812088108,0.00743495832411,0.00765661224421,0.00802196937256,0.00830425266874,0.00793845943583,0.00784417574329,0.00784784333255,0.00791213374715,0.00794246834537,0.00786751688385,0.00804449234747,0.00775731454438,0.008030697364,0.00807251910468,0.00775881960301,0.00778746496758,0.00782473640615,0.007945568543,0.00799390170644,0.00875599370939,0.00745258445338,0.00829210518705,0.00788561252421,0.00775102019069,0.0076694224547,0.00804980943045,0.00759057946423,0.00776877192468,0.00797931728957,0.00836134361084,0.0075475440366,0.00832868379063,0.00809217764196,0.00775957594264,0.00791863332924,0.00780502429122,0.00801135803047,0.00786747813958,0.00825691008205,0.00789820576041,0.00791440164334,0.00793424750219,0.00785157363822,0.00801769266529,0.00765987992365,0.00780635463159,0.00795219325783,0.0075689187208,0.00739551099448,0.00907639089007,0.0078260776299,0.00773341920624,0.0079722063769,0.00787388115359,0.00780895475646,0.00796152673288,0.00798356026236,0.00785421335867,0.00799744127467,0.00796340594202,0.007829251001,0.00762403098454,0.00804782958036,0.00777788739819,0.0075096304737,0.00793149115036,0.00769028513404,0.00778335690256,0.00796203527193,0.007925155324,0.00779841618373,0.00784956435458,0.00787167394594,0.00752322586812,0.00755844482713,0.00809091779818,0.00794891675652,0.00795135008896,0.00793707900216,0.00781816800954,0.00789497734284,0.00787187079194,0.00782029853949,0.0079461099228,0.00790998607656,0.00782944453148,0.00774313176919,0.00795241599832,0.00809771039586,0.00892257020693,0.00751398019817,0.00746755895482,0.00781079128685,0.00807399739546,0.00756744986881,0.00781255259201,0.00780828986893,0.00944582149556,0.00748813325657,0.00742288160874,0.00800543670324,0.00740368784394,0.0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};
const double PHI1596[NST1596] = {
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};
const double THETA1596[NST1596] = {
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};
const int NST1610 = 1610;
const double AREA1610[NST1610] = {
0.00771503984311,0.00783155983693,0.00761471595757,0.00777918555608,0.00791141620966,0.0080217882768,0.00749152743438,0.00764204235133,0.00769057810026,0.00798442227314,0.00785766998554,0.00795615719593,0.00796989063162,0.00771458884476,0.00791503008815,0.00770839579274,0.0079595854035,0.00785271294883,0.00770998847668,0.00770383638623,0.0074759712762,0.00884346048924,0.0077884782018,0.0084490957535,0.0072159936648,0.00806479930367,0.00758070745827,0.00809971114913,0.00740556821427,0.00827592531071,0.00739413560098,0.0075201059156,0.00733655391478,0.00771268604458,0.0077449621368,0.00770827229896,0.00790888027419,0.00771814433879,0.00793061137015,0.00790145957736,0.00793336445721,0.00793179933016,0.00771539163481,0.0078375764227,0.0076592572713,0.00779764381365,0.00773343790266,0.00772006407586,0.0078759568387,0.00778586534801,0.00786207327374,0.00771430098962,0.00790106721573,0.00769839449166,0.00795196290757,0.00781691637162,0.00773123272518,0.00783398689329,0.00782436502583,0.00777517909659,0.00787736981382,0.00793767708824,0.00772379689841,0.00772905493685,0.00782729021564,0.00783347171633,0.00784076283077,0.00770996380578,0.00779509569292,0.00784897978828,0.0075245963651,0.00779458751538,0.00797634768752,0.00778976091918,0.00780080862307,0.00787776816677,0.00777547191858,0.00773833682416,0.00776611506779,0.00778160068711,0.00820824399863,0.00826773186149,0.00791152014857,0.00773935345521,0.00786508471801,0.00783154295374,0.00792586107777,0.00785417730817,0.00764268014425,0.00795650192337,0.00776420399386,0.00791581762682,0.00797495495286,0.00771652735488,0.00794887676029,0.00768973978039,0.00769406081509,0.00795785065113,0.00755571978303,0.00799265604692,0.00749461520731,0.00771167742168,0.00790174625165,0.00801596306083,0.00794274955962,0.00795837912301,0.00770986786525,0.00786565059291,0.00787174098261,0.00779078271412,0.00775523447757,0.00764219749425,0.00757025844981,0.00775961072152,0.00774602324975,0.00796917986708,0.00783555949219,0.00772583650037,0.0078216376343,0.00781729010401,0.00776120744424,0.00793941808756,0.00794617914673,0.00771061893242,0.0076680936725,0.00765585270002,0.00801014713125,0.00755730434038,0.00925850459697,0.00742074644569,0.00735626301417,0.00796936900305,0.00742198384254,0.00807953140765,0.00747116435438,0.0073964879588,0.00751699542749,0.00740954515195,0.00768575874656,0.00770901517772,0.00777013341176,0.00754273370493,0.00920397469626,0.00822570313004,0.0078143432916,0.00781899627533,0.00779358623289,0.00784109841343,0.00775576461388,0.00785854567946,0.00800544793133,0.00798125714345,0.00804723301107,0.00783880478802,0.0077737385004,0.00778723530467,0.00782764185292,0.00798211870506,0.00785891450475,0.00777390216014,0.00778671426087,0.00775317133432,0.00777712527479,0.0079865109801,0.00772685654528,0.00781015112916,0.00783430969516,0.00782107603466,0.00773035076306,0.00786116838549,0.00785679809625,0.00779512090726,0.00779934170361,0.00770041393432,0.00778509124411,0.0078717031972,0.00779507838324,0.00774452121784,0.00790028047001,0.00767927813923,0.00777571430721,0.0078487233728,0.00786952837835,0.0086934613461,0.00740806137969,0.00794230183867,0.00781959926272,0.00734847759835,0.00792603979822,0.00775698584867,0.0077457933569,0.00793112037389,0.00783673310203,0.00780902955435,0.00782999479246,0.00783094230874,0.00781608811334,0.00794782295005,0.00789347167184,0.00772676325301,0.00774301599689,0.00890066780675,0.00770202112385,0.00796666031277,0.00772224353267,0.00792990406499,0.00803164333313,0.00764559464739,0.0074136769891,0.00773063406791,0.0073644897317,0.00913374163661,0.00734227128271,0.00791978414346,0.00810831912314,0.00784468231111,0.00771266431724,0.00790670453254,0.00795270301366,0.00794961356177,0.00772114648734,0.00747869810184,0.00796058379306,0.00793855449633,0.00777387039104,0.0077908350681,0.00823276767915,0.0074629313782,0.00803379457318,0.00763091382472,0.00766436888365,0.00888648588761,0.00761206754866,0.00760592860339,0.00746518120274,0.00781633110023,0.00781883963502,0.00791819625378,0.00766287005191,0.00795783642919,0.00770733666247,0.00760825731401,0.00821181722963,0.00798396996979,0.00771482372472,0.00793592926269,0.00780688682076,0.00783947667818,0.00740953274761,0.00752758176245,0.0076158215182,0.00759180642106,0.00821519283102,0.00743477394919,0.00787707773905,0.0077264884424,0.00788072898921,0.00773454481511,0.00798623340684,0.00798894344355,0.00767779221408,0.00768351131518,0.00787798728797,0.00795804059034,0.00774326577302,0.00793109226422,0.00777026871809,0.00790736007183,0.00773251336195,0.00780601713462,0.00784574320099,0.00779485546602,0.0079600228968,0.00768963431268,0.00783455213675,0.00770937136509,0.00793941956379,0.00791142120654,0.00778946373316,0.00779924999237,0.00776336732,0.00775210297298,0.00782231595188,0.00783285816231,0.00739121641647,0.00798628033387,0.00790612706683,0.00763058939041,0.00783755881389,0.00783085174186,0.00782685292844,0.00781315113146,0.00780186402642,0.00784641850318,0.00821011204296,0.00754956609225,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};
const double PHI1610[NST1610] = {
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};
const double THETA1610[NST1610] = {
3.16383736864,3.22592112967,0.447316867188,1.77438754874,1.6955163572,2.8905268851,2.81187973107,2.93541301582,2.89324955894,0.165367712105,0.892869119268,0.477350922799,0.433691456685,-0.131762220569,-0.0187543814041,0.0395478975425,-0.0740850335772,-0.0868891466392,-0.0276271829491,0.104404587802,0.378992590377,0.37132350609,0.328481047478,0.175753815553,0.247652363501,0.181349564627,0.361816810972,0.365928282068,0.334151990279,0.324372776637,0.253886155326,0.254207592292,1.45531094029,1.61217300278,0.776479725384,0.920269841299,0.861523880524,2.98193404035,3.1355116209,3.13172749008,3.09091674083,3.01710775312,3.09405945793,4.49894222206,4.20609280948,-0.138887839085,1.62241726986,1.50729474651,1.58136011861,1.58784486827,1.82754577154,1.84183702837,1.68801827071,1.72999098369,1.80533412359,2.03524077925,2.19055131979,2.27423945576,2.07542681992,2.19497423591,2.15386246534,1.92016295312,1.9592087451,1.9594227112,2.03756759764,-0.343067455217,-0.202269450291,0.755720218983,0.46689753239,0.539215208107,0.825207010877,0.731135827648,0.644812141887,1.37910112309,1.50539230207,1.4895459297,1.45794607039,1.73350639545,1.56942990751,1.59172882754,2.75204363003,2.87569054096,3.24188545754,3.27337329958,4.6668639341,3.43622473913,2.739766237,2.82553101282,2.92196766822,3.00641894925,3.00711347161,2.92662775853,3.0136646349,3.17348217862,3.12983376365,3.05171397998,3.05271954454,3.13483780523,2.68908530304,2.81001523625,2.77372443915,0.49368262318,0.571415024296,0.457359097338,0.475335722665,0.864546270109,0.960535147896,0.934611894884,0.669393942479,0.830145297376,0.78868295216,0.103674323658,0.212328818786,0.182653950831,0.316934596137,0.237674290072,-0.0567020788071,0.00358314932545,0.687189683566,0.7627810453,-1.5431810216,-0.171259170246,-0.0454944567591,-0.117010206257,-0.00563888198299,0.00806136699341,0.0818230131975,0.135309228173,0.194208000168,0.197985517197,0.11105045368,0.0478133940745,0.124041770697,0.0567878084602,0.333656172779,0.242675985436,0.238468671957,0.387748506241,0.328493517598,0.915625401273,0.993009113697,1.30865541428,1.36221147158,1.19607031889,1.06486234798,1.19571594007,1.32591831006,1.33525297698,1.63723783122,1.67365612708,1.56506400185,1.055740994,1.13158478408,0.970812879259,0.888747664323,1.3648882758,1.1883038206,1.15996738906,1.39308926377,2.4670367303,3.09243613282,3.14955221193,2.92439261172,0.678024550631,0.0801467441636,4.35790743958,4.2659588401,4.56163858223,-0.0981591357556,-0.157619466442,3.13482335784,3.08819005963,3.25577418181,3.21122139618,2.04259227719,2.08929127136,1.92193690146,2.05332614377,1.96469076576,1.67256899333,1.72129025786,1.80011308295,2.07168672109,2.12764231661,2.17968001607,2.14879846802,2.31699081083,2.40981609113,2.4411174995,2.39683147858,2.28192802633,2.33033024725,2.2684208318,2.3107667288,2.07884514053,2.20202564293,2.15806663462,2.16453257468,2.04007451343,2.0814631549,2.53848192151,2.46407143773,0.992761618563,1.02256927533,1.10695786271,1.08508827323,0.912772132486,0.920129262528,0.751379138436,0.791053748491,0.860179988794,0.793384056672,0.894809804872,0.868042501391,0.679461600854,0.526492094007,0.643804927869,0.57159896683,0.97761668335,0.504288600561,0.555707107637,0.670784847974,0.636778007378,0.422578114856,0.790242110469,0.875112405117,0.824550007566,0.896677791288,0.521713327093,0.544452412785,0.482799435761,0.393039516676,0.663275677697,0.736361298669,0.749656449476,-0.253349895267,-0.182999010725,1.80699166677,1.95781121605,1.92011545504,1.84405596705,1.80996582975,1.85411239965,1.91895378433,1.84393040013,1.95280158847,1.87433039286,1.90685871651,1.96162886042,1.84897313179,1.80186485675,1.7304805528,1.81534657681,1.8491254502,1.58425379574,1.61642554043,1.62546217822,1.69830339669,1.73754727296,1.69716626443,1.03948929615,1.67865528878,1.60325349781,1.72123388383,1.68382946162,1.15814171286,1.36006486074,1.21118514903,1.24438431845,1.15673395907,1.282974685,1.22610153215,1.1997384592,1.2515228325,1.32973416107,2.87979923947,2.91374345668,2.62810818183,2.66398451712,2.97464657457,3.01050219214,3.00538713272,2.96728282181,2.88747038999,2.12492761062,2.20400657777,2.15479551114,2.06221659301,2.35573305069,2.36946849835,2.26292248857,2.26212955237,2.45447090108,2.46873389466,1.5063176579,1.60365797945,1.77758678916,1.91941667403,1.8352378134,2.1434834912,2.016121984,1.9866790594,1.30885073605,1.17698667871,2.26851743056,2.34953776925,2.3431614241,2.27387232999,2.82016620039,2.76089843534,2.66266429008,2.68517586554,2.789626489,2.59828841569,2.69755891125,3.02969683318,3.10688420932,3.25638812238,3.62719635714,3.71069411488,3.88029845112,4.2061250649,4.54515946384,4.62406199024,4.66084774904,4.61888163078,4.63349761279,4.57275954718,3.52093847864,3.6865224116,3.49713990379,3.6297153872,3.5492909098,3.30140342294,3.38472825881,3.41687065279,3.25435406792,3.28841249591,3.36798845444,3.17800349951,3.26414757162,3.32817674229,3.46222723514,3.51022959709,3.0525663795,2.9153144949,2.88121420626,2.98038869581,3.04231530035,3.13241343456,3.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};
const int NST1796 = 1796;
const double AREA1796[NST1796] = {
0.00692599989559,0.00710417279517,0.00690379583366,0.00807252480222,0.00660941358854,0.00698787022317,0.00688049591296,0.00707651260945,0.00679992205263,0.00688881157811,0.00801179453387,0.00660485772371,0.00713085788951,0.00696280001851,0.00691826061145,0.00705474302191,0.00699895720716,0.00655356904615,0.00715469159308,0.00670907193504,0.0066559363709,0.00658217547323,0.00714103511184,0.00708596555483,0.00700878674025,0.00695640006306,0.00819080302376,0.00655929944844,0.00715044689307,0.00687103160787,0.00756553583713,0.00669509932191,0.00696174341006,0.00709333660424,0.00710422980888,0.00688077111082,0.00671692926548,0.00701900357319,0.0069992180459,0.00701791689171,0.00702933437887,0.00691773408958,0.00662555908723,0.00695907423578,0.00693141959828,0.00695610589587,0.00698339364758,0.00717573853945,0.00670848442547,0.00710308646798,0.00778197057468,0.00713264466259,0.00702288513012,0.0069390287544,0.0069253486694,0.00704895322726,0.00714066641203,0.00709038816631,0.00737540316544,0.00695276124416,0.00697929107072,0.00694497967348,0.00730324079724,0.00697484096899,0.00702003132512,0.00712851766418,0.00706325183531,0.00698426229123,0.00697547321946,0.00714925605896,0.00695612275916,0.00706435390283,0.00714598043064,0.00697658990131,0.00691448165359,0.00686466313643,0.00688253804416,0.00677246718143,0.00727564266802,0.00723601911965,0.00689038375888,0.00706475655485,0.00700157249276,0.00700023052512,0.00700007449144,0.00700140082026,0.00689050284167,0.00702883225788,0.00670286837742,0.00692667362319,0.00701051609526,0.00654779955093,0.0067614666878,0.00715886704226,0.00651931079504,0.00680164535594,0.00706859962123,0.00722998024816,0.00692658599397,0.00737913326978,0.00711339202994,0.00694945655018,0.00705060348005,0.00709807018821,0.0069763381191,0.00697886891048,0.0070776443463,0.00693675196101,0.00699838198241,0.00702297011107,0.00693256081662,0.00697870245478,0.00718923751482,0.00705226826535,0.00657404509947,0.00705687964187,0.00688738938208,0.00684135510444,0.0071542462222,0.00664806949347,0.00707705193449,0.00686093944027,0.00704033613583,0.00703885700877,0.00709422945549,0.00692279546971,0.00699795574023,0.0070648305986,0.00700791402203,0.00702788751559,0.00693948460818,0.00703692627638,0.00701445691794,0.00700156547815,0.00699982519151,0.00701080225748,0.00705112420964,0.00693141174752,0.0071056039227,0.00699424492776,0.00701741168611,0.0070250256679,0.00701864158232,0.00700416099865,0.00739945788679,0.0069054375062,0.0067512257637,0.00695035580331,0.00734033103101,0.00647582239145,0.00688520212333,0.00680024897461,0.00741971621407,0.00668478224184,0.00660855345393,0.00822373418215,0.00682054678316,0.00702299779109,0.00699055577608,0.00691852567722,0.00721445310731,0.00683651531091,0.00700377121753,0.00655967427848,0.00661930723441,0.00690066979349,0.0067639462358,0.00710272885838,0.0071804423813,0.00687683988381,0.00656308630704,0.00726754807779,0.00684212723994,0.00673776086459,0.00828105304397,0.00667753794435,0.00747435403421,0.00660547327732,0.00696741744056,0.00705539826914,0.00703184822313,0.00694463509627,0.00702778704411,0.00678391055768,0.00724785202683,0.00711052719164,0.00701933556072,0.00692831055049,0.00702107123575,0.00705279369097,0.00708400627395,0.00707025232897,0.00692743074504,0.00695912069561,0.00706463442555,0.00692537737733,0.00748812911043,0.00714630961803,0.00693255057882,0.0068858176212,0.00712489296072,0.00697411977804,0.00674879657805,0.00727886678168,0.00693077829747,0.00695879514842,0.00691820687751,0.00822890543809,0.00661497274063,0.00695628319323,0.00706637174179,0.00733749225609,0.00696519622145,0.00700140943124,0.00706720715137,0.00698717576541,0.00702433864431,0.00698937508997,0.00696513323465,0.00687842107548,0.00709726460203,0.00701234457721,0.00699545469173,0.00706721319651,0.00700380682123,0.0070462536617,0.00696256155107,0.00690532021553,0.00660701020509,0.00719773277242,0.00662088092449,0.00798923805078,0.00702787174439,0.00663228590463,0.00694101327248,0.00709305936932,0.00692136553132,0.00695160124161,0.00707475228646,0.00693856114964,0.00715338299125,0.00677833682089,0.0069793521361,0.00705789224329,0.00702355759063,0.00690111477193,0.00675020234822,0.00697597355664,0.00663149127897,0.00657154590566,0.00658673735391,0.00679627561521,0.00708630112144,0.00687800713005,0.00692201724068,0.00695732062125,0.0070302351423,0.0069701339464,0.00693616975914,0.00710440024815,0.00691354544418,0.00706673811269,0.00687516588577,0.00705416667583,0.00694385918534,0.00710247076129,0.00798645787609,0.00660283660853,0.00677334116727,0.00675262391302,0.00738039698269,0.00695589844069,0.00706331106469,0.006968311192,0.00699013118587,0.00711063304458,0.00687783598806,0.00693830371136,0.00661788684992,0.00660227829141,0.00703283433547,0.00698828656485,0.00687667411885,0.00704804769703,0.00690538521611,0.00686408978787,0.00716742797545,0.00729158193241,0.00715760522465,0.00704559065801,0.00709995971794,0.00683959915414,0.00772332980663,0.00694030690579,0.00755930724977,0.00721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};
const double PHI1796[NST1796] = {
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1.98216865835,2.07661000933,2.02931218295,1.96027959417,2.53049234395,2.5428992254,2.45021962891,2.40669425706,2.47600365032,2.48259293905,1.17478447072,1.23811298794,1.26480259705,1.43146482988,1.48774969826,1.53542226823,1.50751648827,1.3838498226,1.41233872092,1.09673027516,0.242918262944,0.290964130236,0.29789528496,0.167024016301,0.345772952275,0.208035823495,0.489441382609,0.464884202305,0.638660502835,0.743111156163,0.761683874558,0.712579775106,0.593887984678,0.661680942938,0.531446919418,0.54397698185,0.672358828899,0.616769079835,0.303800209567,0.234090569062,0.182390213793,0.221859267166,0.32907456823,0.294988036348,0.246995650997,0.171620115615,0.735302627071,0.697623929603,0.700486241437,0.352074367588,0.280870995949,0.28958450821,0.84422685231,0.812523798274,0.917496688742,0.956472861046,0.924888396233,0.854390350301,1.04575950365,1.18457540201,1.16256788207,1.09352780731,1.14048098101,1.07079894308,0.643918387682,0.628775471599,0.714972952383,0.765388563449,0.685891670949,0.751233220095,0.42427689897,0.430423679776,0.502034596576,0.491532852166,0.556269876985,0.56081311978,0.684890406249,0.813643894801,0.810067605291,0.749111845953,0.593535645971,0.62101963185,0.4717619185,0.519908544525,0.630300976626,0.756383827961,0.688665736029,1.16992139502,1.06177123954,1.13314855632,1.13457273723,1.02488495778,1.06106446187,2.57738422355,2.6613984368,2.5946633352,2.44839185707,2.47316275239,2.37398668357,2.33115549895,2.35333465077,2.42023970316,3.04506816708,2.97300746682,3.03262359869,2.96189260759,2.84287125727,2.77825763708,2.9095500181,2.90589903399,2.75554341575,2.78069255042,2.84075386738,1.89621005983,1.96818097205,1.99614698567,1.95012063067,2.87037214228,2.80510038867,2.88844625845,2.75825382625,2.8251023867,2.76286494127,1.65699231203,1.51010737131,1.53699630961,1.60904354031,1.97544454027,2.01772227876,1.90153227161,1.87285395554,1.91893988375,1.98987115505,1.04202050948,1.0899658952,1.06386956671,0.989044279076,0.966149916537,0.939068791069,0.728984871729,0.803146931542,0.845022947368,0.949691682222,0.91259991329,0.839027007687,0.808349759643,0.922258877423,0.85483729421,1.07214566741,1.14759396845,1.0280794211,1.06219891445,1.17871729789,1.13722478518,0.895173415089,0.936811977655,0.880476672928,0.967028125198,1.50592162084,1.57412676262,1.61727504668,1.48018576241,1.52463161697,1.59344352567,1.6842230706,1.72877964561,1.78350256798,1.71178184187,1.91192094227,1.84849885788,1.79488755359,1.89342517189,1.82209207361,0.715974904262,0.642471196801,0.667065789948,0.614300387007,0.456605814746,0.344889643187,0.334107281228,0.394164948076,0.41739317328,0.470075916147,0.795618251309,0.829144266314,0.793860209285,0.723755919008,0.542675816227,0.509046157554,0.61613743074,0.644279050543,1.69078763421,1.80514618177,1.76434662676,1.77138095267,1.69708173053,1.65717723436,1.28427328013,1.21213032077,1.31609696169,1.33602321116,1.24465021584,1.1923417806,0.97631846333,1.03832466353,0.914494167364,1.07462954236,1.12899981004,1.11453239485,1.04526797212,0.814675631685,0.845913236305,0.917150448892,0.957822291308,0.954077971975,0.883920954005,0.833454269061,0.858080091727,0.975477797374,0.929800233624,0.799502647566,0.763741344901,0.74310927173,0.866790868595,0.835611367556,0.882770428549,0.430371901515,0.429710227769,0.492038251008,0.492094287458,0.360582628518,0.361144936965,1.77901157521,1.83739430455,1.73460568526,1.76277029354,2.2224228909,2.10387334871,2.07214388296,2.17649732809,2.11121770083,2.21864294782,2.18492328668,2.16913233304,2.09732802466,2.21400816574,2.18295731663,2.42370255621,2.32798930135,2.40344795302,1.12945629575,1.01987995373,1.06050371386,1.00415815485,1.16177495927,1.22392325529,1.16660169299,1.30984539984,1.26500955098,1.19327913481,1.30626619716,1.21205121523,1.23677930118,1.18938227222,1.33037903336,1.28340253861,0.338851609819,0.404288336402,0.292648181948,0.275596958506,0.366796636962,0.41645840733,0.109417678754,0.157635539968,0.226966533231,0.256453243699,0.160161172184,0.229786455716,0.398601655397,0.364693766391,0.46465793425,0.398426324772,0.583992853936,0.62587250447,0.509061416467,0.580945743251,0.520663457434,0.472181205604,0.505957470728,2.62467325665,2.70509096032,2.63136592941,2.59473733873,1.85130806788,1.73359033576,1.77967004244,1.7576546513,1.8296940184,1.87735144132,1.63137324417,1.67565695401,1.52920117325,1.55663362059,1.64388526052,1.57226201756,0.69613820301,0.645814780494,0.594481800257,0.621742246828,0.816172412353,0.864671222275,0.842531882267,0.770818882529,0.718322512862,0.741883689825,0.761005541058,0.832781317031,0.794868828585,0.740020254712,0.677220537581,0.600388937548,0.686985458415,0.714031450439,0.545798524496,0.560957235597,0.621612488133,1.88217336621,1.85182079054,1.95434696082,1.89213731685,2.35058036811,2.36092599671,2.28103751664,2.22796244593,2.24171104847,2.30528512215,1.18897956013,1.2389575982,1.1149040846,1.09278799174,1.21807535401,1.14606176396,1.12147792539,1.00624757863,1.07410894781,0.988513256188,1.04159329698,1.10660489467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};
const double THETA1796[NST1796] = {
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};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FEFiberIntegrationGeodesic.cpp | .cpp | 4,412 | 154 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFiberIntegrationGeodesic.h"
#include <FECore/log.h>
#ifndef SQR
#define SQR(x) ((x)*(x))
#endif
class FEFiberIntegrationGeodesic::Iterator : public FEFiberIntegrationSchemeIterator
{
public:
Iterator(int nint, const double* cth, const double* cph, const double* sth, const double* sph, const double* wn)
{
m_nint = nint;
m_cth = cth;
m_cph = cph;
m_sth = sth;
m_sph = sph;
m_wn = wn;
n = -1;
Next();
}
bool IsValid()
{
return (n < m_nint);
}
// move to the next integration point
bool Next()
{
n++;
if (n < m_nint)
{
m_fiber.x = m_cth[n] * m_sph[n];
m_fiber.y = m_sth[n] * m_sph[n];
m_fiber.z = m_cph[n];
m_weight = m_wn[n];
return true;
}
else return false;
}
public:
int n;
int m_nint;
const double* m_cth;
const double* m_cph;
const double* m_sth;
const double* m_sph;
const double* m_wn;
};
//-----------------------------------------------------------------------------
// FEFiberIntegrationGeodesic
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEFiberIntegrationGeodesic, FEFiberIntegrationScheme)
ADD_PARAMETER(m_nres, "resolution")->setEnums("low\0high\0");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
void FEFiberIntegrationGeodesic::Serialize(DumpStream& ar)
{
FEFiberIntegrationScheme::Serialize(ar);
if (ar.IsSaving() == false)
{
InitIntegrationRule();
}
}
//-----------------------------------------------------------------------------
FEFiberIntegrationGeodesic::FEFiberIntegrationGeodesic(FEModel* pfem) : FEFiberIntegrationScheme(pfem)
{
m_nres = 0;
}
//-----------------------------------------------------------------------------
FEFiberIntegrationGeodesic::~FEFiberIntegrationGeodesic()
{
}
//-----------------------------------------------------------------------------
bool FEFiberIntegrationGeodesic::Init()
{
if ((m_nres != 0) && (m_nres != 1)) {
feLogError("resolution must be 0 (low) or 1 (high)."); return false;
}
// initialize integration rule data
InitIntegrationRule();
// also initialize the parent class
return FEFiberIntegrationScheme::Init();
}
//-----------------------------------------------------------------------------
void FEFiberIntegrationGeodesic::InitIntegrationRule()
{
// select the integration rule
m_nint = (m_nres == 0? NSTL : NSTH );
const double* phi = (m_nres == 0? PHIL : PHIH );
const double* the = (m_nres == 0? THETAL: THETAH);
const double* w = (m_nres == 0? AREAL : AREAH );
for (int n=0; n<m_nint; ++n)
{
m_cth[n] = cos(the[n]);
m_sth[n] = sin(the[n]);
m_cph[n] = cos(phi[n]);
m_sph[n] = sin(phi[n]);
m_w[n] = w[n];
}
}
//-----------------------------------------------------------------------------
FEFiberIntegrationSchemeIterator* FEFiberIntegrationGeodesic::GetIterator(FEMaterialPoint* mp)
{
return new Iterator(m_nint, &m_cth[0], &m_cph[0], &m_sth[0], &m_sph[0], &m_w[0]);
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEHolmesMowUC.cpp | .cpp | 3,668 | 111 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2022 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEHolmesMowUC.h"
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FEHolmesMowUC, FEUncoupledMaterial)
ADD_PARAMETER(m_mu, FE_RANGE_GREATER(0.0), "mu")->setLongName("shear modulus");
ADD_PARAMETER(m_b, FE_RANGE_GREATER_OR_EQUAL(0.0), "beta")->setLongName("power exponent");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
mat3ds FEHolmesMowUC::DevStress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate left Cauchy-Green tensor
mat3ds bt = pt.DevLeftCauchyGreen();
// calculate invariants of B
double I1 = bt.tr();
// Exponential term
double eQ = exp(m_b*(I1-3));
// calculate stress
mat3ds st = bt*(m_mu*eQ/pt.m_J);
return st.dev();
}
//-----------------------------------------------------------------------------
tens4ds FEHolmesMowUC::DevTangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate left Cauchy-Green tensor
mat3ds bt = pt.DevLeftCauchyGreen();
// calculate invariants of B
double I1 = bt.tr();
// Exponential term
double eQ = exp(m_b*(I1-3));
// calculate stress
mat3ds st = bt*(m_mu*eQ/pt.m_J);
// calculate identity tensor
mat3dd I(1);
// calculate elasticity tensor
tens4ds ct = dyad1s(bt)*(2*m_b*m_mu*eQ/pt.m_J);
// This is the final value of the elasticity tensor
tens4ds IxI = dyad1s(I);
tens4ds I4 = dyad4s(I);
ct += - 1./3.*(ddots(ct,IxI) - IxI*(ct.tr()/3.))
+ 2./3.*((I4-IxI/3.)*st.tr()-dyad1s(st.dev(),I));
return ct;
}
//-----------------------------------------------------------------------------
double FEHolmesMowUC::DevStrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// calculate left Cauchy-Green tensor
mat3ds bt = pt.DevLeftCauchyGreen();
// calculate invariants of B
double I1 = bt.tr();
// Exponential term
double eQ = exp(m_b*(I1-3));
// calculate strain energy density
double sed = m_mu/(2*m_b)*(eQ-1);
return sed;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/ObjectDataRecord.h | .h | 2,161 | 60 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FECoreBase.h>
#include <FECore/DataRecord.h>
#include "FERigidBody.h"
//-----------------------------------------------------------------------------
//! Base class for object log data (e.g. rigid bodies)
class FEBIOMECH_API FELogObjectData : public FELogData
{
FECORE_SUPER_CLASS(FELOGOBJECTDATA_ID)
FECORE_BASE_CLASS(FELogObjectData)
public:
FELogObjectData(FEModel* fem) : FELogData(fem) {}
virtual ~FELogObjectData(){}
virtual double value(FERigidBody& rb) = 0;
};
//-----------------------------------------------------------------------------
class FEBIOMECH_API ObjectDataRecord : public DataRecord
{
public:
ObjectDataRecord(FEModel* pfem);
double Evaluate(int item, int ndata) override;
void SetData(const char* sz) override;
void SelectAllItems() override;
int Size() const override;
private:
vector<FELogObjectData*> m_Data;
};
| Unknown |
3D | febiosoftware/FEBio | FEBioMech/FENeoHookean.cpp | .cpp | 4,812 | 167 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FENeoHookean.h"
//-----------------------------------------------------------------------------
// define the material parameters
BEGIN_FECORE_CLASS(FENeoHookean, FEElasticMaterial)
ADD_PARAMETER(m_E, FE_RANGE_GREATER(0.0), "E")->setUnits(UNIT_PRESSURE)->setLongName("Young's modulus");
ADD_PARAMETER(m_v, FE_RANGE_RIGHT_OPEN(-1, 0.5), "v")->setLongName("Poisson's ratio");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FENeoHookean::FENeoHookean(FEModel* pfem) : FEElasticMaterial(pfem) {}
//-----------------------------------------------------------------------------
mat3ds FENeoHookean::Stress(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
double detF = pt.m_J;
double detFi = 1.0/detF;
double lndetF = log(detF);
// get the material parameters
double E = m_E(mp);
double v = m_v(mp);
// calculate left Cauchy-Green tensor
mat3ds b = pt.LeftCauchyGreen();
// lame parameters
double lam = v*E/((1+v)*(1-2*v));
double mu = 0.5*E/(1+v);
// Identity
mat3dd I(1);
// calculate stress
mat3ds s = (b - I)*(mu*detFi) + I*(lam*lndetF*detFi);
return s;
}
//-----------------------------------------------------------------------------
tens4ds FENeoHookean::Tangent(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
// deformation gradient
double detF = pt.m_J;
// get the material parameters
double E = m_E(mp);
double v = m_v(mp);
// lame parameters
double lam = v*E/((1+v)*(1-2*v));
double mu = 0.5*E/(1+v);
double lam1 = lam / detF;
double mu1 = (mu - lam*log(detF)) / detF;
mat3dd I(1);
return dyad1s(I)*lam1 + dyad4s(I)*(2*mu1);
}
//-----------------------------------------------------------------------------
double FENeoHookean::StrainEnergyDensity(FEMaterialPoint& mp)
{
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
double J = pt.m_J;
double lnJ = log(J);
// get the material parameters
double E = m_E(mp);
double v = m_v(mp);
// calculate left Cauchy-Green tensor
mat3ds b = pt.LeftCauchyGreen();
double I1 = b.tr();
// lame parameters
double lam = v*E/((1+v)*(1-2*v));
double mu = 0.5*E/(1+v);
double sed = mu*((I1-3)/2.0 - lnJ)+lam*lnJ*lnJ/2.0;
return sed;
}
//-----------------------------------------------------------------------------
mat3ds FENeoHookean::PK2Stress(FEMaterialPoint& pt, const mat3ds ES)
{
// Identity
mat3dd I(1);
// calculate right Cauchy-Green tensor
mat3ds C = I + ES*2;
mat3ds Ci = C.inverse();
double detF = sqrt(C.det());
double lndetF = log(detF);
// get the material parameters
double E = m_E(pt);
double v = m_v(pt);
// lame parameters
double lam = v*E/((1+v)*(1-2*v));
double mu = 0.5*E/(1+v);
// calculate stress
mat3ds S = (I - Ci)*mu + Ci*(lam*lndetF);
return S;
}
//-----------------------------------------------------------------------------
tens4dmm FENeoHookean::MaterialTangent(FEMaterialPoint& pt, const mat3ds ES)
{
// calculate right Cauchy-Green tensor
mat3ds C = mat3dd(1) + ES*2;
mat3ds Ci = C.inverse();
double J = sqrt(C.det());
// get the material parameters
double E = m_E(pt);
double v = m_v(pt);
// lame parameters
double lam = v*E/((1+v)*(1-2*v));
double mu = 0.5*E/(1+v);
tens4dmm c = dyad1s(Ci)*lam + dyad4s(Ci)*(2*(mu-lam*log(J)));
return c;
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FERigidRevoluteJoint.cpp | .cpp | 28,800 | 958 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FERigidRevoluteJoint.h"
#include "FERigidBody.h"
#include "FECore/log.h"
#include <FECore/FELinearSystem.h>
//-----------------------------------------------------------------------------
BEGIN_FECORE_CLASS(FERigidRevoluteJoint, FERigidConnector);
ADD_PARAMETER(m_laugon, "laugon")->setLongName("Enforcement method")->setEnums("PENALTY\0AUGLAG\0LAGMULT\0");
ADD_PARAMETER(m_atol, "tolerance" );
ADD_PARAMETER(m_gtol, "gaptol" );
ADD_PARAMETER(m_qtol, "angtol" );
ADD_PARAMETER(m_eps , "force_penalty" );
ADD_PARAMETER(m_ups , "moment_penalty");
ADD_PARAMETER(m_cps , "force_damping" );
ADD_PARAMETER(m_rps , "moment_damping");
ADD_PARAMETER(m_q0 , "joint_origin" );
ADD_PARAMETER(m_e0[0], "rotation_axis" );
ADD_PARAMETER(m_e0[1], "transverse_axis");
ADD_PARAMETER(m_naugmin, "minaug" );
ADD_PARAMETER(m_naugmax, "maxaug" );
ADD_PARAMETER(m_bq , "prescribed_rotation");
ADD_PARAMETER(m_qp , "rotation" );
ADD_PARAMETER(m_Mp , "moment" );
ADD_PARAMETER(m_bautopen, "auto_penalty");
ADD_PARAMETER(m_torsion_stiffness, "torsion_stiffness");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FERigidRevoluteJoint::FERigidRevoluteJoint(FEModel* pfem) : FERigidConnector(pfem)
{
m_nID = m_ncount++;
m_laugon = FECore::AUGLAG_METHOD; // for backward compatibility
m_atol = 0;
m_gtol = 0;
m_qtol = 0;
m_naugmin = 0;
m_naugmax = 10;
m_qp = 0;
m_Mp = 0;
m_bq = false;
m_eps = m_ups = 1.0;
m_cps = m_rps = 0.0;
m_e0[0] = vec3d(0,0,1);
m_e0[1] = vec3d(1,0,0);
m_bautopen = false;
}
//-----------------------------------------------------------------------------
FERigidRevoluteJoint::~FERigidRevoluteJoint()
{
}
//-----------------------------------------------------------------------------
//! initial position
vec3d FERigidRevoluteJoint::InitialPosition() const
{
return m_q0;
}
//-----------------------------------------------------------------------------
//! current position
vec3d FERigidRevoluteJoint::Position() const
{
FERigidBody& RBa = *m_rbA;
vec3d qa = m_qa0;
RBa.GetRotation().RotateVector(qa);
return RBa.m_rt + qa;
}
//-----------------------------------------------------------------------------
//! current axis
quatd FERigidRevoluteJoint::Orientation() const
{
quatd Q0(vec3d(0, 0, 1), m_e0[0]);
FERigidBody& RBa = *m_rbA;
return RBa.GetRotation()*Q0;
}
//-----------------------------------------------------------------------------
//! TODO: This function is called twice: once in the Init and once in the Solve
//! phase. Is that necessary?
bool FERigidRevoluteJoint::Init()
{
if (m_bq && (m_Mp != 0)) {
feLogError("Rotation and moment cannot be prescribed simultaneously in rigid connector %d (revolute joint)\n", m_nID+1);
return false;
}
// initialize joint basis
m_e0[0].unit();
m_e0[2] = m_e0[0] ^ m_e0[1]; m_e0[2].unit();
m_e0[1] = m_e0[2] ^ m_e0[0];
// reset force
m_F = vec3d(0,0,0); m_L = vec3d(0,0,0); m_Fp = vec3d(0,0,0);
m_M = vec3d(0,0,0); m_U = vec3d(0,0,0); m_Up = vec3d(0,0,0);
// base class first
if (FERigidConnector::Init() == false) return false;
m_qa0 = m_q0 - m_rbA->m_r0;
m_qb0 = m_q0 - m_rbB->m_r0;
m_ea0[0] = m_e0[0]; m_ea0[1] = m_e0[1]; m_ea0[2] = m_e0[2];
m_eb0[0] = m_e0[0]; m_eb0[1] = m_e0[1]; m_eb0[2] = m_e0[2];
return true;
}
//-----------------------------------------------------------------------------
void FERigidRevoluteJoint::Serialize(DumpStream& ar)
{
FERigidConnector::Serialize(ar);
ar & m_qa0 & m_qb0;
ar & m_L & m_U;
ar & m_e0;
ar & m_ea0;
ar & m_eb0;
ar & m_LM;
}
//-----------------------------------------------------------------------------
//! \todo Why is this class not using the FESolver for assembly?
void FERigidRevoluteJoint::LoadVector(FEGlobalVector& R, const FETimeInfo& tp)
{
vector<double> fa(6);
vector<double> fb(6);
vec3d eat[3], eap[3], ea[3];
vec3d ebt[3], ebp[3], eb[3];
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
double alpha = tp.alphaf;
// body A
vec3d ra = RBa.m_rt*alpha + RBa.m_rp*(1-alpha);
vec3d zat = m_qa0; RBa.GetRotation().RotateVector(zat);
vec3d zap = m_qa0; RBa.m_qp.RotateVector(zap);
vec3d za = zat*alpha + zap*(1-alpha);
eat[0] = m_ea0[0]; RBa.GetRotation().RotateVector(eat[0]);
eat[1] = m_ea0[1]; RBa.GetRotation().RotateVector(eat[1]);
eat[2] = m_ea0[2]; RBa.GetRotation().RotateVector(eat[2]);
eap[0] = m_ea0[0]; RBa.m_qp.RotateVector(eap[0]);
eap[1] = m_ea0[1]; RBa.m_qp.RotateVector(eap[1]);
eap[2] = m_ea0[2]; RBa.m_qp.RotateVector(eap[2]);
ea[0] = eat[0]*alpha + eap[0]*(1-alpha);
ea[1] = eat[1]*alpha + eap[1]*(1-alpha);
ea[2] = eat[2]*alpha + eap[2]*(1-alpha);
// body b
vec3d rb = RBb.m_rt*alpha + RBb.m_rp*(1-alpha);
vec3d zbt = m_qb0; RBb.GetRotation().RotateVector(zbt);
vec3d zbp = m_qb0; RBb.m_qp.RotateVector(zbp);
vec3d zb = zbt*alpha + zbp*(1-alpha);
ebt[0] = m_eb0[0]; RBb.GetRotation().RotateVector(ebt[0]);
ebt[1] = m_eb0[1]; RBb.GetRotation().RotateVector(ebt[1]);
ebt[2] = m_eb0[2]; RBb.GetRotation().RotateVector(ebt[2]);
ebp[0] = m_eb0[0]; RBb.m_qp.RotateVector(ebp[0]);
ebp[1] = m_eb0[1]; RBb.m_qp.RotateVector(ebp[1]);
ebp[2] = m_eb0[2]; RBb.m_qp.RotateVector(ebp[2]);
eb[0] = ebt[0]*alpha + ebp[0]*(1-alpha);
eb[1] = ebt[1]*alpha + ebp[1]*(1-alpha);
eb[2] = ebt[2]*alpha + ebp[2]*(1-alpha);
if (m_laugon != FECore::LAGMULT_METHOD)
{
vec3d c = rb + zb - ra - za;
m_F = m_L + c * m_eps;
vec3d ksi;
if (m_bq) {
quatd q = (alpha * RBb.GetRotation() + (1 - alpha) * RBb.m_qp) * (alpha * RBa.GetRotation() + (1 - alpha) * RBa.m_qp).Inverse();
quatd a(m_qp, ea[0]);
quatd r = a * q.Inverse();
r.MakeUnit();
ksi = r.GetVector() * r.GetAngle();
}
else
ksi = (ea[0] ^ eb[0]) / 2;
m_M = m_U + ksi * m_ups + ea[0] * m_Mp;
// add damping
if (m_cps > 0) {
// body A
vec3d vat = RBa.m_vt + (RBa.m_wt ^ zat);
vec3d vap = RBa.m_vp + (RBa.m_wp ^ zap);
vec3d va = vat * alpha + vap * (1 - alpha);
// body b
vec3d vbt = RBb.m_vt + (RBb.m_wt ^ zbt);
vec3d vbp = RBb.m_vp + (RBb.m_wp ^ zbp);
vec3d vb = vbt * alpha + vbp * (1 - alpha);
m_F += (vb - va)*m_cps;
}
if (m_rps > 0) {
// body A
vec3d wa = RBa.m_wt * alpha + RBa.m_wp * (1 - alpha);
// body b
vec3d wb = RBb.m_wt * alpha + RBb.m_wp * (1 - alpha);
mat3ds P = m_bq ? mat3dd(1) : mat3dd(1) - dyad(ea[0]);
m_M += P * (wb - wa) * m_rps;
}
fa[0] = m_F.x;
fa[1] = m_F.y;
fa[2] = m_F.z;
fa[3] = za.y * m_F.z - za.z * m_F.y + m_M.x;
fa[4] = za.z * m_F.x - za.x * m_F.z + m_M.y;
fa[5] = za.x * m_F.y - za.y * m_F.x + m_M.z;
fb[0] = -m_F.x;
fb[1] = -m_F.y;
fb[2] = -m_F.z;
fb[3] = -zb.y * m_F.z + zb.z * m_F.y - m_M.x;
fb[4] = -zb.z * m_F.x + zb.x * m_F.z - m_M.y;
fb[5] = -zb.x * m_F.y + zb.y * m_F.x - m_M.z;
for (int i = 0; i < 6; ++i) if (RBa.m_LM[i] >= 0) R[RBa.m_LM[i]] += fa[i];
for (int i = 0; i < 6; ++i) if (RBb.m_LM[i] >= 0) R[RBb.m_LM[i]] += fb[i];
}
else
{
vec3d Ma = (za ^ m_F) + (ea[0] ^ m_M);
vec3d Mb = (zb ^ m_F) + (eb[0] ^ m_M);
fa[0] = -m_F.x;
fa[1] = -m_F.y;
fa[2] = -m_F.z;
fa[3] = -Ma.x;
fa[4] = -Ma.y;
fa[5] = -Ma.z;
fb[0] = m_F.x;
fb[1] = m_F.y;
fb[2] = m_F.z;
fb[3] = Mb.x;
fb[4] = Mb.y;
fb[5] = Mb.z;
for (int i = 0; i < 6; ++i) if (RBa.m_LM[i] >= 0) R[RBa.m_LM[i]] += fa[i];
for (int i = 0; i < 6; ++i) if (RBb.m_LM[i] >= 0) R[RBb.m_LM[i]] += fb[i];
// translational constraint
vec3d c = rb + zb - ra - za;
R[m_LM[0]] += c.x;
R[m_LM[1]] += c.y;
R[m_LM[2]] += c.z;
// rotational constraint
vec3d ksi1 = eb[0] - ea[0];
R[m_LM[3]] += ksi1.x;
R[m_LM[4]] += ksi1.y;
R[m_LM[5]] += ksi1.z;
}
if (m_torsion_stiffness != 0)
{
vec3d zbat = m_qb0; RBa.GetRotation().RotateVector(zbat);
vec3d zbap = m_qb0; RBa.m_qp.RotateVector(zbap);
vec3d zba = zbat * alpha + zbap * (1 - alpha);
vec3d nb(zb); nb.unit();
vec3d nba(zba); nba.unit();
vec3d t = (nb ^ nba)*m_torsion_stiffness;
double ma[3] = { -t.x, -t.y, -t.z };
double mb[3] = { t.x, t.y, t.z };
for (int i=0;i <3; ++i)
{
if (RBa.m_LM[3 + i] >= 0) R[RBa.m_LM[3 + i]] += ma[i];
if (RBb.m_LM[3 + i] >= 0) R[RBb.m_LM[3 + i]] += mb[i];
}
}
RBa.m_Fr -= vec3d(fa[0],fa[1],fa[2]);
RBa.m_Mr -= vec3d(fa[3],fa[4],fa[5]);
RBb.m_Fr -= vec3d(fb[0],fb[1],fb[2]);
RBb.m_Mr -= vec3d(fb[3],fb[4],fb[5]);
}
//-----------------------------------------------------------------------------
//! \todo Why is this class not using the FESolver for assembly?
void FERigidRevoluteJoint::StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp)
{
double alpha = tp.alphaf;
double beta = tp.beta;
double gamma = tp.gamma;
// get time increment
double dt = tp.timeIncrement;
vec3d eat[3], eap[3], ea[3];
vec3d ebt[3], ebp[3], eb[3];
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
// body A
quatd Qat = RBa.GetRotation();
quatd Qap = RBa.m_qp;
vec3d rat = RBa.m_rt;
vec3d rap = RBa.m_rp;
vec3d ra = rat * alpha + rap * (1 - alpha);
vec3d zat = Qat * m_qa0;
vec3d zap = Qap * m_qa0;
vec3d za = zat*alpha + zap*(1-alpha);
eat[0] = m_ea0[0]; RBa.GetRotation().RotateVector(eat[0]);
eat[1] = m_ea0[1]; RBa.GetRotation().RotateVector(eat[1]);
eat[2] = m_ea0[2]; RBa.GetRotation().RotateVector(eat[2]);
eap[0] = m_ea0[0]; RBa.m_qp.RotateVector(eap[0]);
eap[1] = m_ea0[1]; RBa.m_qp.RotateVector(eap[1]);
eap[2] = m_ea0[2]; RBa.m_qp.RotateVector(eap[2]);
ea[0] = eat[0]*alpha + eap[0]*(1-alpha);
ea[1] = eat[1]*alpha + eap[1]*(1-alpha);
ea[2] = eat[2]*alpha + eap[2]*(1-alpha);
mat3d zahat; zahat.skew(za);
mat3d zathat; zathat.skew(zat);
// body b
quatd Qbt = RBb.GetRotation();
quatd Qbp = RBb.m_qp;
vec3d rbt = RBb.m_rt;
vec3d rbp = RBb.m_rp;
vec3d rb = rbt * alpha + rbp * (1 - alpha);
vec3d zbt = Qbt * m_qb0;
vec3d zbp = Qbp * m_qb0;
vec3d zb = zbt*alpha + zbp*(1-alpha);
ebt[0] = m_eb0[0]; RBb.GetRotation().RotateVector(ebt[0]);
ebt[1] = m_eb0[1]; RBb.GetRotation().RotateVector(ebt[1]);
ebt[2] = m_eb0[2]; RBb.GetRotation().RotateVector(ebt[2]);
ebp[0] = m_eb0[0]; RBb.m_qp.RotateVector(ebp[0]);
ebp[1] = m_eb0[1]; RBb.m_qp.RotateVector(ebp[1]);
ebp[2] = m_eb0[2]; RBb.m_qp.RotateVector(ebp[2]);
eb[0] = ebt[0]*alpha + ebp[0]*(1-alpha);
eb[1] = ebt[1]*alpha + ebp[1]*(1-alpha);
eb[2] = ebt[2]*alpha + ebp[2]*(1-alpha);
mat3d zbhat; zbhat.skew(zb);
mat3d zbthat; zbthat.skew(zbt);
mat3d eahat[3], ebhat[3], eathat[3], ebthat[3];
for (int j = 0; j < 3; ++j) {
eahat[j] = skew(ea[j]);
ebhat[j] = skew(eb[j]);
eathat[j] = skew(eat[j]);
ebthat[j] = skew(ebt[j]);
}
if (m_laugon != FECore::LAGMULT_METHOD)
{
vec3d c = rb + zb - ra - za;
m_F = m_L + c * m_eps;
mat3dd I(1);
vec3d ksi;
quatd q, a, r;
if (m_bq) {
q = (alpha * RBb.GetRotation() + (1 - alpha) * RBb.m_qp) * (alpha * RBa.GetRotation() + (1 - alpha) * RBa.m_qp).Inverse();
a = quatd(m_qp, ea[0]);
r = a * q.Inverse();
r.MakeUnit();
ksi = r.GetVector() * r.GetAngle();
}
else
ksi = (ea[0] ^ eb[0]) / 2;
m_M = m_U + ksi * m_ups + ea[0] * m_Mp;
mat3d K, Wba, Wab;
Wba = (ebhat[0] * eathat[0]) / 2;
Wab = (eahat[0] * ebthat[0]) / 2;
if (m_bq) {
quatd qa = RBa.GetRotation() * (alpha * RBa.GetRotation() + (1 - alpha) * RBa.m_qp).Inverse();
quatd qb = RBb.GetRotation() * (alpha * RBb.GetRotation() + (1 - alpha) * RBb.m_qp).Inverse();
qa.MakeUnit();
qb.MakeUnit();
mat3d Qa = qa.RotationMatrix();
mat3d Qb = qb.RotationMatrix();
mat3d A = a.RotationMatrix();
mat3d R = r.RotationMatrix();
mat3dd I(1);
Wba = A *(I * Qa.trace() - Qa) / 2;
Wab = R *(I * Qb.trace() - Qb) / 2;
}
// add damping
mat3ds A;
mat3d Ba, Bb, Ca, Cb, W;
A.zero(); Ba.zero(); Bb.zero(); Ca.zero(); Cb.zero(); W.zero();
if ((m_cps > 0) || (m_rps > 0)) {
// body A
vec3d vat = RBa.m_vt + (RBa.m_wt ^ zat);
vec3d vap = RBa.m_vp + (RBa.m_wp ^ zap);
vec3d va = vat * alpha + vap * (1 - alpha);
quatd qai = RBa.GetRotation() * RBa.m_qp.Inverse(); qai.MakeUnit();
vec3d cai = qai.GetVector() * (2 * tan(qai.GetAngle() / 2));
mat3d Ta = I + skew(cai) / 2 + dyad(cai) / 4;
vec3d wa = RBa.m_wt * alpha + RBa.m_wp * (1 - alpha);
// body b
vec3d vbt = RBb.m_vt + (RBb.m_wt ^ zbt);
vec3d vbp = RBb.m_vp + (RBb.m_wp ^ zbp);
vec3d vb = vbt * alpha + vbp * (1 - alpha);
quatd qbi = RBb.GetRotation() * RBb.m_qp.Inverse(); qbi.MakeUnit();
vec3d cbi = qbi.GetVector() * (2 * tan(qbi.GetAngle() / 2));
mat3d Tb = I + skew(cbi) / 2 + dyad(cbi) / 4;
vec3d wb = RBb.m_wt * alpha + RBb.m_wp * (1 - alpha);
m_F += (vb - va)*m_cps;
vec3d w = wb - wa;
// angular damping along all directions if rotation is prescribed
mat3ds P = m_bq ? I : I - dyad(ea[0]);
m_M += P*w*m_rps;
A = I*(gamma/beta/dt);
Ba = zathat * Ta.transpose() * (gamma / beta / dt) + skew(RBa.m_wt) * zathat;
Bb = zbthat * Tb.transpose() * (gamma / beta / dt) + skew(RBb.m_wt) * zbthat;
Ca = P * Ta.transpose() * (gamma / beta / dt);
Cb = P * Tb.transpose() * (gamma / beta / dt);
W = (mat3dd(ea[0] * w) + (ea[0] & w)) * eathat[0];
}
mat3d Fhat; Fhat.skew(m_F);
mat3d Mhat; Mhat.skew(m_M);
FEElementMatrix ke(12, 12);
ke.zero();
// row 1
ke.set(0, 0, I * (m_eps) + A * (m_cps));
ke.set(0, 3, zathat * (-m_eps) + Ba * (-m_cps));
ke.set(0, 6, I * (-m_eps) + A * (-m_cps));
ke.set(0, 9, zbthat * (m_eps) + Bb * (m_cps));
// row 2
ke.set(3, 0, zahat* (m_eps) + zahat * A * (m_cps));
ke.set(3, 3, (zahat * zathat * m_eps + Fhat * zathat + Wba * m_ups) * (-1.0));
ke.set(3, 6, zahat * (-m_eps) + zahat * A * (-m_cps));
ke.set(3, 9, (zahat* zbthat* m_eps + Wab * m_ups));
if (m_cps)
{
ke.add(3, 3, eathat[0] * (m_Mp)+(zahat * Ba) * (-m_cps));
ke.add(3, 9, (zahat * Bb) * (m_cps));
}
if (m_rps)
{
ke.add(3, 3, (W - Ca) * (m_rps));
ke.add(3, 9, Cb * (m_rps));
}
// row 3
ke.set(6, 0, I* (-m_eps) + A * (-m_cps));
ke.set(6, 3, zathat * (m_eps) + Ba * (m_cps));
ke.set(6, 6, I * (m_eps) + A * (m_cps));
ke.set(6, 9, zbthat * (-m_eps) + Bb * (-m_cps));
// row 4
ke.set(9, 0, zbhat* (-m_eps) + zbhat * A * (-m_cps));
ke.set(9, 3, zbhat* zathat* m_eps + Wba * m_ups);
ke.set(9, 6, zbhat* (m_eps) + zbhat * A * (m_cps));
ke.set(9, 9, (zbhat * zbthat * m_eps - Fhat * zbthat + Wab * m_ups) * (-1.0));
if (m_cps)
{
ke.add(9, 0, -eathat[0] * (m_Mp)+(zbhat * Ba) * (m_cps));
ke.add(9, 9, (zbhat * Bb) * (-m_cps));
}
if (m_rps)
{
ke.add(9, 0, -(W - Ca) * (m_rps));
ke.add(9, 9, -Cb * (m_rps));
}
ke *= alpha;
vector<int> LM(12);
for (int j = 0; j < 6; ++j)
{
LM[j] = RBa.m_LM[j];
LM[j + 6] = RBb.m_LM[j];
}
ke.SetIndices(LM);
LS.Assemble(ke);
}
else
{
FEElementMatrix ke; ke.resize(18, 18);
ke.zero();
mat3dd I(1.0);
// translation constraint
mat3da Fhat(m_F);
ke.sub( 3, 3, -Fhat * zahat);
ke.sub( 9, 9, Fhat* zbhat);
ke.sub( 0, 12, -I);
ke.sub( 3, 12, -zahat);
ke.sub( 6, 12, I);
ke.sub( 9, 12, zbhat);
ke.sub(12, 0, -I);
ke.sub(12, 3, zahat);
ke.sub(12, 6, I);
ke.sub(12, 9, -zbhat);
// rotational constraint 1
mat3da Mhat(m_M);
ke.sub(3, 3, -Mhat*eahat[0]);
ke.sub(9, 9, Mhat*ebhat[0]);
ke.sub(3, 15, -eahat[0]);
ke.sub(9, 15, ebhat[0]);
ke.sub(15, 3, eahat[0]);
ke.sub(15, 9, -ebhat[0]);
vector<int> LM;
UnpackLM(LM);
ke.SetIndices(LM);
LS.Assemble(ke);
}
if (m_torsion_stiffness != 0)
{
vec3d zbat = m_qb0; RBa.GetRotation().RotateVector(zbat);
vec3d zbap = m_qb0; RBa.m_qp.RotateVector(zbap);
vec3d zba = zbat * alpha + zbap * (1 - alpha);
vec3d nb(zb); nb.unit();
vec3d nba(zba); nba.unit();
mat3d nbhat = skew(nb);
mat3d nbahat = skew(nba);
mat3d Kbba = nbhat * nbahat * m_torsion_stiffness;
mat3d Kbab = nbahat * nbhat * m_torsion_stiffness;
FEElementMatrix ke(12, 12);
ke.zero();
ke.sub(3, 3, Kbba); ke.sub(3, 9, -Kbab);
ke.sub(9, 3, -Kbba); ke.sub(9, 9, Kbab);
ke *= alpha;
vector<int> LM(12);
for (int j = 0; j < 6; ++j)
{
LM[j ] = RBa.m_LM[j];
LM[j + 6] = RBb.m_LM[j];
}
ke.SetIndices(LM);
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
bool FERigidRevoluteJoint::Augment(int naug, const FETimeInfo& tp)
{
if (m_laugon != FECore::AUGLAG_METHOD) return true;
vec3d ra, rb, qa, qb, c, ksi, Lm;
vec3d za, zb;
vec3d eat[3], eap[3], ea[3];
vec3d ebt[3], ebp[3], eb[3];
double normF0, normF1;
vec3d Um;
double normM0, normM1;
bool bconv = true;
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
double alpha = tp.alphaf;
ra = RBa.m_rt*alpha + RBa.m_rp*(1-alpha);
rb = RBb.m_rt*alpha + RBb.m_rp*(1-alpha);
vec3d zat = m_qa0; RBa.GetRotation().RotateVector(zat);
vec3d zap = m_qa0; RBa.m_qp.RotateVector(zap);
za = zat*alpha + zap*(1-alpha);
eat[0] = m_ea0[0]; RBa.GetRotation().RotateVector(eat[0]);
eat[1] = m_ea0[1]; RBa.GetRotation().RotateVector(eat[1]);
eat[2] = m_ea0[2]; RBa.GetRotation().RotateVector(eat[2]);
eap[0] = m_ea0[0]; RBa.m_qp.RotateVector(eap[0]);
eap[1] = m_ea0[1]; RBa.m_qp.RotateVector(eap[1]);
eap[2] = m_ea0[2]; RBa.m_qp.RotateVector(eap[2]);
ea[0] = eat[0]*alpha + eap[0]*(1-alpha);
ea[1] = eat[1]*alpha + eap[1]*(1-alpha);
ea[2] = eat[2]*alpha + eap[2]*(1-alpha);
vec3d zbt = m_qb0; RBb.GetRotation().RotateVector(zbt);
vec3d zbp = m_qb0; RBb.m_qp.RotateVector(zbp);
zb = zbt*alpha + zbp*(1-alpha);
ebt[0] = m_eb0[0]; RBb.GetRotation().RotateVector(ebt[0]);
ebt[1] = m_eb0[1]; RBb.GetRotation().RotateVector(ebt[1]);
ebt[2] = m_eb0[2]; RBb.GetRotation().RotateVector(ebt[2]);
ebp[0] = m_eb0[0]; RBb.m_qp.RotateVector(ebp[0]);
ebp[1] = m_eb0[1]; RBb.m_qp.RotateVector(ebp[1]);
ebp[2] = m_eb0[2]; RBb.m_qp.RotateVector(ebp[2]);
eb[0] = ebt[0]*alpha + ebp[0]*(1-alpha);
eb[1] = ebt[1]*alpha + ebp[1]*(1-alpha);
eb[2] = ebt[2]*alpha + ebp[2]*(1-alpha);
c = rb + zb - ra - za;
normF0 = sqrt(m_L*m_L);
// calculate trial multiplier
Lm = m_L + c*m_eps;
normF1 = sqrt(Lm*Lm);
if (m_bq) {
quatd q = (alpha*RBb.GetRotation() + (1 - alpha)*RBb.m_qp)*(alpha*RBa.GetRotation() + (1 - alpha)*RBa.m_qp).Inverse();
quatd a(m_qp,ea[0]);
quatd r = a*q.Inverse();
r.MakeUnit();
ksi = r.GetVector()*r.GetAngle();
}
else
ksi = (ea[0] ^ eb[0])/2;
normM0 = sqrt(m_U*m_U);
// calculate trial multiplier
Um = m_U + ksi*m_ups;
normM1 = sqrt(Um*Um);
// check convergence of constraints
feLog(" rigid connector # %d (revolute joint)\n", m_nID+1);
feLog(" CURRENT REQUIRED\n");
double pctn = 0;
double gap = c.norm();
double qap = ksi.norm();
if (fabs(normF1) > 1e-10) pctn = fabs((normF1 - normF0)/normF1);
if (m_atol) feLog(" force : %15le %15le\n", pctn, m_atol);
else feLog(" force : %15le ***\n", pctn);
if (m_gtol) feLog(" gap : %15le %15le\n", gap, m_gtol);
else feLog(" gap : %15le ***\n", gap);
double qctn = 0;
if (fabs(normM1) > 1e-10) qctn = fabs((normM1 - normM0)/normM1);
if (m_atol) feLog(" moment: %15le %15le\n", qctn, m_atol);
else feLog(" moment: %15le ***\n", qctn);
if (m_qtol) feLog(" angle : %15le %15le\n", qap, m_qtol);
else feLog(" angle : %15le ***\n", qap);
if (m_atol && ((pctn >= m_atol) || (qctn >= m_atol))) bconv = false;
if (m_gtol && (gap >= m_gtol)) bconv = false;
if (m_qtol && (qap >= m_qtol)) bconv = false;
if (naug < m_naugmin ) bconv = false;
if (naug >= m_naugmax) bconv = true;
if (!bconv)
{
// update multipliers
m_L = Lm;
m_U = Um;
}
// auto-penalty update (works only with gaptol and angtol)
if (m_bautopen)
{
if (m_gtol && (gap > m_gtol)) {
m_eps = fmax(gap / m_gtol, 100)*m_eps;
feLog(" force_penalty : %15le\n", m_eps);
}
if (m_qtol && (qap > m_qtol)) {
m_ups = fmax(qap / m_qtol, 100)*m_ups;
feLog(" moment_penalty : %15le\n", m_ups);
}
}
return bconv;
}
//-----------------------------------------------------------------------------
void FERigidRevoluteJoint::Update()
{
if (m_laugon == FECore::LAGMULT_METHOD) return;
vec3d ra, rb;
vec3d za, zb;
vec3d eat[3], eap[3], ea[3];
vec3d ebt[3], ebp[3], eb[3];
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
const FETimeInfo& tp = GetTimeInfo();
double alpha = tp.alphaf;
ra = RBa.m_rt*alpha + RBa.m_rp*(1-alpha);
rb = RBb.m_rt*alpha + RBb.m_rp*(1-alpha);
vec3d zat = m_qa0; RBa.GetRotation().RotateVector(zat);
vec3d zap = m_qa0; RBa.m_qp.RotateVector(zap);
za = zat*alpha + zap*(1-alpha);
eat[0] = m_ea0[0]; RBa.GetRotation().RotateVector(eat[0]);
eat[1] = m_ea0[1]; RBa.GetRotation().RotateVector(eat[1]);
eat[2] = m_ea0[2]; RBa.GetRotation().RotateVector(eat[2]);
eap[0] = m_ea0[0]; RBa.m_qp.RotateVector(eap[0]);
eap[1] = m_ea0[1]; RBa.m_qp.RotateVector(eap[1]);
eap[2] = m_ea0[2]; RBa.m_qp.RotateVector(eap[2]);
ea[0] = eat[0]*alpha + eap[0]*(1-alpha);
ea[1] = eat[1]*alpha + eap[1]*(1-alpha);
ea[2] = eat[2]*alpha + eap[2]*(1-alpha);
vec3d zbt = m_qb0; RBb.GetRotation().RotateVector(zbt);
vec3d zbp = m_qb0; RBb.m_qp.RotateVector(zbp);
zb = zbt*alpha + zbp*(1-alpha);
ebt[0] = m_eb0[0]; RBb.GetRotation().RotateVector(ebt[0]);
ebt[1] = m_eb0[1]; RBb.GetRotation().RotateVector(ebt[1]);
ebt[2] = m_eb0[2]; RBb.GetRotation().RotateVector(ebt[2]);
ebp[0] = m_eb0[0]; RBb.m_qp.RotateVector(ebp[0]);
ebp[1] = m_eb0[1]; RBb.m_qp.RotateVector(ebp[1]);
ebp[2] = m_eb0[2]; RBb.m_qp.RotateVector(ebp[2]);
eb[0] = ebt[0]*alpha + ebp[0]*(1-alpha);
eb[1] = ebt[1]*alpha + ebp[1]*(1-alpha);
eb[2] = ebt[2]*alpha + ebp[2]*(1-alpha);
vec3d c = rb + zb - ra - za;
m_F = m_L + c*m_eps;
vec3d ksi;
if (m_bq) {
quatd q = (alpha*RBb.GetRotation() + (1 - alpha)*RBb.m_qp)*(alpha*RBa.GetRotation() + (1 - alpha)*RBa.m_qp).Inverse();
quatd a(m_qp,ea[0]);
quatd r = a*q.Inverse();
r.MakeUnit();
ksi = r.GetVector()*r.GetAngle();
}
else
ksi = (ea[0] ^ eb[0])/2;
m_M = m_U + ksi*m_ups + ea[0]*m_Mp;
// add damping
if (m_cps > 0) {
// body A
vec3d vat = RBa.m_vt + (RBa.m_wt ^ zat);
vec3d vap = RBa.m_vp + (RBa.m_wp ^ zap);
vec3d va = vat*alpha + vap*(1-alpha);
// body b
vec3d vbt = RBb.m_vt + (RBb.m_wt ^ zbt);
vec3d vbp = RBb.m_vp + (RBb.m_wp ^ zbp);
vec3d vb = vbt*alpha + vbp*(1-alpha);
m_F += (vb - va)*m_cps;
}
if (m_rps > 0) {
// body A
vec3d wa = RBa.m_wt*alpha + RBa.m_wp*(1-alpha);
// body b
vec3d wb = RBb.m_wt*alpha + RBb.m_wp*(1-alpha);
mat3ds P = m_bq ? mat3dd(1) : mat3dd(1) - dyad(ea[0]);
m_M += P*(wb - wa)*m_rps;
}
}
//-----------------------------------------------------------------------------
void FERigidRevoluteJoint::Reset()
{
m_F = vec3d(0,0,0);
m_L = vec3d(0,0,0);
m_M = vec3d(0,0,0);
m_U = vec3d(0,0,0);
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
m_qa0 = m_q0 - RBa.m_r0;
m_qb0 = m_q0 - RBb.m_r0;
m_ea0[0] = m_e0[0]; m_ea0[1] = m_e0[1]; m_ea0[2] = m_e0[2];
m_eb0[0] = m_e0[0]; m_eb0[1] = m_e0[1]; m_eb0[2] = m_e0[2];
}
//-----------------------------------------------------------------------------
vec3d FERigidRevoluteJoint::RelativeTranslation(const bool global)
{
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
// body A
vec3d ra = RBa.m_rt;
vec3d za = m_qa0; RBa.GetRotation().RotateVector(za);
// body B
vec3d rb = RBb.m_rt;
vec3d zb = m_qb0; RBb.GetRotation().RotateVector(zb);
// relative translation in global coordinate system
vec3d x = rb + zb - ra - za;
if (global) return x;
// evaluate local basis for body A
vec3d ea[3];
ea[0] = m_ea0[0]; RBa.GetRotation().RotateVector(ea[0]);
ea[1] = m_ea0[1]; RBa.GetRotation().RotateVector(ea[1]);
ea[2] = m_ea0[2]; RBa.GetRotation().RotateVector(ea[2]);
// project relative translation onto local basis
vec3d y(x*ea[0], x*ea[1], x*ea[2]);
return y;
}
//-----------------------------------------------------------------------------
vec3d FERigidRevoluteJoint::RelativeRotation(const bool global)
{
FERigidBody& RBa = *m_rbA;
FERigidBody& RBb = *m_rbB;
// get relative rotation
quatd Q = RBb.GetRotation()*RBa.GetRotation().Inverse(); Q.MakeUnit();
// relative rotation vector
vec3d q = Q.GetRotationVector();
if (global) return q;
// evaluate local basis for body A
vec3d ea[3];
ea[0] = m_ea0[0]; RBa.GetRotation().RotateVector(ea[0]);
ea[1] = m_ea0[1]; RBa.GetRotation().RotateVector(ea[1]);
ea[2] = m_ea0[2]; RBa.GetRotation().RotateVector(ea[2]);
// project relative rotation onto local basis
vec3d y(q*ea[0], q*ea[1], q*ea[2]);
return y;
}
// allocate equations
int FERigidRevoluteJoint::InitEquations(int neq)
{
const int LMeq = 6;
m_LM.resize(LMeq, -1);
if (m_laugon == FECore::LAGMULT_METHOD)
{
for (int i = 0; i < LMeq; ++i) m_LM[i] = neq + i;
return LMeq;
}
else return 0;
}
// Build the matrix profile
void FERigidRevoluteJoint::BuildMatrixProfile(FEGlobalMatrix& M)
{
vector<int> lm;
UnpackLM(lm);
// add it to the pile
M.build_add(lm);
}
void FERigidRevoluteJoint::UnpackLM(vector<int>& lm)
{
// add the dofs of rigid body A
lm.resize(21);
lm[0] = m_rbA->m_LM[0];
lm[1] = m_rbA->m_LM[1];
lm[2] = m_rbA->m_LM[2];
lm[3] = m_rbA->m_LM[3];
lm[4] = m_rbA->m_LM[4];
lm[5] = m_rbA->m_LM[5];
// add the dofs of rigid body B
lm[ 6] = m_rbB->m_LM[0];
lm[ 7] = m_rbB->m_LM[1];
lm[ 8] = m_rbB->m_LM[2];
lm[ 9] = m_rbB->m_LM[3];
lm[10] = m_rbB->m_LM[4];
lm[11] = m_rbB->m_LM[5];
// add the LM equations
if (m_laugon == FECore::LAGMULT_METHOD)
{
for (int i = 0; i < m_LM.size(); ++i) lm[12 + i] = m_LM[i];
}
}
void FERigidRevoluteJoint::PrepStep()
{
m_Fp = m_F;
m_Up = m_M;
}
void FERigidRevoluteJoint::Update(const std::vector<double>& Ui, const std::vector<double>& ui)
{
if (m_laugon == FECore::LAGMULT_METHOD)
{
m_F.x = m_Fp.x + Ui[m_LM[0]] + ui[m_LM[0]];
m_F.y = m_Fp.y + Ui[m_LM[1]] + ui[m_LM[1]];
m_F.z = m_Fp.z + Ui[m_LM[2]] + ui[m_LM[2]];
m_M.x = m_Up.x + Ui[m_LM[3]] + ui[m_LM[3]];
m_M.y = m_Up.y + Ui[m_LM[4]] + ui[m_LM[4]];
m_M.z = m_Up.z + Ui[m_LM[5]] + ui[m_LM[5]];
}
}
void FERigidRevoluteJoint::UpdateIncrements(std::vector<double>& Ui, const std::vector<double>& ui)
{
if (m_laugon == FECore::LAGMULT_METHOD)
{
Ui[m_LM[0]] += ui[m_LM[0]];
Ui[m_LM[1]] += ui[m_LM[1]];
Ui[m_LM[2]] += ui[m_LM[2]];
Ui[m_LM[3]] += ui[m_LM[3]];
Ui[m_LM[4]] += ui[m_LM[4]];
Ui[m_LM[5]] += ui[m_LM[5]];
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FESolidMaterial.cpp | .cpp | 6,257 | 186 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FESolidMaterial.h"
#include "FEElasticMaterial.h"
// Material parameters for FEElasticMaterial
BEGIN_FECORE_CLASS(FESolidMaterial, FEMaterial)
ADD_PARAMETER(m_density, "density")->setUnits(UNIT_DENSITY)->MakeTopLevel(true);
END_FECORE_CLASS();
FESolidMaterial::FESolidMaterial(FEModel* pfem) : FEMaterial(pfem)
{
m_density = 1.0;
}
//! set the material density
void FESolidMaterial::SetDensity(const double d)
{
m_density = d;
}
//! evaluate density
double FESolidMaterial::Density(FEMaterialPoint& pt)
{
return m_density(pt);
}
tens4dmm FESolidMaterial::SolidTangent(FEMaterialPoint& mp)
{
return (UseSecantTangent() ? SecantTangent(mp) : Tangent(mp));
}
//-----------------------------------------------------------------------------
mat3ds FESolidMaterial::SecantStress(FEMaterialPoint& pt, bool PK2)
{
assert(false);
return mat3ds(0.0);
}
//-----------------------------------------------------------------------------
//! calculate the 2nd Piola-Kirchhoff stress at material point, using prescribed Lagrange strain
//! needed for EAS analyses where the compatible strain (calculated from displacements) is enhanced
mat3ds FESolidMaterial::PK2Stress(FEMaterialPoint& mp, const mat3ds E)
{
// Evaluate right Cauchy-Green tensor from E
mat3ds C = mat3dd(1) + E*2;
// Evaluate right stretch tensor U from C
vec3d v[3];
double lam[3];
C.eigen2(lam, v);
lam[0] = sqrt(lam[0]); lam[1] = sqrt(lam[1]); lam[2] = sqrt(lam[2]);
mat3ds U = dyad(v[0])*lam[0] + dyad(v[1])*lam[1] + dyad(v[2])*lam[2];
double J = lam[0]*lam[1]*lam[2];
// temporarily replace F in material point with U
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d Fsafe = pt.m_F;
double Jsafe = pt.m_J;
pt.m_F = U;
pt.m_J = J;
// Evaluate Cauchy stress
mat3ds s = Stress(mp);
// Restore original F
pt.m_F = Fsafe;
pt.m_J = Jsafe;
// Convert Cauchy stress to 2nd P-K stress
mat3ds Ui = dyad(v[0])/lam[0] + dyad(v[1])/lam[1] + dyad(v[2])/lam[2];
mat3ds S = (Ui*s*Ui).sym()*J;
return S;
}
//-----------------------------------------------------------------------------
//! calculate material tangent stiffness at material point, using prescribed Lagrange strain
//! needed for EAS analyses where the compatible strain (calculated from displacements) is enhanced
tens4dmm FESolidMaterial::MaterialTangent(FEMaterialPoint& mp, const mat3ds E)
{
// Evaluate right Cauchy-Green tensor from E
mat3ds C = mat3dd(1) + E*2;
// Evaluate right stretch tensor U from C
vec3d v[3];
double lam[3];
C.eigen2(lam, v);
lam[0] = sqrt(lam[0]); lam[1] = sqrt(lam[1]); lam[2] = sqrt(lam[2]);
mat3d U = dyad(v[0])*lam[0] + dyad(v[1])*lam[1] + dyad(v[2])*lam[2];
double J = lam[0]*lam[1]*lam[2];
// temporarily replace F in material point with U
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d Fsafe = pt.m_F;
double Jsafe = pt.m_J;
pt.m_F = U;
pt.m_J = J;
// Evaluate Cauchy stress
tens4dmm c = SolidTangent(mp);
// Restore original F
pt.m_F = Fsafe;
pt.m_J = Jsafe;
// Convert spatial tangent to material tangent
mat3d Ui = dyad(v[0])/lam[0] + dyad(v[1])/lam[1] + dyad(v[2])/lam[2];
tens4dmm Cm = c.pp(Ui)*J;
return Cm;
}
//-----------------------------------------------------------------------------
//! calculate spatial tangent stiffness at material point, using secant method
tens4dmm FESolidMaterial::SecantTangent(FEMaterialPoint& mp, bool mat)
{
// extract the deformation gradient
FEElasticMaterialPoint& pt = *mp.ExtractData<FEElasticMaterialPoint>();
mat3d F = pt.m_F;
double J = pt.m_J;
mat3ds E = pt.Strain();
mat3dd I(1);
// calculate the 2nd P-K stress at the current deformation gradient
mat3ds S = PK2Stress(mp,E);
// create deformation gradient increment
double eps = 1e-9;
vec3d e[3];
e[0] = vec3d(1,0,0); e[1] = vec3d(0,1,0); e[2] = vec3d(0,0,1);
tens4dmm C;
for (int k=0; k<3; ++k) {
for (int l=k; l<3; ++l) {
// evaluate incremental stress
mat3ds dE = dyads(e[k], e[l])*(eps/2);
mat3ds dS = (PK2Stress(mp,E+dE) - S)/eps;
// evaluate the secant modulus
C(0,0,k,l) = C(0,0,l,k) = dS.xx();
C(1,1,k,l) = C(1,1,l,k) = dS.yy();
C(2,2,k,l) = C(2,2,l,k) = dS.zz();
C(0,1,k,l) = C(1,0,k,l) = C(0,1,l,k) = C(1,0,l,k) = dS.xy();
C(1,2,k,l) = C(2,1,k,l) = C(1,2,l,k) = C(2,1,l,k) = dS.yz();
C(2,0,k,l) = C(0,2,k,l) = C(2,0,l,k) = C(0,2,l,k) = dS.xz();
}
}
if (mat) return C;
else {
// push from material to spatial frame
tens4dmm c = C.pp(F)/J;
// return secant tangent
return c;
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioMech/FEEFDMooneyRivlin.cpp | .cpp | 2,841 | 74 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEEFDMooneyRivlin.h"
// define the material parameters
BEGIN_FECORE_CLASS(FEEFDMooneyRivlin, FEUncoupledMaterial)
ADD_PARAMETER(m_MR.m_c1, "c1")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_MR.m_c2, "c2")->setUnits(UNIT_PRESSURE);
ADD_PARAMETER(m_EFD.m_beta, 3, "beta");
ADD_PARAMETER(m_EFD.m_ksi , 3, "ksi" )->setUnits(UNIT_PRESSURE);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEEFDMooneyRivlin::FEEFDMooneyRivlin(FEModel* pfem) : FEUncoupledMaterial(pfem), m_EFD(pfem), m_MR(pfem)
{
m_EFD.SetParent(this);
m_MR.SetParent(this);
}
//-----------------------------------------------------------------------------
bool FEEFDMooneyRivlin::Init()
{
if (FEUncoupledMaterial::Init() == false) return false;
if (m_MR.Init() == false) return false;
if (m_EFD.Init() == false) return false;
return true;
}
//-----------------------------------------------------------------------------
mat3ds FEEFDMooneyRivlin::DevStress(FEMaterialPoint& pt)
{
return m_MR.DevStress(pt) + m_EFD.DevStress(pt);
}
//-----------------------------------------------------------------------------
tens4ds FEEFDMooneyRivlin::DevTangent(FEMaterialPoint& pt)
{
return m_MR.DevTangent(pt) + m_EFD.DevTangent(pt);
}
//-----------------------------------------------------------------------------
//! calculate deviatoric strain energy density
double FEEFDMooneyRivlin::DevStrainEnergyDensity(FEMaterialPoint& pt)
{
return m_MR.DevStrainEnergyDensity(pt) + m_EFD.DevStrainEnergyDensity(pt);
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidDomain3D.cpp | .cpp | 24,396 | 786 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFluidDomain3D.h"
#include "FEFluidSolver.h"
#include "FECore/log.h"
#include "FECore/DOFS.h"
#include <FECore/FEModel.h>
#include <FECore/FEAnalysis.h>
#include <FECore/sys.h>
#include "FEBioFluid.h"
#include <FECore/FELinearSystem.h>
//-----------------------------------------------------------------------------
//! constructor
//! Some derived classes will pass 0 to the pmat, since the pmat variable will be
//! to initialize another material. These derived classes will set the m_pMat variable as well.
FEFluidDomain3D::FEFluidDomain3D(FEModel* pfem) : FESolidDomain(pfem), FEFluidDomain(pfem), m_dofW(pfem), m_dofAW(pfem), m_dof(pfem)
{
m_pMat = 0;
m_btrans = true;
if (pfem)
{
m_dofW.AddVariable(FEBioFluid::GetVariableName(FEBioFluid::RELATIVE_FLUID_VELOCITY));
m_dofAW.AddVariable(FEBioFluid::GetVariableName(FEBioFluid::RELATIVE_FLUID_ACCELERATION));
m_dofEF = pfem->GetDOFIndex(FEBioFluid::GetVariableName(FEBioFluid::FLUID_DILATATION), 0);
m_dofAEF = pfem->GetDOFIndex(FEBioFluid::GetVariableName(FEBioFluid::FLUID_DILATATION_TDERIV), 0);
FEDofList dofs(pfem);
dofs.AddDofs(m_dofW);
dofs.AddDof(m_dofEF);
m_dof = dofs;
}
}
//-----------------------------------------------------------------------------
// \todo I don't think this is being used
FEFluidDomain3D& FEFluidDomain3D::operator = (FEFluidDomain3D& d)
{
m_Elem = d.m_Elem;
m_pMesh = d.m_pMesh;
return (*this);
}
//-----------------------------------------------------------------------------
//! serialize data to archive
void FEFluidDomain3D::Serialize(DumpStream& ar)
{
FESolidDomain::Serialize(ar);
if (ar.IsShallow()) return;
ar & m_dofW & m_dofAW & m_dof;
ar & m_dofEF & m_dofAEF;
ar & m_pMat;
}
//-----------------------------------------------------------------------------
// get total dof list
const FEDofList& FEFluidDomain3D::GetDOFList() const
{
return m_dof;
}
//-----------------------------------------------------------------------------
//! Assign material
void FEFluidDomain3D::SetMaterial(FEMaterial* pmat)
{
FEDomain::SetMaterial(pmat);
if (pmat)
{
m_pMat = dynamic_cast<FEFluid*>(pmat);
assert(m_pMat);
}
else m_pMat = 0;
}
//-----------------------------------------------------------------------------
//! Initialize element data
void FEFluidDomain3D::PreSolveUpdate(const FETimeInfo& timeInfo)
{
const int NE = FEElement::MAX_NODES;
vec3d x0[NE], r0, v;
FEMesh& m = *GetMesh();
for (size_t i=0; i<m_Elem.size(); ++i)
{
FESolidElement& el = m_Elem[i];
int neln = el.Nodes();
for (int i=0; i<neln; ++i)
{
x0[i] = m.Node(el.m_node[i]).m_r0;
}
int n = el.GaussPoints();
for (int j=0; j<n; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
pt.m_r0 = el.Evaluate(x0, j);
mp.m_rt = mp.m_r0;
if (pt.m_ef <= -1) {
throw NegativeJacobianDetected();
}
mp.Update(timeInfo);
}
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::InternalForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i=0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 4*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInternalForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the internal equivalent nodal forces for solid elements
void FEFluidDomain3D::ElementInternalForce(FESolidElement& el, vector<double>& fe)
{
int i, n;
// jacobian matrix, inverse jacobian matrix and determinants
double Ji[3][3], detJ;
mat3ds sv;
vec3d gradp;
const double *H, *Gr, *Gs, *Gt;
int nint = el.GaussPoints();
int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double* gw = el.GaussWeights();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
// calculate the jacobian
detJ = invjac0(el, Ji, n)*gw[n];
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
// get the viscous stress tensor for this integration point
sv = m_pMat->GetViscous()->Stress(mp);
// get the gradient of the elastic pressure
gradp = pt.m_gradef*m_pMat->Tangent_Pressure_Strain(mp);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
{
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
}
// Jdot/J
double dJoJ = pt.m_efdot/(pt.m_ef+1);
for (i=0; i<neln; ++i)
{
vec3d fs = sv*gradN[i] + gradp*H[i];
double fJ = dJoJ*H[i] + gradN[i]*pt.m_vft;
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[4*i ] -= fs.x*detJ;
fe[4*i+1] -= fs.y*detJ;
fe[4*i+2] -= fs.z*detJ;
fe[4*i+3] -= fJ*detJ;
}
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::BodyForce(FEGlobalVector& R, FEBodyForce& BF)
{
int NE = (int)m_Elem.size();
for (int i=0; i<NE; ++i)
{
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 4*el.Nodes();
fe.assign(ndof, 0);
// apply body forces
ElementBodyForce(BF, el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the body forces
void FEFluidDomain3D::ElementBodyForce(FEBodyForce& BF, FESolidElement& el, vector<double>& fe)
{
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d f;
// number of nodes
int neln = el.Nodes();
// nodal coordinates
vec3d r0[FEElement::MAX_NODES];
for (int i=0; i<neln; ++i)
r0[i] = m_pMesh->Node(el.m_node[i]).m_r0;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
double dens = m_pMat->Density(mp);
pt.m_r0 = el.Evaluate(r0, n);
detJ = detJ0(el, n)*gw[n];
// get the force
f = BF.force(mp);
H = el.H(n);
for (int i=0; i<neln; ++i)
{
fe[4*i ] -= H[i]*dens*f.x*detJ;
fe[4*i+1] -= H[i]*dens*f.y*detJ;
fe[4*i+2] -= H[i]*dens*f.z*detJ;
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the stiffness due to body forces
void FEFluidDomain3D::ElementBodyForceStiffness(FEBodyForce& BF, FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int neln = el.Nodes();
int ndof = ke.columns()/neln;
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d f, k;
mat3d K, Kvv;
// gradient of shape functions
vec3d gradN;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
// calculate the jacobian
detJ = detJ0(el, n)*gw[n]*tp.alphaf;
H = el.H(n);
double dens = m_pMat->Density(mp);
// get the force
f = BF.force(mp);
K = BF.stiffness(mp);
H = el.H(n);
for (int i=0; i<neln; ++i) {
for (int j=0; j<neln; ++j)
{
k = f*(-H[i]*H[j]*dens/(pt.m_ef+1)*detJ);
Kvv = K*(H[i]*H[j]*dens*detJ);
ke[ndof*i ][ndof*j ] += Kvv(0,0); ke[ndof*i ][ndof*j+1] += Kvv(0,1); ke[ndof*i ][ndof*j+2] += Kvv(0,2);
ke[ndof*i+1][ndof*j ] += Kvv(1,0); ke[ndof*i+1][ndof*j+1] += Kvv(1,1); ke[ndof*i+1][ndof*j+2] += Kvv(1,2);
ke[ndof*i+2][ndof*j ] += Kvv(2,0); ke[ndof*i+2][ndof*j+1] += Kvv(2,1); ke[ndof*i+2][ndof*j+2] += Kvv(2,2);
ke[ndof*i ][ndof*j+3] += k.x;
ke[ndof*i+1][ndof*j+3] += k.y;
ke[ndof*i+2][ndof*j+3] += k.z;
}
}
}
}
//-----------------------------------------------------------------------------
//! Calculates element material stiffness element matrix
void FEFluidDomain3D::ElementStiffness(FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i4, j, j4, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double dt = tp.timeIncrement;
double ksi = tp.alpham/(tp.gamma*tp.alphaf);
double *H, *Gr, *Gs, *Gt;
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjac0(el, Ji, n)*gw[n]*tp.alphaf;
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
double Jf = 1 + pt.m_ef;
// get the tangents
mat3ds svJ = m_pMat->GetViscous()->Tangent_Strain(mp);
tens4ds cv = m_pMat->Tangent_RateOfDeformation(mp);
double dp = m_pMat->Tangent_Pressure_Strain(mp);
double d2p = m_pMat->Tangent_Pressure_Strain_Strain(mp);
// Jdot/J
double dJoJ = pt.m_efdot/Jf;
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate stiffness matrix
for (i=0, i4=0; i<neln; ++i, i4 += 4)
{
for (j=0, j4 = 0; j<neln; ++j, j4 += 4)
{
mat3d Kvv = vdotTdotv(gradN[i], cv, gradN[j]);
vec3d kJv = (pt.m_gradef*(H[i]/Jf) + gradN[i])*H[j];
vec3d kvJ = (svJ*gradN[i])*H[j] + (gradN[j]*dp+pt.m_gradef*(H[j]*d2p))*H[i];
double kJJ = (H[j]*(ksi/dt - dJoJ) + gradN[j]*pt.m_vft)*H[i]/Jf;
ke[i4 ][j4 ] += Kvv(0,0)*detJ;
ke[i4 ][j4+1] += Kvv(0,1)*detJ;
ke[i4 ][j4+2] += Kvv(0,2)*detJ;
ke[i4 ][j4+3] += kvJ.x*detJ;
ke[i4+1][j4 ] += Kvv(1,0)*detJ;
ke[i4+1][j4+1] += Kvv(1,1)*detJ;
ke[i4+1][j4+2] += Kvv(1,2)*detJ;
ke[i4+1][j4+3] += kvJ.y*detJ;
ke[i4+2][j4 ] += Kvv(2,0)*detJ;
ke[i4+2][j4+1] += Kvv(2,1)*detJ;
ke[i4+2][j4+2] += Kvv(2,2)*detJ;
ke[i4+2][j4+3] += kvJ.z*detJ;
ke[i4+3][j4 ] += kJv.x*detJ;
ke[i4+3][j4+1] += kJv.y*detJ;
ke[i4+3][j4+2] += kJv.z*detJ;
ke[i4+3][j4+3] += kJJ*detJ;
}
}
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::StiffnessMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 4*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate material stiffness
ElementStiffness(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::MassMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared(NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 4*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementMassMatrix(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 4*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementBodyForceStiffness(bf, el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
//! calculates element inertial stiffness matrix
void FEFluidDomain3D::ElementMassMatrix(FESolidElement& el, matrix& ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i4, j, j4, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double *H;
double *Gr, *Gs, *Gt;
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
double dt = tp.timeIncrement;
double ksi = tp.alpham/(tp.gamma*tp.alphaf)*m_btrans;
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjac0(el, Ji, n)*gw[n]*tp.alphaf;
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
double dens = m_pMat->Density(mp);
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate stiffness matrix
for (i=0, i4=0; i<neln; ++i, i4 += 4)
{
for (j=0, j4 = 0; j<neln; ++j, j4 += 4)
{
mat3d Mv = ((mat3dd(ksi/dt) + pt.m_Lf)*H[j] + mat3dd(gradN[j]*pt.m_vft))*(H[i]*dens*detJ);
vec3d mJ = pt.m_aft*(-H[i]*H[j]*dens/(pt.m_ef+1)*detJ);
ke[i4 ][j4 ] += Mv(0,0);
ke[i4 ][j4+1] += Mv(0,1);
ke[i4 ][j4+2] += Mv(0,2);
ke[i4 ][j4+3] += mJ.x;
ke[i4+1][j4 ] += Mv(1,0);
ke[i4+1][j4+1] += Mv(1,1);
ke[i4+1][j4+2] += Mv(1,2);
ke[i4+1][j4+3] += mJ.y;
ke[i4+2][j4 ] += Mv(2,0);
ke[i4+2][j4+1] += Mv(2,1);
ke[i4+2][j4+2] += Mv(2,2);
ke[i4+2][j4+3] += mJ.z;
}
}
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::Update(const FETimeInfo& tp)
{
bool berr = false;
int NE = (int) m_Elem.size();
#pragma omp parallel for shared(NE, berr)
for (int i=0; i<NE; ++i)
{
try
{
UpdateElementStress(i, tp);
}
catch (NegativeJacobian e)
{
#pragma omp critical
{
// reset the logfile mode
berr = true;
if (NegativeJacobian::DoOutput()) feLogError(e.what());
}
}
}
if (berr) throw NegativeJacobianDetected();
}
//-----------------------------------------------------------------------------
//! Update element state data (mostly stresses, but some other stuff as well)
void FEFluidDomain3D::UpdateElementStress(int iel, const FETimeInfo& tp)
{
double alphaf = tp.alphaf;
double alpham = tp.alpham;
// get the solid element
FESolidElement& el = m_Elem[iel];
// get the number of integration points
int nint = el.GaussPoints();
// number of nodes
int neln = el.Nodes();
// nodal coordinates
const int NELN = FEElement::MAX_NODES;
vec3d vt[NELN], vp[NELN];
vec3d at[NELN], ap[NELN];
double et[NELN], ep[NELN];
double aet[NELN], aep[NELN];
for (int j=0; j<neln; ++j) {
FENode& node = m_pMesh->Node(el.m_node[j]);
vt[j] = node.get_vec3d(m_dofW[0], m_dofW[1], m_dofW[2]);
vp[j] = node.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2]);
at[j] = node.get_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
ap[j] = node.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
et[j] = node.get(m_dofEF);
ep[j] = node.get_prev(m_dofEF);
aet[j] = node.get(m_dofAEF);
aep[j] = node.get_prev(m_dofAEF);
}
// loop over the integration points and update
// velocity, velocity gradient, acceleration
// stress and pressure at the integration point
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
// material point data
pt.m_vft = el.Evaluate(vt, n)*alphaf + el.Evaluate(vp, n)*(1-alphaf);
pt.m_Lf = gradient(el, vt, n)*alphaf + gradient(el, vp, n)*(1-alphaf);
pt.m_aft = pt.m_Lf*pt.m_vft;
if (m_btrans) pt.m_aft += el.Evaluate(at, n)*alpham + el.Evaluate(ap, n)*(1-alpham);
pt.m_ef = el.Evaluate(et, n)*alphaf + el.Evaluate(ep, n)*(1-alphaf);
pt.m_gradef = gradient(el, et, n)*alphaf + gradient(el, ep, n)*(1-alphaf);
pt.m_efdot = pt.m_gradef*pt.m_vft;
if (m_btrans) pt.m_efdot += el.Evaluate(aet, n)*alpham + el.Evaluate(aep, n)*(1-alpham);
// calculate the stress at this material point
pt.m_sf = m_pMat->Stress(mp);
// calculate the fluid pressure
pt.m_pf = m_pMat->Pressure(mp);
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::InertialForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared(NE)
for (int i=0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 4*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInertialForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
void FEFluidDomain3D::ElementInertialForce(FESolidElement& el, vector<double>& fe)
{
int i, n;
// jacobian determinant
double detJ;
const double* H;
int nint = el.GaussPoints();
int neln = el.Nodes();
double* gw = el.GaussWeights();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
double dens = m_pMat->Density(mp);
// calculate the jacobian
detJ = detJ0(el, n)*gw[n];
H = el.H(n);
for (i=0; i<neln; ++i)
{
vec3d f = pt.m_aft*(dens*H[i]);
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[4*i ] -= f.x*detJ;
fe[4*i+1] -= f.y*detJ;
fe[4*i+2] -= f.z*detJ;
}
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidSolutes.h | .h | 7,536 | 177 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FEBioMech/FEElasticMaterial.h>
#include "FEFluid.h"
#include <FEBioMix/FESolute.h>
#include <FEBioMix/FESoluteInterface.h>
#include <FEBioMix/FEOsmoticCoefficient.h>
#include <FEBioMix/FEChemicalReaction.h>
#include <FECore/FEModelParam.h>
//-----------------------------------------------------------------------------
//! FSI material point class.
//
class FEBIOFLUID_API FEFluidSolutesMaterialPoint : public FEMaterialPointData
{
public:
//! constructor
FEFluidSolutesMaterialPoint(FEMaterialPointData* pt);
//! create a shallow copy
FEMaterialPointData* Copy();
//! data serialization
void Serialize(DumpStream& ar);
//! Data initialization
void Init();
public:
double Osmolarity() const;
public:
// solutes material data
int m_nsol; //!< number of solutes
vector<double> m_c; //!< effective solute concentration
vector<double> m_ca; //!< actual solute concentration
vector<vec3d> m_gradc; //!< spatial gradient of solute concentration
vector<vec3d> m_j; //!< solute molar flux
vector<double> m_cdot; //!< material time derivative of solute concentration following fluid
double m_psi; //!< electric potential
vec3d m_Ie; //!< current density
double m_pe; //!< effective fluid pressure
vector<double> m_k; //!< solute partition coefficient
vector<double> m_dkdJ; //!< 1st deriv of m_k with strain (J)
vector<double> m_dkdJJ; //!< 2nd deriv of m_k with strain (J)
vector< vector<double> > m_dkdc; //!< 1st deriv of m_k with effective concentration
vector< vector<double> > m_dkdJc; //!< cross deriv of m_k with J and c
vector< vector< vector<double> > > m_dkdcc; // 2nd deriv of m_k with c
};
//-----------------------------------------------------------------------------
//! Base class for FluidFSI materials.
class FEBIOFLUID_API FEFluidSolutes : public FEMaterial, public FESoluteInterface_T<FEFluidSolutesMaterialPoint>
{
public:
FEFluidSolutes(FEModel* pfem);
// returns a pointer to a new material point object
FEMaterialPointData* CreateMaterialPointData() override;
//! performs initialization
bool Init() override;
//! Serialization
void Serialize(DumpStream& ar) override;
public:
FEFluid* Fluid() { return m_pFluid; }
//! calculate solute molar flux
vec3d SoluteFlux(const FEMaterialPoint& pt, const int sol);
//! calculate diffusive solute molar flux
vec3d SoluteDiffusiveFlux(const FEMaterialPoint& pt, const int sol);
//! actual concentration (as opposed to effective concentration)
double ConcentrationActual(const FEMaterialPoint& pt, const int sol);
//! actual fluid pressure (as opposed to effective pressure)
double PressureActual(const FEMaterialPoint& pt);
//! partition coefficient
double PartitionCoefficient(const FEMaterialPoint& pt, const int sol);
//! partition coefficients and their derivatives
void PartitionCoefficientFunctions(const FEMaterialPoint& mp, vector<double>& kappa,
vector<double>& dkdJ,
vector< vector<double> >& dkdc);
//! electric potential
double ElectricPotential(const FEMaterialPoint& pt, const bool eform=false);
//! current density
vec3d CurrentDensity(const FEMaterialPoint& pt);
//! solute density
double SoluteDensity(const int sol) { return m_pSolute[sol]->Density(); }
//! solute molar mass
double SoluteMolarMass(const int sol) { return m_pSolute[sol]->MolarMass(); }
//! solute charge number
int SoluteChargeNumber(const int sol) { return m_pSolute[sol]->ChargeNumber(); }
//! Add a chemical reaction
void AddChemicalReaction(FEChemicalReaction* pcr);
// solute interface
public:
typedef FEFluidSolutesMaterialPoint SoluteMaterialPoint_t;
int Solutes() override { return (int)m_pSolute.size(); }
FESolute* GetSolute(int i) override { return m_pSolute[i]; }
FEOsmoticCoefficient* GetOsmoticCoefficient() override { return m_pOsmC; }
double GetEffectiveSoluteConcentration(FEMaterialPoint& mp, int soluteIndex) override;
double GetActualSoluteConcentration(FEMaterialPoint& mp, int soluteIndex) override { return ConcentrationActual(mp, soluteIndex); }
double GetFreeDiffusivity(FEMaterialPoint& mp, int soluteIndex) override;
double GetPartitionCoefficient(FEMaterialPoint& mp, int soluteIndex) override;
vec3d GetSoluteFlux(FEMaterialPoint& mp, int soluteIndex) override { return SoluteFlux(mp, soluteIndex); }
double GetOsmolarity(const FEMaterialPoint& mp) override;
double GetElectricPotential(const FEMaterialPoint& mp) override { return ElectricPotential(mp); }
vec3d GetCurrentDensity(const FEMaterialPoint& mp) override { return CurrentDensity(mp); }
double dkdc(const FEMaterialPoint& mp, int i, int j) override;
public:
FEChemicalReaction* GetReaction (int i) { return m_pReact[i]; }
int Reactions () { return (int) m_pReact.size(); }
public:
double m_Rgas; //!< universal gas constant
double m_Tabs; //!< absolute temperature
double m_Fc; //!< Faraday's constant
bool m_diffMtmSupp; //!< Toggle on or off diffusive mtm supply for fluid
int m_zmin; //!< minimum charge number in mixture
int m_ndeg; //!< polynomial degree of zeta in electroneutrality
double m_penalty; //!< penalty for enforcing electroneutrality
private: // material properties
FEFluid* m_pFluid; //!< pointer to fluid material
std::vector<FESolute*> m_pSolute; //!< pointer to solute materials
FEOsmoticCoefficient* m_pOsmC; //!< pointer to osmotic coefficient material
std::vector<FEChemicalReaction*> m_pReact; //!< pointer to chemical reactions
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidSolutesDomainFactory.h | .h | 1,614 | 39 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FECoreKernel.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
class FEBIOFLUID_API FEFluidSolutesDomainFactory : public FEDomainFactory
{
public:
virtual FEDomain* CreateDomain(const FE_Element_Spec& spec, FEMesh* pm, FEMaterial* pmat);
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEMultiphasicFSIPressure.h | .h | 1,260 | 53 | //
// FEFluidSolutesPressure.hpp
// FEBioFluid
//
// Created by Jay Shim on 12/10/20.
// Copyright © 2020 febio.org. All rights reserved.
//
#pragma once
#include <FECore/FESurfaceLoad.h>
#include "FEMultiphasicFSI.h"
//-----------------------------------------------------------------------------
//! FEFluidResistanceBC is a fluid surface that has a normal
//! pressure proportional to the flow rate (resistance).
//!
class FEBIOFLUID_API FEMultiphasicFSIPressure : public FESurfaceLoad
{
public:
//! constructor
FEMultiphasicFSIPressure(FEModel* pfem);
//! calculate traction stiffness (there is none)
void StiffnessMatrix(FELinearSystem& LS) override {}
//! calculate load vector
void LoadVector(FEGlobalVector& R) override;
//! set the dilatation
void Update() override;
//! initialize
bool Init() override;
//! activate
void Activate() override;
//! serialization
void Serialize(DumpStream& ar) override;
private:
double m_p; //!< prescribed fluid pressure
private:
FEMultiphasicFSI* m_pfs; //!< pointer to fluid-solutes material
int m_dofEF;
int m_dofC;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEBiphasicFSIDomain.h | .h | 3,202 | 81 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "febiofluid_api.h"
#include <vector>
class FEModel;
class FELinearSystem;
class FEBodyForce;
class FEGlobalVector;
class FETimeInfo;
//-----------------------------------------------------------------------------
//! Abstract interface class for fluid-FSI domains.
//! A fluid-FSI domain is used by the fluid-FSI solver.
//! This interface defines the functions that have to be implemented by a
//! fluid-FSI domain. There are basically two categories: residual functions
//! that contribute to the global residual vector. And stiffness matrix
//! function that calculate contributions to the global stiffness matrix.
class FEBIOFLUID_API FEBiphasicFSIDomain
{
public:
FEBiphasicFSIDomain(FEModel* pfem);
virtual ~FEBiphasicFSIDomain(){}
// --- R E S I D U A L ---
//! calculate the internal forces
virtual void InternalForces(FEGlobalVector& R) = 0;
//! Calculate the body force vector
virtual void BodyForce(FEGlobalVector& R, FEBodyForce& bf) = 0;
//! calculate the interial forces (for dynamic problems)
virtual void InertialForces(FEGlobalVector& R) = 0;
// --- S T I F F N E S S M A T R I X ---
//! Calculate global stiffness matrix (only contribution from internal force derivative)
//! \todo maybe I should rename this the InternalStiffness matrix?
virtual void StiffnessMatrix (FELinearSystem& LS) = 0;
//! Calculate stiffness contribution of body forces
virtual void BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf) = 0;
//! calculate the mass matrix (for dynamic problems)
virtual void MassMatrix(FELinearSystem& LS) = 0;
//! transient analysis
void SetTransientAnalysis() { m_btrans = true; }
void SetSteadyStateAnalysis() { m_btrans = false; }
protected:
bool m_btrans; // flag for transient (true) or steady-state (false) analysis
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEThermoFluidAnalysis.cpp | .cpp | 1,692 | 38 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "FEThermoFluidAnalysis.h"
BEGIN_FECORE_CLASS(FEThermoFluidAnalysis, FEAnalysis)
// The analysis parameter is already defined in the FEAnalysis base class.
// Here, we just need to set the enum values for the analysis parameter.
FindParameterFromData(&m_nanalysis)->setEnums("STEADY-STATE\0DYNAMIC\0");
END_FECORE_CLASS()
FEThermoFluidAnalysis::FEThermoFluidAnalysis(FEModel* fem) : FEAnalysis(fem)
{
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FECentrifugalFluidBodyForce.h | .h | 1,944 | 55 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEMaterialPoint.h>
#include <FEBioMech/FEBodyForce.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! This class defines a centrigufal force
class FEBIOFLUID_API FECentrifugalFluidBodyForce : public FEBodyForce
{
public:
FECentrifugalFluidBodyForce(FEModel* pfem);
vec3d force(FEMaterialPoint& mp) override;
double divforce(FEMaterialPoint& mp) override;
mat3d stiffness(FEMaterialPoint& mp) override;
public:
vec3d n; // rotation axis
vec3d c; // point on axis of rotation (e.g., center of rotation)
double w; // angular speed
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidFSIAnalysis.h | .h | 1,549 | 43 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEAnalysis.h>
#include "febiofluid_api.h"
class FEBIOFLUID_API FEFluidFSIAnalysis : public FEAnalysis
{
public:
enum FluidFSIAnalysisType {
STEADY_STATE,
DYNAMIC
};
public:
FEFluidFSIAnalysis(FEModel* fem);
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFixedFluidVelocity.h | .h | 1,489 | 40 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEFixedBC.h>
class FEFixedFluidVelocity : public FEFixedBC
{
public:
FEFixedFluidVelocity(FEModel* fem);
bool Init() override;
private:
bool m_dof[3];
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEElasticFluid.cpp | .cpp | 10,738 | 299 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEElasticFluid.h"
#include "FEThermoFluidMaterialPoint.h"
#include "FEThermoFluid.h"
//-----------------------------------------------------------------------------
//! tangent of pressure with respect to strain J
double FEElasticFluid::Tangent_Strain(FEMaterialPoint& mp)
{
double d = 1e-6;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef+d;
ft->m_T = tf.m_T;
FEMaterialPoint tmp(ft);
double pp = Pressure(tmp);
fp->m_ef = pf.m_ef-d;
double pm = Pressure(tmp);
delete ft;
double dpJ = (pp - pm)/(2*d);
return dpJ;
}
//-----------------------------------------------------------------------------
//! 2nd tangent of pressure with respect to strain J
double FEElasticFluid::Tangent_Strain_Strain(FEMaterialPoint& mp)
{
double d = 1e-6;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef+d;
ft->m_T = tf.m_T;
FEMaterialPoint tmp(ft);
double dpp = Tangent_Strain(tmp);
fp->m_ef = pf.m_ef-d;
double dpm = Tangent_Strain(tmp);
delete ft;
double dpJ2 = (dpp - dpm)/(2*d);
return dpJ2;
}
//-----------------------------------------------------------------------------
//! tangent of pressure with respect to temperature T
double FEElasticFluid::Tangent_Temperature(FEMaterialPoint& mp)
{
double Tr = GetGlobalConstant("T");
double d = 1e-6*Tr;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef;
ft->m_T = tf.m_T+d;
FEMaterialPoint tmp(ft);
double pp = Pressure(tmp);
ft->m_T = tf.m_T-d;
double pm = Pressure(tmp);
delete ft;
double dpT = (pp - pm)/(2*d);
return dpT;
}
//-----------------------------------------------------------------------------
//! 2nd tangent of pressure with respect to temperature T
double FEElasticFluid::Tangent_Temperature_Temperature(FEMaterialPoint& mp)
{
double Tr = GetGlobalConstant("T");
double d = 1e-6*Tr;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef;
ft->m_T = tf.m_T+d;
FEMaterialPoint tmp(ft);
double dpp = Tangent_Temperature(tmp);
ft->m_T = tf.m_T-d;
double dpm = Tangent_Temperature(tmp);
delete ft;
double dpT2 = (dpp - dpm)/(2*d);
return dpT2;
}
//-----------------------------------------------------------------------------
//! tangent of pressure with respect to strain J and temperature T
double FEElasticFluid::Tangent_Strain_Temperature(FEMaterialPoint& mp)
{
double Tr = GetGlobalConstant("T");
double dJ = 1e-6;
double dT = 1e-6*Tr;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef+dJ;
ft->m_T = tf.m_T;
FEMaterialPoint tmp(ft);
double dpp = Tangent_Temperature(tmp);
fp->m_ef = pf.m_ef-dJ;
double dpm = Tangent_Temperature(tmp);
delete ft;
double dpTJ = (dpp - dpm)/(2*dJ);
return dpTJ;
}
//-----------------------------------------------------------------------------
//! tangent of isochoric specific heat capacity with respect to strain J
double FEElasticFluid::Tangent_cv_Strain(FEMaterialPoint& mp)
{
double d = 1e-6;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef+d;
ft->m_T = tf.m_T;
FEMaterialPoint tmp(ft);
double cvp = IsochoricSpecificHeatCapacity(tmp);
fp->m_ef = pf.m_ef-d;
double cvm = IsochoricSpecificHeatCapacity(tmp);
delete ft;
double dcvJ = (cvp - cvm)/(2*d);
return dcvJ;
}
//-----------------------------------------------------------------------------
//! tangent of isochoric specific heat capacity with respect to temperature T
double FEElasticFluid::Tangent_cv_Temperature(FEMaterialPoint& mp)
{
double Tr = GetGlobalConstant("T");
double d = 1e-6*Tr;
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
FEFluidMaterialPoint& pf = *mp.ExtractData<FEFluidMaterialPoint>();
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = pf.m_ef;
ft->m_T = tf.m_T+d;
FEMaterialPoint tmp(ft);
double cvp = IsochoricSpecificHeatCapacity(tmp);
ft->m_T = tf.m_T-d;
double cvm = IsochoricSpecificHeatCapacity(tmp);
delete ft;
double dcvT = (cvp - cvm)/(2*d);
return dcvT;
}
//-----------------------------------------------------------------------------
//! specific internal energy
double FEElasticFluid::SpecificInternalEnergy(FEMaterialPoint& mp)
{
double Tr = GetGlobalConstant("T");
FEThermoFluidMaterialPoint& tf = *mp.ExtractData<FEThermoFluidMaterialPoint>();
double T = tf.m_T + Tr;
double u = SpecificFreeEnergy(mp) + T*SpecificEntropy(mp);
return u;
}
//-----------------------------------------------------------------------------
//! specific gauge enthalpy
double FEElasticFluid::SpecificGaugeEnthalpy(FEMaterialPoint& mp)
{
FEThermoFluid* pMat = dynamic_cast<FEThermoFluid*>(GetParent());
double h = SpecificInternalEnergy(mp) + Pressure(mp)/pMat->Density(mp);
return h;
}
//-----------------------------------------------------------------------------
//! specific free enthalpy
double FEElasticFluid::SpecificFreeEnthalpy(FEMaterialPoint& mp)
{
FEThermoFluid* pMat = dynamic_cast<FEThermoFluid*>(GetParent());
double g = SpecificFreeEnergy(mp) + Pressure(mp)/pMat->Density(mp);
return g;
}
//-----------------------------------------------------------------------------
//! pressure from state variables
double FEElasticFluid::Pressure(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double p = Pressure(tmp);
return p;
}
//-----------------------------------------------------------------------------
//! dp/dJ
double FEElasticFluid::Tangent_Strain(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double dpJ = Tangent_Strain(tmp);
return dpJ;
}
//-----------------------------------------------------------------------------
//! dp/dT
double FEElasticFluid::Tangent_Temperature(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double dpT = Tangent_Temperature(tmp);
return dpT;
}
//-----------------------------------------------------------------------------
//! d2p/dJ2
double FEElasticFluid::Tangent_Strain_Strain(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double dpJ2 = Tangent_Strain_Strain(tmp);
return dpJ2;
}
//-----------------------------------------------------------------------------
//! d2p/dJdT
double FEElasticFluid::Tangent_Strain_Temperature(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double dpJT = Tangent_Strain_Temperature(tmp);
return dpJT;
}
//-----------------------------------------------------------------------------
//! d2p/dT2
double FEElasticFluid::Tangent_Temperature_Temperature(const double ef, const double T)
{
FEFluidMaterialPoint* fp = new FEFluidMaterialPoint();
FEThermoFluidMaterialPoint* ft = new FEThermoFluidMaterialPoint(fp);
fp->m_ef = ef;
ft->m_T = T;
FEMaterialPoint tmp(ft);
double dpT2 = Tangent_Temperature_Temperature(tmp);
return dpT2;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEInitialFluidPressure.cpp | .cpp | 5,509 | 164 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "FEInitialFluidPressure.h"
#include "FEBioFluid.h"
#include "FEFluid.h"
#include <FECore/FEModel.h>
#include <FECore/FEAnalysis.h>
//=============================================================================
BEGIN_FECORE_CLASS(FEInitialFluidPressure, FEInitialCondition)
// material properties
ADD_PARAMETER(m_Pdata, "value" )->setUnits(UNIT_PRESSURE);
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEInitialFluidPressure::FEInitialFluidPressure(FEModel* fem) : FENodalIC(fem)
{
}
//-----------------------------------------------------------------------------
bool FEInitialFluidPressure::Init()
{
if (SetPDOF("ef") == false) return false;
m_e.assign(m_nodeSet->Size(), 0.0);
FEDofList dofs(GetFEModel());
if (dofs.AddVariable(FEBioFluid::GetVariableName(FEBioFluid::FLUID_DILATATION)) == false) return false;
SetDOFList(dofs);
return FENodalIC::Init();
}
//-----------------------------------------------------------------------------
void FEInitialFluidPressure::SetPDOF(int ndof) { m_dofEF = ndof; }
//-----------------------------------------------------------------------------
bool FEInitialFluidPressure::SetPDOF(const char* szdof)
{
FEModel* fem = GetFEModel();
int ndof = fem->GetDOFIndex(szdof);
assert(ndof >= 0);
if (ndof < 0) return false;
SetPDOF(ndof);
return true;
}
//-----------------------------------------------------------------------------
void FEInitialFluidPressure::Activate()
{
// prescribe this dilatation at the nodes
FEModel* fem = GetFEModel();
FENodeList nodeList = m_nodeSet->GetNodeList();
int N = nodeList.Size();
std::vector<vector<double>> efNodes(N, vector<double>());
FEMesh& mesh = *m_nodeSet->GetMesh();
// evaluate average prescribed pressure and temperature in each element
// project them from int points to nodes
for (int i=0; i<mesh.Elements(); ++i)
{
FEElement& el = *mesh.Element(i);
// get material
FEMaterial* pm = GetFEModel()->GetMaterial(el.GetMatID());
FEFluid* pfl = pm->ExtractProperty<FEFluid>();
if (pfl) {
double efi[FEElement::MAX_INTPOINTS] = {0};
double efo[FEElement::MAX_NODES] = {0};
bool good = true;
for (int j=0; j<el.GaussPoints(); ++j) {
FEMaterialPoint* pt = el.GetMaterialPoint(j);
good = good && pfl->Dilatation(0, m_Pdata(*pt), efi[j]);
}
// project dilatations from integration points to nodes
el.project_to_nodes(efi, efo);
if (good) {
for (int j=0; j<el.Nodes(); ++j)
efNodes[el.m_node[j]].push_back(efo[j]);
}
else {
for (int j=0; j<el.Nodes(); ++j) {
efo[j] = 0;
efNodes[el.m_node[j]].push_back(efo[j]);
}
}
}
else break;
}
//For each node, average the nodal ef
for (int i=0; i<nodeList.Size(); ++i)
{
double ef = 0;
for (int j = 0; j < efNodes[i].size(); ++j)
ef += efNodes[i][j];
ef /= efNodes[i].size();
// store value for now
m_e[i] = ef;
}
FEStepComponent::Activate();
if (m_dofs.IsEmpty()) return;
int dofs = (int)m_dofs.Size();
std::vector<double> val(dofs, 0.0);
for (int i = 0; i<N; ++i)
{
FENode& node = *m_nodeSet->Node(i);
// get the nodal values
GetNodalValues(i, val);
for (int j = 0; j < dofs; ++j)
{
node.set(m_dofs[j], val[j]);
}
}
}
//-----------------------------------------------------------------------------
void FEInitialFluidPressure::GetNodalValues(int inode, std::vector<double>& values)
{
values[0] = m_e[inode];
}
//-----------------------------------------------------------------------------
void FEInitialFluidPressure::Serialize(DumpStream& ar)
{
FENodalIC::Serialize(ar);
if (ar.IsLoading())
m_e.assign(m_nodeSet->Size(), 0.0);
ar & m_e;
if (ar.IsShallow()) return;
ar & m_dofEF;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidSolutesDomainFactory.cpp | .cpp | 2,126 | 57 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFluidSolutesDomainFactory.h"
#include "FEFluidSolutes.h"
#include "FEFluidDomain.h"
#include <FECore/FESolidDomain.h>
//-----------------------------------------------------------------------------
FEDomain* FEFluidSolutesDomainFactory::CreateDomain(const FE_Element_Spec& spec, FEMesh* pm, FEMaterial* pmat)
{
FEModel* pfem = pmat->GetFEModel();
FE_Element_Class eclass = spec.eclass;
FE_Element_Shape eshape = spec.eshape;
const char* sztype = 0;
if (dynamic_cast<FEFluidSolutes*>(pmat))
{
// fluid elements
if (eclass==FE_ELEM_SOLID) sztype = "fluid-solutes-3D";
else return 0;
}
if (sztype)
{
FEDomain* pd = fecore_new<FESolidDomain>(sztype, pfem);
if (pd) pd->SetMaterial(pmat);
return pd;
}
else return 0;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEPrescribedFluidDilatation.h | .h | 1,489 | 37 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEPrescribedDOF.h>
class FEPrescribedFluidDilatation : public FEPrescribedDOF
{
public:
FEPrescribedFluidDilatation(FEModel* fem);
bool Init() override;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidRCRLoad.h | .h | 3,050 | 84 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESurfaceLoad.h>
#include "FEFluidMaterial.h"
//-----------------------------------------------------------------------------
//! FEFluidRCRLoad is a fluid surface load that implements a 3-element Windkessel model
//!
class FEBIOFLUID_API FEFluidRCRLoad : public FESurfaceLoad
{
public:
//! constructor
FEFluidRCRLoad(FEModel* pfem);
//! calculate traction stiffness (there is none)
void StiffnessMatrix(FELinearSystem& LS) override {}
//! calculate load vector
void LoadVector(FEGlobalVector& R) override;
//! set the dilatation
void Update() override;
//! evaluate flow rate
double FlowRate();
//! initialize
bool Init() override;
//! activate
void Activate() override;
//! serialization
void Serialize(DumpStream& ar) override;
private:
double m_R; //!< flow resistance
double m_Rd; //!< distal resistance
double m_p0; //!< initial fluid pressure
double m_C; //!< capacitance
double m_pd; //!< downstream pressure
private:
double m_pn; //!< fluid pressure at current time point
double m_pp; //!< fluid pressure at previous time point
double m_qn; //!< flow rate at current time point
double m_qp; //!< flow rate at previous time point
double m_pdn; //!< downstream fluid pressure at current time point
double m_pdp; //!< downstream fluid pressure at previous time point
double m_tp; //!< previous time
FEFluidMaterial* m_pfluid; //!< pointer to fluid
FEDofList m_dofW;
int m_dofEF;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidFSISolver.h | .h | 6,233 | 173 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FENewtonSolver.h>
#include <FECore/FETimeInfo.h>
#include <FECore/FEGlobalVector.h>
#include <FEBioMech/FERigidSolver.h>
#include <FECore/FEDofList.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! The FEFluidFSISolver class solves fluid-FSI problems
//! It can deal with quasi-static and dynamic problems
//!
class FEBIOFLUID_API FEFluidFSISolver : public FENewtonSolver
{
public:
//! constructor
FEFluidFSISolver(FEModel* pfem);
//! destructor
~FEFluidFSISolver();
//! serialize data to/from dump file
void Serialize(DumpStream& ar) override;
//! Initializes data structures
bool Init() override;
//! initialize the step
bool InitStep(double time) override;
//! Initialize linear equation system
bool InitEquations() override;
//! Generate warnings if needed
void SolverWarnings();
//! preferred matrix type should be unsymmetric.
Matrix_Type PreferredMatrixType() const override { return REAL_UNSYMMETRIC; };
public:
//{ --- evaluation and update ---
//! Perform an update
void Update(vector<double>& ui) override;
//! update nodal positions, velocities, accelerations, etc.
void UpdateKinematics(vector<double>& ui);
//! Update EAS
void UpdateEAS(vector<double>& ui);
void UpdateIncrementsEAS(vector<double>& ui, const bool binc);
//! update DOF increments
virtual void UpdateIncrements(vector<double>& Ui, vector<double>& ui, bool emap);
//}
//{ --- Solution functions ---
//! prepares the data for the first QN iteration
void PrepStep() override;
//! Performs a Newton-Raphson iteration
bool Quasin() override;
//{ --- Stiffness matrix routines ---
//! calculates the global stiffness matrix
bool StiffnessMatrix() override;
//! contact stiffness
void ContactStiffness(FELinearSystem& LS);
//! calculates stiffness contributon of nonlinear constraints
void NonLinearConstraintStiffness(FELinearSystem& LS, const FETimeInfo& tp);
//{ --- Residual routines ---
//! Calculate the contact forces
void ContactForces(FEGlobalVector& R);
//! Calculates residual
bool Residual(vector<double>& R) override;
//! Calculate nonlinear constraint forces
void NonLinearConstraintForces(FEGlobalVector& R, const FETimeInfo& tp);
protected:
void GetDisplacementData(vector<double>& xi, vector<double>& ui);
void GetVelocityData(vector<double>& vi, vector<double>& ui);
void GetDilatationData(vector<double>& ei, vector<double>& ui);
public:
// convergence tolerances
double m_Dtol; //!< displacement tolerance
double m_Vtol; //!< velocity tolerance
double m_Ftol; //!< dilatation tolerance
double m_minJf; //!< minimum allowable compression ratio
public:
// equation numbers
int m_nreq; //!< start of rigid body equations
int m_ndeq; //!< number of equations related to displacement dofs
int m_nveq; //!< number of equations related to velocity dofs
int m_nfeq; //!< number of equations related to dilatation dofs
public:
vector<double> m_Fn; //!< concentrated nodal force vector
vector<double> m_Fr; //!< nodal reaction forces
vector<double> m_di; //!< displacement increment vector
vector<double> m_Di; //!< Total displacement vector for iteration
vector<double> m_vi; //!< velocity increment vector
vector<double> m_Vi; //!< Total velocity vector for iteration
vector<double> m_fi; //!< dilatation increment vector
vector<double> m_Fi; //!< Total dilatation vector for iteration
// generalized alpha method
double m_rhoi; //!< spectral radius (rho infinity)
double m_alphaf; //!< alpha step for Y={v,e}
double m_alpham; //!< alpha step for Ydot={∂v/∂t,∂e/∂t}
double m_beta; //!< beta
double m_gamma; //!< gamma
int m_pred; //!< predictor method
int m_order; //!< generalized-alpha integration order
protected:
FEDofList m_dofU; // solid displacement
FEDofList m_dofV; // solid velocity
FEDofList m_dofSU; // shell displacement
FEDofList m_dofSV; // shell velocity
FEDofList m_dofSA; // shell acceleration
FEDofList m_dofQ; // rotation
FEDofList m_dofRQ; // rigid rotation
FEDofList m_dofVF; // fluid velocity
FEDofList m_dofAF; // material time derivative of fluid velocity
FEDofList m_dofW; // fluid velocity relative to solid
FEDofList m_dofAW; // material time derivative of fluid velocity relative to solid
FEDofList m_dofEF; // fluid dilatation
int m_dofAEF; // material time derivative of fluid dilatation
protected:
FERigidSolverNew m_rigidSolver;
// declare the parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFixedFluidTemperature.cpp | .cpp | 1,593 | 42 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFixedFluidTemperature.h"
BEGIN_FECORE_CLASS(FEFixedFluidTemperature, FEFixedBC)
END_FECORE_CLASS();
FEFixedFluidTemperature::FEFixedFluidTemperature(FEModel* fem) : FEFixedBC(fem)
{
}
bool FEFixedFluidTemperature::Init()
{
SetDOFList(GetDOFIndex("T"));
return FEFixedBC::Init();
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FENewtonianFluid.cpp | .cpp | 4,052 | 122 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FENewtonianFluid.h"
#include "FEFluid.h"
#include "FEBiphasicFSI.h"
#include "FEThermoFluid.h"
#include <FECore/log.h>
// define the material parameters
BEGIN_FECORE_CLASS(FENewtonianFluid, FEViscousFluid)
ADD_PARAMETER(m_kappa, FE_RANGE_GREATER_OR_EQUAL(0.0), "kappa")->setUnits(UNIT_VISCOSITY)->setLongName("bulk viscosity");
ADD_PARAMETER(m_mu , FE_RANGE_GREATER_OR_EQUAL(0.0), "mu" )->setUnits(UNIT_VISCOSITY)->setLongName("shear viscosity");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! Constructor.
FENewtonianFluid::FENewtonianFluid(FEModel* pfem) : FEViscousFluid(pfem)
{
m_kappa = 0;
m_mu = 0;
}
//-----------------------------------------------------------------------------
//! initialization
bool FENewtonianFluid::Init()
{
return FEViscousFluid::Init();
}
//-----------------------------------------------------------------------------
void FENewtonianFluid::Serialize(DumpStream& ar)
{
FEViscousFluid::Serialize(ar);
if (ar.IsShallow()) return;
}
//-----------------------------------------------------------------------------
//! viscous stress
mat3ds FENewtonianFluid::Stress(FEMaterialPoint& pt)
{
FEFluidMaterialPoint& vt = *pt.ExtractData<FEFluidMaterialPoint>();
mat3ds D = vt.RateOfDeformation();
double mu = ShearViscosity(pt);
double kappa = BulkViscosity(pt);
mat3ds s = mat3dd(1.0)*(D.tr()*(kappa - 2.*mu/3.)) + D*(2*mu);
return s;
}
//-----------------------------------------------------------------------------
//! tangent of stress with respect to strain J
mat3ds FENewtonianFluid::Tangent_Strain(FEMaterialPoint& mp)
{
return mat3ds(0,0,0,0,0,0);
}
//-----------------------------------------------------------------------------
//! tangent of stress with respect to rate of deformation tensor D
tens4ds FENewtonianFluid::Tangent_RateOfDeformation(FEMaterialPoint& mp)
{
mat3dd I(1.0);
double mu = ShearViscosity(mp);
double kappa = BulkViscosity(mp);
tens4ds c = dyad1s(I)*(kappa - 2.*mu/3.) + dyad4s(I)*(2*mu);
return c;
}
//-----------------------------------------------------------------------------
//! tangent of stress with respect to temperature T
mat3ds FENewtonianFluid::Tangent_Temperature(FEMaterialPoint& mp)
{
return mat3ds(0);
}
//-----------------------------------------------------------------------------
//! dynamic shear viscosity
double FENewtonianFluid::ShearViscosity(FEMaterialPoint& mp)
{
return m_mu;
}
//-----------------------------------------------------------------------------
//! bulk viscosity
double FENewtonianFluid::BulkViscosity(FEMaterialPoint& mp)
{
return m_kappa;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidFSIDomainFactory.h | .h | 1,607 | 39 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FECoreKernel.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
class FEBIOFLUID_API FEFluidFSIDomainFactory : public FEDomainFactory
{
public:
virtual FEDomain* CreateDomain(const FE_Element_Spec& spec, FEMesh* pm, FEMaterial* pmat);
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEBackFlowFSIStabilization.h | .h | 2,279 | 66 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESurfaceLoad.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! Backflow stabilization prescribes a normal traction that opposes
//! backflow on a boundary surface.
class FEBIOFLUID_API FEBackFlowFSIStabilization : public FESurfaceLoad
{
public:
//! constructor
FEBackFlowFSIStabilization(FEModel* pfem);
//! calculate pressure stiffness
void StiffnessMatrix(FELinearSystem& LS) override;
//! calculate residual
void LoadVector(FEGlobalVector& R) override;
//! serialize data
void Serialize(DumpStream& ar) override;
//! initialization
bool Init() override;
protected:
vec3d FluidVelocity(FESurfaceMaterialPoint& mp, double alpha);
protected:
double m_beta; //!< backflow stabilization coefficient
// degrees of freedom
FEDofList m_dofU;
FEDofList m_dofW;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidThermalConductivity.cpp | .cpp | 1,317 | 30 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "FEFluidThermalConductivity.h"
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidThermalConductivity.h | .h | 2,166 | 54 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEMaterial.h>
#include "FEThermoFluidMaterialPoint.h"
//-----------------------------------------------------------------------------
//! Base class for fluid thermal conductivity materials.
class FEBIOFLUID_API FEFluidThermalConductivity : public FEMaterialProperty
{
public:
FEFluidThermalConductivity(FEModel* pfem) : FEMaterialProperty(pfem) {}
virtual ~FEFluidThermalConductivity() {}
public:
//! calculate thermal conductivity at material point
virtual double ThermalConductivity(FEMaterialPoint& pt) = 0;
//! tangent of thermal conductivity with respect to strain J
virtual double Tangent_Strain(FEMaterialPoint& mp) = 0;
//! tangent of thermal conductivity with respect to temperature T
virtual double Tangent_Temperature(FEMaterialPoint& mp) = 0;
FECORE_BASE_CLASS(FEFluidThermalConductivity)
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/febiofluid_api.h | .h | 1,541 | 44 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#ifdef WIN32
#ifdef FECORE_DLL
#ifdef febiofluid_EXPORTS
#define FEBIOFLUID_API __declspec(dllexport)
#else
#define FEBIOFLUID_API __declspec(dllimport)
#endif
#else
#define FEBIOFLUID_API
#endif
#else
#define FEBIOFLUID_API
#endif
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEBioFluid.h | .h | 1,766 | 51 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! The FEBioFluid module
//! The FEBioFluid module adds fluid capabilities to FEBio.
//!
namespace FEBioFluid {
FEBIOFLUID_API void InitModule();
enum FLUID_VARIABLE {
DISPLACEMENT,
RELATIVE_FLUID_VELOCITY,
FLUID_DILATATION,
RELATIVE_FLUID_ACCELERATION,
FLUID_DILATATION_TDERIV,
};
FEBIOFLUID_API const char* GetVariableName(FLUID_VARIABLE var);
}
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEBioFSI.h | .h | 1,732 | 54 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "febiofluid_api.h"
namespace FEBioFSI {
FEBIOFLUID_API void InitModule();
enum FSI_VARIABLE {
DISPLACEMENT,
VELOCITY,
ROTATION,
SHELL_DISPLACEMENT,
SHELL_VELOCITY,
SHELL_ACCELERATION,
RIGID_ROTATION,
RELATIVE_FLUID_VELOCITY,
RELATIVE_FLUID_ACCELERATION,
FLUID_VELOCITY,
FLUID_ACCELERATION,
FLUID_DILATATION,
FLUID_DILATATION_TDERIV
};
FEBIOFLUID_API const char* GetVariableName(FSI_VARIABLE var);
}
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFSIErosionVolumeRatio.cpp | .cpp | 9,106 | 261 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFSIErosionVolumeRatio.h"
#include "FEFluidFSIDomain3D.h"
#include <FECore/FEModel.h>
#include <FECore/FEMesh.h>
#include <FECore/FEDomain.h>
#include <FECore/log.h>
#include "FEBioMech/FEElasticMaterial.h"
#include <FECore/FELinearConstraintManager.h>
#include <algorithm>
BEGIN_FECORE_CLASS(FEFSIErosionVolumeRatio, FEMeshAdaptor)
ADD_PARAMETER(m_minJ, FE_RANGE_GREATER(0.0), "min_volume_ratio");
ADD_PARAMETER(m_maxElems, "max_elems");
ADD_PARAMETER(m_maxIters, "max_iters");
ADD_PARAMETER(m_metric , "metric");
END_FECORE_CLASS();
FEFSIErosionVolumeRatio::FEFSIErosionVolumeRatio(FEModel* fem) : FEMeshAdaptor(fem)
{
m_minJ = 0.0;
m_maxElems = 0;
m_maxIters = -1;
m_metric = 0;
}
bool FEFSIErosionVolumeRatio::Apply(int iteration)
{
FEModel& fem = *GetFEModel();
FEMesh& mesh = fem.GetMesh();
if ((m_maxIters >= 0) && (iteration >= m_maxIters))
{
feLog("Max iterations reached.");
return false;
}
int deactiveElems = 0;
int activeElems = 0;
map<int, bool> melem;
for (int i = 0; i < mesh.Domains(); ++i)
{
FEDomain& dom = mesh.Domain(i);
FEFluidFSIDomain* fsidom = dynamic_cast<FEFluidFSIDomain*>(&dom);
if (fsidom) {
int NE = dom.Elements();
for (int j = 0; j < NE; ++j)
{
FEElement& el = dom.ElementRef(j);
if (el.isActive())
{
bool bdeactivate = false;
int nint = el.GaussPoints();
double elemVal = 0;
for (int n = 0; n < nint; ++n)
{
FEMaterialPoint* mp = el.GetMaterialPoint(n);
FEElasticMaterialPoint* ep = mp->ExtractData<FEElasticMaterialPoint>();
if (ep)
{
mat3ds C = ep->RightCauchyGreen();
switch (m_metric)
{
case 0: elemVal = ep->m_J; break;
case 1:
{
double lam[3];
C.eigen(lam);
elemVal = sqrt(lam[2]);
}
break;
default:
break;
}
if (elemVal <= m_minJ)
{
bdeactivate = true;
break;
}
}
}
if (bdeactivate)
{
melem[el.GetID()] = true;
deactiveElems++;
}
}
// if an element is inactive, check whether we need to activate it again
else
{
// nodal coordinates
const int NELN = FEElement::MAX_NODES;
vec3d r[NELN];
FESolidElement* sel = dynamic_cast<FESolidElement*>(&el);
if (sel) {
FEFluidFSIDomain3D* fsi3D = dynamic_cast<FEFluidFSIDomain3D*>(fsidom);
fsi3D->GetCurrentNodalCoordinates(*sel, r);
int nint = el.GaussPoints();
double minJ = 1;
for (int n = 0; n < nint; ++n)
{
FEMaterialPoint* mp = el.GetMaterialPoint(n);
FEElasticMaterialPoint* ep = mp->ExtractData<FEElasticMaterialPoint>();
// get the deformation gradient and determinant at intermediate time
double Jt;
mat3d Ft, Fp;
Jt = fsi3D->defgrad(*sel, Ft, n, r);
ep->m_J = Jt;
ep->m_F = Ft;
mat3ds C = ep->RightCauchyGreen();
switch (m_metric)
{
case 0: minJ = min(ep->m_J,minJ); break;
case 1:
{
double lam[3];
C.eigen(lam);
minJ = min(sqrt(lam[2]),minJ);
}
break;
default:
break;
}
}
if (minJ > m_minJ) {
melem[el.GetID()] = false;
activeElems++;
}
}
}
}
}
}
if ((deactiveElems == 0) && (activeElems == 0))
{
feLog("Nothing to do.");
return false;
}
int melems = melem.size();
if (melems > m_maxElems) melems = m_maxElems;
int nel = 0;
for (std::map<int,bool>::iterator it=melem.begin(); it!=melem.end(); ++it)
{
FEElement* pe = mesh.FindElementFromID(it->first); assert(pe);
if (it->second) {
pe->setInactive();
if (++nel > m_maxElems) break;
}
else {
pe->setActive();
}
}
// if any nodes were orphaned, we need to deactivate them as well
int NN = mesh.Nodes();
vector<int> tag(NN, 0);
for (int i = 0; i < mesh.Domains(); ++i)
{
FEDomain& dom = mesh.Domain(i);
int NE = dom.Elements();
for (int j = 0; j < NE; ++j)
{
FEElement& el = dom.ElementRef(j);
if (el.isActive())
{
int neln = el.Nodes();
for (int n = 0; n < neln; ++n) tag[el.m_node[n]] = 1;
}
}
}
for (int i = 0; i < NN; ++i)
{
FENode& node = mesh.Node(i);
if (tag[i] == 0)
{
node.SetFlags(FENode::EXCLUDE);
int ndofs = node.dofs();
for (int j = 0; j < ndofs; ++j)
node.set_inactive(j);
}
}
// remove any linear constraints of exclude nodes
FELinearConstraintManager& LCM = fem.GetLinearConstraintManager();
for (int j = 0; j < LCM.LinearConstraints();)
{
FELinearConstraint& lc = LCM.LinearConstraint(j);
if (mesh.Node(lc.GetParentNode()).HasFlags(FENode::EXCLUDE))
{
LCM.RemoveLinearConstraint(j);
}
else ++j;
}
// also remove any linear constraints that have excluded child nodes
for (int j = 0; j < LCM.LinearConstraints();)
{
FELinearConstraint& lc = LCM.LinearConstraint(j);
bool del = false;
int n = lc.Size();
for (int k = 0; k < n; ++k)
{
if (mesh.Node(lc.GetChildDof(k).node).HasFlags(FENode::EXCLUDE))
{
del = true;
break;
}
}
if (del) LCM.RemoveLinearConstraint(j); else ++j;
}
// reactivate the linear constraints
LCM.Activate();
// feLog("Deactivate elements: %d\n", elems);
// return (elems == 0);
feLog("Deactivate elements: %d\n", melems);
feLog("Reactivate elements: %d\n", activeElems);
return (melems != 0);
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidRCRBC.h | .h | 3,301 | 90 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEPrescribedBC.h>
#include "FEFluidMaterial.h"
//-----------------------------------------------------------------------------
//! FEFluidRCRBC is a fluid surface load that implements a 3-element Windkessel model
//!
class FEBIOFLUID_API FEFluidRCRBC : public FEPrescribedSurface
{
public:
//! constructor
FEFluidRCRBC(FEModel* pfem);
//! set the dilatation
void Update() override;
void UpdateModel() override;
//! evaluate flow rate
double FlowRate();
//! initialize
bool Init() override;
//! serialization
void Serialize(DumpStream& ar) override;
public:
void PrepStep(std::vector<double>& ui, bool brel) override;
// return the value for node i, dof j
void GetNodalValues(int nodelid, std::vector<double>& val) override;
// copy data from another class
void CopyFrom(FEBoundaryCondition* pbc) override;
private:
//! set the dilatation
void UpdateDilatation();
private:
double m_R; //!< flow resistance
double m_Rd; //!< distal resistance
double m_p0; //!< initial fluid pressure
double m_C; //!< capacitance
double m_pd; //!< downstream pressure
private:
double m_pn; //!< fluid pressure at current time point
double m_pp; //!< fluid pressure at previous time point
double m_qn; //!< flow rate at current time point
double m_qp; //!< flow rate at previous time point
double m_pdn; //!< downstream fluid pressure at current time point
double m_pdp; //!< downstream fluid pressure at previous time point
double m_tp; //!< previous time
double m_e;
FEFluidMaterial* m_pfluid; //!< pointer to fluid
FESurface* m_psurf; //!< pointer to surface
FEDofList m_dofW;
int m_dofEF;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FETiedFluidInterface.h | .h | 5,747 | 158 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FEBioMech/FEContactInterface.h>
#include <FEBioMech/FEContactSurface.h>
#include "FEFluidMaterial.h"
//-----------------------------------------------------------------------------
class FEBIOFLUID_API FETiedFluidSurface : public FEContactSurface
{
public:
//! Integration point data
class Data : public FEContactMaterialPoint
{
public:
Data();
void Serialize(DumpStream& ar) override;
public:
vec3d m_Gap; //!< initial gap in reference configuration
vec3d m_vg; //!< tangential velocity gap function at integration points
vec3d m_nu; //!< normal at integration points
vec2d m_rs; //!< natural coordinates of projection of integration point
vec3d m_Lmd; //!< lagrange multipliers for tangential velocity
vec3d m_tv; //!< viscous tangential traction
double m_Lmp; //!< lagrange multipliers for fluid pressures
double m_epst; //!< viscous traction penalty factor
double m_epsn; //!< normal velocity penalty factor
double m_pg; //!< pressure "gap"
double m_vn; //!< normal fluid velocity gap
};
//! constructor
FETiedFluidSurface(FEModel* pfem);
//! initialization
bool Init() override;
//! Unpack surface element data
void UnpackLM(FEElement& el, vector<int>& lm) override;
//! create material point data
FEMaterialPoint* CreateMaterialPoint() override;
public:
void GetVelocityGap (int nface, vec3d& vg);
void GetPressureGap (int nface, double& pg);
void GetViscousTraction (int nface, vec3d& tv);
void GetNormalVelocity (int nface, double& vn);
public:
FEDofList m_dofWE;
};
//-----------------------------------------------------------------------------
class FEBIOFLUID_API FETiedFluidInterface : public FEContactInterface
{
public:
//! constructor
FETiedFluidInterface(FEModel* pfem);
//! destructor
~FETiedFluidInterface();
//! initialization
bool Init() override;
//! interface activation
void Activate() override;
//! serialize data to archive
void Serialize(DumpStream& ar) override;
//! return the primary and secondary surfaces
FESurface* GetPrimarySurface() override { return &m_ss; }
FESurface* GetSecondarySurface() override { return &m_ms; }
//! return integration rule class
bool UseNodalIntegration() override { return false; }
//! build the matrix profile for use in the stiffness matrix
void BuildMatrixProfile(FEGlobalMatrix& K) override;
public:
//! calculate contact forces
void LoadVector(FEGlobalVector& R, const FETimeInfo& tp) override;
//! calculate contact stiffness
void StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) override;
//! calculate Lagrangian augmentations
bool Augment(int naug, const FETimeInfo& tp) override;
//! update
void Update() override;
protected:
void InitialProjection(FETiedFluidSurface& ss, FETiedFluidSurface& ms);
void ProjectSurface(FETiedFluidSurface& ss, FETiedFluidSurface& ms);
//! calculate penalty factor
void CalcAutoPressurePenalty(FETiedFluidSurface& s);
double AutoPressurePenalty(FESurfaceElement& el, FETiedFluidSurface& s);
public:
FETiedFluidSurface m_ss; //!< primary surface
FETiedFluidSurface m_ms; //!< secondary surface
bool m_btwo_pass; //!< two-pass flag
double m_atol; //!< augmentation tolerance
double m_gtol; //!< gap tolerance
double m_ptol; //!< pressure gap tolerance
double m_stol; //!< search tolerance
double m_srad; //!< contact search radius
int m_naugmax; //!< maximum nr of augmentations
int m_naugmin; //!< minimum nr of augmentations
double m_epst; //!< tangential viscous traction penalty factor
double m_epsn; //!< normal fluid velocity penalty factor
bool m_bautopen; //!< use autopenalty factor
bool m_bfreedofs; //!< flag to free constrained/fixed DOFS on secondary surface
FEFluidMaterial* m_pfluid; //!< fluid pointer
FEDofList m_dofWE;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEFixedFluidAngularVelocity.cpp | .cpp | 2,104 | 52 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFixedFluidAngularVelocity.h"
BEGIN_FECORE_CLASS(FEFixedFluidAngularVelocity, FEFixedBC)
ADD_PARAMETER(m_dof[0], "gx_dof")->setLongName("x-angular-velocity");
ADD_PARAMETER(m_dof[1], "gy_dof")->setLongName("y-angular-velocity");
ADD_PARAMETER(m_dof[2], "gz_dof")->setLongName("z-angular-velocity");
END_FECORE_CLASS();
FEFixedFluidAngularVelocity::FEFixedFluidAngularVelocity(FEModel* fem) : FEFixedBC(fem)
{
m_dof[0] = false;
m_dof[1] = false;
m_dof[2] = false;
}
bool FEFixedFluidAngularVelocity::Init()
{
vector<int> dofs;
if (m_dof[0]) dofs.push_back(GetDOFIndex("gx"));
if (m_dof[1]) dofs.push_back(GetDOFIndex("gy"));
if (m_dof[2]) dofs.push_back(GetDOFIndex("gz"));
SetDOFList(dofs);
return FEFixedBC::Init();
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEBiphasicFSITraction.cpp | .cpp | 12,644 | 350 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEBiphasicFSITraction.h"
#include "FECore/FEModel.h"
#include "FEFluid.h"
#include "FEBiphasicFSI.h"
#include "FEBioFSI.h"
//-----------------------------------------------------------------------------
// Parameter block for pressure loads
BEGIN_FECORE_CLASS(FEBiphasicFSITraction, FESurfaceLoad)
ADD_PARAMETER(m_bshellb , "shell_bottom");
END_FECORE_CLASS()
//-----------------------------------------------------------------------------
//! constructor
FEBiphasicFSITraction::FEBiphasicFSITraction(FEModel* pfem) : FESurfaceLoad(pfem), m_dofU(pfem), m_dofSU(pfem), m_dofW(pfem)
{
m_bshellb = false;
// get the degrees of freedom
// TODO: Can this be done in Init, since there is no error checking
if (pfem)
{
m_dofU.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::DISPLACEMENT));
m_dofSU.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::SHELL_DISPLACEMENT));
m_dofW.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::RELATIVE_FLUID_VELOCITY));
m_dofEF = pfem->GetDOFIndex(FEBioFSI::GetVariableName(FEBioFSI::FLUID_DILATATION), 0);
m_dof.Clear();
m_dof.AddDofs(m_dofU);
m_dof.AddDofs(m_dofSU);
m_dof.AddDofs(m_dofW);
m_dof.AddDof(m_dofEF);
}
}
//-----------------------------------------------------------------------------
//! initialize
bool FEBiphasicFSITraction::Init()
{
FESurface& surf = GetSurface();
surf.SetShellBottom(m_bshellb);
surf.SetInterfaceStatus(true);
if (FESurfaceLoad::Init() == false) return false;
// get the list of fluid-FSI elements connected to this interface
FEModel* fem = GetFEModel();
int NF = surf.Elements();
m_elem.resize(NF);
m_s.resize(NF, 1);
for (int j = 0; j<NF; ++j)
{
bool bself = false;
FESurfaceElement& el = surf.Element(j);
// extract the first of two elements on this interface
m_elem[j] = el.m_elem[0].pe;
if (el.m_elem[1].pe == nullptr) bself = true;
// get its material and check if FEBiphasicFSI
FEMaterial* pm = fem->GetMaterial(m_elem[j]->GetMatID());
FEBiphasicFSI* pfsi = dynamic_cast<FEBiphasicFSI*>(pm);
if (pfsi) {
double s = m_psurf->FacePointing(el, *m_elem[j]);
m_s[j] = bself ? -s : s;
if (m_s[j] == 0) return false;
}
else if (!bself) {
// extract the second of two elements on this interface
m_elem[j] = el.m_elem[1].pe;
pm = fem->GetMaterial(m_elem[j]->GetMatID());
pfsi = dynamic_cast<FEBiphasicFSI*>(pm);
if (pfsi == nullptr) return false;
m_s[j] = m_psurf->FacePointing(el, *m_elem[j]);
if (m_s[j] == 0) return false;
}
else
return false;
}
// TODO: Deal with the case when the surface is a shell domain separating two FSI domains
// that use different fluid bulk moduli
return true;
}
//-----------------------------------------------------------------------------
double FEBiphasicFSITraction::GetFluidDilatation(FESurfaceMaterialPoint& mp, double alpha)
{
double ef = 0;
FESurfaceElement& el = *mp.SurfaceElement();
double* H = el.H(mp.m_index);
int neln = el.Nodes();
for (int j = 0; j < neln; ++j) {
FENode& node = m_psurf->Node(el.m_lnode[j]);
double ej = node.get(m_dofEF)*alpha + node.get_prev(m_dofEF)*(1.0 - alpha);
ef += ej*H[j];
}
return ef;
}
//-----------------------------------------------------------------------------
mat3ds FEBiphasicFSITraction::GetFluidStress(FESurfaceMaterialPoint& pt)
{
FEModel* fem = GetFEModel();
FESurfaceElement& face = *pt.SurfaceElement();
int iel = face.m_lid;
// Get the fluid stress from the fluid-FSI element
mat3ds sv(mat3dd(0));
FEElement* pe = m_elem[iel];
int nint = pe->GaussPoints();
FEBiphasicFSI* pfsi = dynamic_cast<FEBiphasicFSI*>(fem->GetMaterial(pe->GetMatID()));
for (int n = 0; n<nint; ++n)
{
FEMaterialPoint& mp = *pe->GetMaterialPoint(n);
sv += pfsi->Fluid()->GetViscous()->Stress(mp);
}
sv /= nint;
return sv;
}
//-----------------------------------------------------------------------------
void FEBiphasicFSITraction::LoadVector(FEGlobalVector& R)
{
const FETimeInfo& tp = GetTimeInfo();
// If surface is bottom of shell, we should take shell displacement dofs (i.e. m_dofSU).
FEDofList dof = m_bshellb ? m_dofSU : m_dofU;
m_psurf->LoadVector(R, dof, false, [&](FESurfaceMaterialPoint& mp, const FESurfaceDofShape& dof_a, vector<double>& fa) {
// get the surface element
FESurfaceElement& el = *mp.SurfaceElement();
int iel = el.m_lid;
FEBiphasicFSI* pfsi = dynamic_cast<FEBiphasicFSI*>(GetFEModel()->GetMaterial(m_elem[iel]->GetMatID()));
// nodal coordinates
vec3d rt[FEElement::MAX_NODES];
m_psurf->GetNodalCoordinates(el, tp.alphaf, rt);
// evaluate covariant basis vectors at integration point
vec3d gr = el.eval_deriv1(rt, mp.m_index)*m_s[iel];
vec3d gs = el.eval_deriv2(rt, mp.m_index);
vec3d gt = gr ^ gs;
// Get the fluid stress at integration point
// necessarily using the attached solid element
mat3ds sv = GetFluidStress(mp);
// fluid dilatation at integration point
// only from surface element
double ef = GetFluidDilatation(mp, tp.alphaf);
double p = pfsi->Fluid()->Pressure(ef);
// evaluate traction
vec3d f = gt*p - sv*gt;
double H = dof_a.shape;
fa[0] = H * f.x;
fa[1] = H * f.y;
fa[2] = H * f.z;
});
}
//-----------------------------------------------------------------------------
void FEBiphasicFSITraction::StiffnessMatrix(FELinearSystem& LS)
{
const FETimeInfo& tp = GetTimeInfo();
FEModel* fem = GetFEModel();
FESurface* ps = &GetSurface();
// build dof list
// TODO: If surface is bottom of shell, we should take shell displacement dofs (i.e. m_dofSU).
FEDofList dofs(fem);
if (!m_bshellb) dofs.AddDofs(m_dofU); else dofs.AddDofs(m_dofSU);
dofs.AddDofs(m_dofW);
dofs.AddDof(m_dofEF);
// evaluate stiffness
m_psurf->LoadStiffness(LS, dofs, dofs, [&](FESurfaceMaterialPoint& mp, const FESurfaceDofShape& dof_a, const FESurfaceDofShape& dof_b, matrix& Kab) {
FESurfaceElement& el = *mp.SurfaceElement();
int iel = el.m_lid;
int neln = el.Nodes();
double dt = tp.timeIncrement;
double alpha = tp.alphaf;
double a = tp.gamma / (tp.beta*dt);
vector<vec3d> gradN(neln);
// nodal coordinates
vec3d rt[FEElement::MAX_NODES];
ps->GetNodalCoordinates(el, tp.alphaf, rt);
// Get the fluid stress and its tangents from the fluid-FSI element
mat3ds sv(mat3dd(0)), svJ(mat3dd(0));
tens4ds cv; cv.zero();
mat3d Ls; Ls.zero();
mat3d Dw; Dw.zero();
double phif=0.0;
double phis=0.0;
double J=0.0;
vec3d gradphif = vec3d(0.0);
vec3d gradJ = vec3d(0.0);
FEElement* pe = m_elem[iel];
int pint = pe->GaussPoints();
FEBiphasicFSI* pfsi = dynamic_cast<FEBiphasicFSI*>(fem->GetMaterial(pe->GetMatID()));
for (int n = 0; n<pint; ++n)
{
FEMaterialPoint& mp = *pe->GetMaterialPoint(n);
FEElasticMaterialPoint& ep = *(mp.ExtractData<FEElasticMaterialPoint>());
FEBiphasicFSIMaterialPoint& ft = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
sv += pfsi->Fluid()->GetViscous()->Stress(mp);
svJ += pfsi->Fluid()->GetViscous()->Tangent_Strain(mp);
cv += pfsi->Fluid()->Tangent_RateOfDeformation(mp);
Ls += ep.m_L;
phif += pfsi->Porosity(mp);
phis += pfsi->SolidVolumeFrac(mp);
gradphif += pfsi->gradPorosity(mp);
gradJ += ft.m_gradJ;
Dw += ft.m_Lw.sym();
J += ep.m_J;
}
sv /= pint;
svJ /= pint;
cv /= pint;
Ls /= pint;
phif /= pint;
phis /=pint;
gradphif /=pint;
gradJ /=pint;
Dw /=pint;
J /=pint;
mat3d M = mat3dd(a) - Ls;
double* N = el.H (mp.m_index);
double* Gr = el.Gr(mp.m_index);
double* Gs = el.Gs(mp.m_index);
// evaluate fluid dilatation
double ef = GetFluidDilatation(mp, tp.alphaf);
// covariant basis vectors
vec3d gr = el.eval_deriv1(rt, mp.m_index)*m_s[iel];
vec3d gs = el.eval_deriv2(rt, mp.m_index);
vec3d gt = gr ^ gs;
// evaluate fluid pressure
double p = pfsi->Fluid()->Pressure(ef);
vec3d f = gt*pfsi->Fluid()->GetElastic()->Tangent_Strain(ef, 0);
//TODO include second order gradgrad term for surface
vec3d gcnt[2], gcntp[2];
ps->ContraBaseVectors(el, mp.m_index, gcnt);
ps->ContraBaseVectorsP(el, mp.m_index, gcntp);
for (int i = 0; i<neln; ++i)
gradN[i] = ((gcnt[0] * alpha + gcntp[0] * (1 - alpha))*(Gr[i]*m_s[iel]) +
(gcnt[1] * alpha + gcntp[1] * (1 - alpha))*Gs[i]);
// calculate stiffness component
int i = dof_a.index;
int j = dof_b.index;
vec3d v = gr*Gs[j] - gs*Gr[j];
mat3d A; A.skew(v);
mat3d Kv1 = vdotTdotv(gt, cv, gradN[j]);
mat3d Kv2 = vdotTdotv(gt, cv, gradN[j]);
mat3d Kw = vdotTdotv(gt, cv, (gradN[j]-gradphif*N[j]/phif)/phif);
mat3d Kuu = (sv*A + Kv1*(-Dw*phis/(phif*phif)+M) + Kv2*((gradphif&gradN[j])*2.0*phis/(phif*phif*phif)+(gradN[j]&gradphif)/(phif*phif)) - Kv2*(-gradJ&gradN[j])/J*phis/(phif*phif) - ((sv*gt)&gradN[j])*phis/phif)*N[i] - A*(N[i] * p); Kuu *= -alpha;
mat3d Kuw = Kw*N[i]; Kuw *= -alpha;
vec3d kuJ = svJ*gt*(N[i] * N[j]) - f*(N[i] * N[j]); kuJ *= -alpha;
Kab.zero();
Kab.sub(0, 0, Kuu);
Kab.sub(0, 3, Kuw);
Kab[0][6] -= kuJ.x;
Kab[1][6] -= kuJ.y;
Kab[2][6] -= kuJ.z;
});
}
//-----------------------------------------------------------------------------
void FEBiphasicFSITraction::Serialize(DumpStream& ar)
{
FESurfaceLoad::Serialize(ar);
ar & m_s;
if (ar.IsShallow() == false)
{
if (ar.IsSaving())
{
int NE = (int)m_elem.size();
ar << NE;
for (int i = 0; i < NE; ++i)
{
FEElement* pe = m_elem[i];
int nid = (pe ? pe->GetID() : -1);
ar << nid;
}
}
else
{
FEMesh& mesh = ar.GetFEModel().GetMesh();
int NE, nid;
ar >> NE;
m_elem.resize(NE, nullptr);
for (int i = 0; i < NE; ++i)
{
ar >> nid;
if (nid != -1)
{
FEElement* pe = mesh.FindElementFromID(nid);
assert(pe);
m_elem[i] = pe;
}
}
}
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEPrescribedFluidDilatation.cpp | .cpp | 1,977 | 47 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEPrescribedFluidDilatation.h"
//=======================================================================================
// NOTE: I'm setting FEBoundaryCondition is the base class since I don't want to pull
// in the parameters of FEPrescribedDOF.
BEGIN_FECORE_CLASS(FEPrescribedFluidDilatation, FEBoundaryCondition)
ADD_PARAMETER(m_scale, "value")->SetFlags(FE_PARAM_ADDLC | FE_PARAM_VOLATILE);
ADD_PARAMETER(m_brelative, "relative");
END_FECORE_CLASS();
FEPrescribedFluidDilatation::FEPrescribedFluidDilatation(FEModel* fem) : FEPrescribedDOF(fem)
{
}
bool FEPrescribedFluidDilatation::Init()
{
SetDOF(GetDOFIndex("ef"));
return FEPrescribedDOF::Init();
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidSolutesNaturalFlux.h | .h | 2,504 | 74 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESurfaceLoad.h>
#include "febiofluid_api.h"
#include "FEFluidSolutes.h"
//-----------------------------------------------------------------------------
//! Backflow stabilization prescribes a normal traction that opposes
//! backflow on a boundary surface.
class FEBIOFLUID_API FEFluidSolutesNaturalFlux : public FESurfaceLoad
{
public:
//! constructor
FEFluidSolutesNaturalFlux(FEModel* pfem);
//! Initialization
bool Init() override;
//! serialization
void Serialize(DumpStream& ar) override;
//! Set the surface to apply the load to
void SetSurface(FESurface* ps) override;
void SetSolute(int isol) { m_isol = isol; }
//! calculate flux stiffness
void StiffnessMatrix(FELinearSystem& LS) override;
//! calculate residual
void LoadVector(FEGlobalVector& R) override;
//! update
void Update() override;
protected:
int m_isol; //!< solute index
bool m_bup; //!< flag to call Update function
// degrees of freedom
FEDofList m_dofW;
FEDofList m_dofEF;
FEDofList m_dofC;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEPrescribedFluidTemperature.h | .h | 1,494 | 37 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FEPrescribedDOF.h>
class FEPrescribedFluidTemperature : public FEPrescribedDOF
{
public:
FEPrescribedFluidTemperature(FEModel* fem);
bool Init() override;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEMultiphasicFSIPressureBC.cpp | .cpp | 7,132 | 185 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEMultiphasicFSIPressureBC.h"
#include "FEMultiphasicFSI.h"
#include "FEBioMultiphasicFSI.h"
#include <FECore/FEModel.h>
//=============================================================================
BEGIN_FECORE_CLASS(FEMultiphasicFSIPressureBC, FEPrescribedSurface)
ADD_PARAMETER(m_p, "pressure")->setUnits("P")->setLongName("fluid pressure");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! constructor
FEMultiphasicFSIPressureBC::FEMultiphasicFSIPressureBC(FEModel* pfem) : FEPrescribedSurface(pfem)
{
m_p = 0;
m_dofEF = -1;
m_dofC = -1;
m_Rgas = 0;
m_Tabs = 0;
}
//-----------------------------------------------------------------------------
//! initialize
bool FEMultiphasicFSIPressureBC::Init()
{
m_dofEF = GetDOFIndex(FEBioMultiphasicFSI::GetVariableName(FEBioMultiphasicFSI::FLUID_DILATATION), 0);
m_dofC = GetDOFIndex(FEBioMultiphasicFSI::GetVariableName(FEBioMultiphasicFSI::FLUID_CONCENTRATION), 0);
SetDOFList(m_dofEF);
if (FEPrescribedSurface::Init() == false) return false;
m_Rgas = GetFEModel()->GetGlobalConstant("R");
m_Tabs = GetFEModel()->GetGlobalConstant("T");
m_e.assign(GetSurface()->Nodes(), 0.0);
return true;
}
//-----------------------------------------------------------------------------
//! Evaluate and prescribe the resistance pressure
void FEMultiphasicFSIPressureBC::Update()
{
// prescribe this dilatation at the nodes
FESurface* ps = GetSurface();
int N = ps->Nodes();
std::vector<vector<double>> efNodes(N, vector<double>());
std::vector<vector<double>> caNodes(N, vector<double>());
//Project sum of all ca and osc values from int points to nodes on surface
//All values put into map, including duplicates
for (int i=0; i<ps->Elements(); ++i)
{
FESurfaceElement& el = ps->Element(i);
// evaluate average prescribed pressure on this face
double p = 0;
for (int j=0; j<el.GaussPoints(); ++j) {
FEMaterialPoint* pt = el.GetMaterialPoint(j);
p += m_p(*pt);
}
p /= el.GaussPoints();
FEElement* e = el.m_elem[0].pe;
FEMaterial* pm = GetFEModel()->GetMaterial(e->GetMatID());
FEFluid* pfl = pm->ExtractProperty<FEFluid>();
FESoluteInterface* psi = pm->ExtractProperty<FESoluteInterface>();
FESolidElement* se = dynamic_cast<FESolidElement*>(e);
if (se) {
double efo[FEElement::MAX_NODES] = {0};
if (psi) {
const int nsol = psi->Solutes();
std::vector<double> kappa(nsol,0);
double osc = 0;
const int nint = se->GaussPoints();
// get the average osmotic coefficient and partition coefficients in the solid element
for (int j=0; j<nint; ++j) {
FEMaterialPoint* pt = se->GetMaterialPoint(j);
osc += psi->GetOsmoticCoefficient()->OsmoticCoefficient(*pt);
for (int k=0; k<nsol; ++k)
kappa[k] += psi->GetPartitionCoefficient(*pt, k);
}
osc /= nint;
for (int k=0; k<nsol; ++k) kappa[k] /= nint;
// loop over face nodes
for (int j=0; j<el.Nodes(); ++j) {
double osm = 0;
FENode& node = ps->Node(el.m_lnode[j]);
// calculate osmolarity at this node, using nodal effective solute concentrations
for (int k=0; k<nsol; ++k)
osm += node.get(m_dofC+psi->GetSolute(k)->GetSoluteID()-1)*kappa[k];
// evaluate dilatation at this node
bool good = pfl->Dilatation(0, p - m_Rgas*m_Tabs*osc*osm, efo[j]);
assert(good);
}
}
else {
// loop over face nodes
for (int j=0; j<el.Nodes(); ++j) {
FENode& node = ps->Node(el.m_lnode[j]);
// evaluate dilatation at this node
bool good = pfl->Dilatation(0, p, efo[j]);
assert(good);
}
}
// only keep the dilatations at the nodes of the surface face
for (int j=0; j<el.Nodes(); ++j)
efNodes[el.m_lnode[j]].push_back(efo[j]);
}
//If no solid element, insert all 0s
else {
for (int j=0; j<el.Nodes(); ++j)
efNodes[el.m_lnode[j]].push_back(0);
}
}
//For each node, average the nodal ef
for (int i=0; i<ps->Nodes(); ++i)
{
double ef = 0;
for (int j = 0; j < efNodes[i].size(); ++j)
ef += efNodes[i][j];
ef /= efNodes[i].size();
// store value for now
m_e[i] = ef;
}
FEPrescribedSurface::Update();
}
//-----------------------------------------------------------------------------
// return the value for node i, dof j
void FEMultiphasicFSIPressureBC::GetNodalValues(int nodelid, std::vector<double>& val)
{
val[0] = m_e[nodelid];
}
//-----------------------------------------------------------------------------
// copy data from another class
void FEMultiphasicFSIPressureBC::CopyFrom(FEBoundaryCondition* pbc)
{
// TODO: implement this
assert(false);
}
//-----------------------------------------------------------------------------
//! serialization
void FEMultiphasicFSIPressureBC::Serialize(DumpStream& ar)
{
FEPrescribedSurface::Serialize(ar);
if (ar.IsLoading()) {
m_e.assign(GetSurface()->Nodes(), 0.0);
}
ar & m_e;
if (ar.IsShallow()) return;
ar & m_Rgas & m_Tabs;
ar & m_dofEF & m_dofC;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidFSIDomain.h | .h | 3,177 | 82 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "febiofluid_api.h"
class FEModel;
class FELinearSystem;
class FEBodyForce;
class FEGlobalVector;
class FETimeInfo;
//-----------------------------------------------------------------------------
//! Abstract interface class for fluid-FSI domains.
//! A fluid-FSI domain is used by the fluid-FSI solver.
//! This interface defines the functions that have to be implemented by a
//! fluid-FSI domain. There are basically two categories: residual functions
//! that contribute to the global residual vector. And stiffness matrix
//! function that calculate contributions to the global stiffness matrix.
class FEBIOFLUID_API FEFluidFSIDomain
{
public:
FEFluidFSIDomain(FEModel* pfem);
virtual ~FEFluidFSIDomain(){}
// --- R E S I D U A L ---
//! calculate the internal forces
virtual void InternalForces(FEGlobalVector& R) = 0;
//! Calculate the body force vector
virtual void BodyForce(FEGlobalVector& R, FEBodyForce& bf) = 0;
//! calculate the interial forces (for dynamic problems)
virtual void InertialForces(FEGlobalVector& R) = 0;
// --- S T I F F N E S S M A T R I X ---
//! Calculate global stiffness matrix (only contribution from internal force derivative)
//! \todo maybe I should rename this the InternalStiffness matrix?
virtual void StiffnessMatrix (FELinearSystem& LS) = 0;
//! Calculate stiffness contribution of body forces
virtual void BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf) = 0;
//! calculate the mass matrix (for dynamic problems)
virtual void MassMatrix(FELinearSystem& LS) = 0;
//! transient analysis
void SetTransientAnalysis() { m_btrans = true; }
void SetSteadyStateAnalysis() { m_btrans = false; }
protected:
bool m_btrans; // flag for transient (true) or steady-state (false) analysis
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FESolutesDomain.cpp | .cpp | 17,701 | 571 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FESolutesDomain.h"
#include "FECore/log.h"
#include "FECore/DOFS.h"
#include <FECore/FEModel.h>
#include <FECore/FEAnalysis.h>
#include <FECore/sys.h>
#include "FEBioFluidSolutes.h"
#include <FECore/FELinearSystem.h>
//-----------------------------------------------------------------------------
//! constructor
//! Some derived classes will pass 0 to the pmat, since the pmat variable will be
//! to initialize another material. These derived classes will set the m_pMat variable as well.
FESolutesDomain::FESolutesDomain(FEModel* pfem) : FESolidDomain(pfem), m_dof(pfem)
{
m_pMat = 0;
m_btrans = true;
m_dofC = pfem->GetDOFIndex(FEBioFluidSolutes::GetVariableName(FEBioFluidSolutes::FLUID_CONCENTRATION), 0);
m_dofAC = pfem->GetDOFIndex(FEBioFluidSolutes::GetVariableName(FEBioFluidSolutes::FLUID_CONCENTRATION_TDERIV), 0);
// list the degrees of freedom
// (This allows the FEDomain base class to handle several tasks such as UnpackLM)
// vector<int> dof;
// SetDOFList(dof);
}
//-----------------------------------------------------------------------------
//! get the total dofs
const FEDofList& FESolutesDomain::GetDOFList() const
{
return m_dof;
}
//-----------------------------------------------------------------------------
//! Assign material
void FESolutesDomain::SetMaterial(FEMaterial* pmat)
{
FEDomain::SetMaterial(pmat);
if (pmat)
{
m_pMat = dynamic_cast<FESolutesMaterial*>(pmat);
assert(m_pMat);
}
else m_pMat = 0;
}
//-----------------------------------------------------------------------------
bool FESolutesDomain::Init()
{
// initialize base class
if (FESolidDomain::Init() == false) return false;
const int nsol = m_pMat->Solutes();
// set the active degrees of freedom list
m_dof.Clear();
for (int i = 0; i<nsol; ++i)
{
int m = m_pMat->GetSolute(i)->GetSoluteDOF();
m_dof.AddDof(m_dofC + m);
}
return true;
}
//-----------------------------------------------------------------------------
void FESolutesDomain::Reset()
{
// reset base class
FESolidDomain::Reset();
const int nsol = m_pMat->Solutes();
for (int i = 0; i<(int)m_Elem.size(); ++i)
{
// get the solid element
FESolidElement& el = m_Elem[i];
// get the number of integration points
int nint = el.GaussPoints();
// loop over the integration points
for (int n = 0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FESolutesMaterial::Point& ps = *(mp.ExtractData<FESolutesMaterial::Point>());
// initialize solutes
ps.m_nsol = nsol;
ps.m_c.assign(nsol,0);
ps.m_ca.assign(nsol,0);
ps.m_cdot.assign(nsol,0);
ps.m_gradc.assign(nsol,vec3d(0,0,0));
ps.m_j.assign(nsol,vec3d(0,0,0));
ps.m_k.assign(nsol, 0);
ps.m_dkdJ.assign(nsol, 0);
ps.m_dkdc.resize(nsol, vector<double>(nsol,0));
for (int j=0; j<m_pMat->Reactions(); ++j)
m_pMat->GetReaction(j)->ResetElementData(mp);
}
}
}
//-----------------------------------------------------------------------------
void FESolutesDomain::Serialize(DumpStream& ar)
{
FESolidDomain::Serialize(ar);
if (ar.IsShallow()) return;
ar & m_pMat;
ar & m_dofC & m_dofAC;
ar & m_dof;
}
//-----------------------------------------------------------------------------
void FESolutesDomain::Activate()
{
const int nsol = m_pMat->Solutes();
for (int i = 0; i<Nodes(); ++i)
{
FENode& node = Node(i);
if (node.HasFlags(FENode::EXCLUDE) == false)
{
for (int isol = 0; isol<nsol; ++isol)
node.set_active(m_dofC + m_pMat->GetSolute(isol)->GetSoluteDOF());
}
}
}
//-----------------------------------------------------------------------------
void FESolutesDomain::InitMaterialPoints()
{
const int nsol = m_pMat->Solutes();
FEMesh& m = *GetMesh();
const int NE = FEElement::MAX_NODES;
vector< vector<double> > c0(nsol, vector<double>(NE));
vector<int> sid(nsol);
for (int j = 0; j<nsol; ++j) sid[j] = m_pMat->GetSolute(j)->GetSoluteDOF();
for (int j = 0; j<(int)m_Elem.size(); ++j)
{
// get the solid element
FESolidElement& el = m_Elem[j];
// get the number of nodes
int neln = el.Nodes();
// get initial values of fluid pressure and solute concentrations
for (int i = 0; i<neln; ++i)
{
FENode& ni = m.Node(el.m_node[i]);
for (int isol = 0; isol<nsol; ++isol)
c0[isol][i] = ni.get(m_dofC + sid[isol]);
}
// get the number of integration points
int nint = el.GaussPoints();
// loop over the integration points
for (int n = 0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FESolutesMaterial::Point& ps = *(mp.ExtractData<FESolutesMaterial::Point>());
// initialize solutes
ps.m_nsol = nsol;
// initialize effective solute concentrations
for (int isol = 0; isol<nsol; ++isol) {
ps.m_c[isol] = el.Evaluate(c0[isol], n);
ps.m_ca[isol] = m_pMat->ConcentrationActual(mp, isol);
ps.m_gradc[isol] = gradient(el, c0[isol], n);
}
for (int isol = 0; isol<nsol; ++isol)
ps.m_j[isol] = m_pMat->SoluteFlux(mp, isol);
}
}
}
//-----------------------------------------------------------------------------
//! Initialize element data
void FESolutesDomain::PreSolveUpdate(const FETimeInfo& timeInfo)
{
const int NE = FEElement::MAX_NODES;
vec3d x0[NE], r0, v;
FEMesh& m = *GetMesh();
for (size_t i = 0; i<m_Elem.size(); ++i)
{
FESolidElement& el = m_Elem[i];
int neln = el.Nodes();
for (int i = 0; i<neln; ++i)
{
x0[i] = m.Node(el.m_node[i]).m_r0;
}
int n = el.GaussPoints();
for (int j = 0; j<n; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
mp.m_r0 = el.Evaluate(x0, j);
// reset chemical reaction element data
for (int j=0; j<m_pMat->Reactions(); ++j)
m_pMat->GetReaction(j)->InitializeElementData(mp);
mp.Update(timeInfo);
}
}
}
//-----------------------------------------------------------------------------
void FESolutesDomain::InternalForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i = 0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int nsol = m_pMat->Solutes();
int ndof = nsol*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInternalForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the internal equivalent nodal forces for solid elements
void FESolutesDomain::ElementInternalForce(FESolidElement& el, vector<double>& fe)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
// jacobian matrix, inverse jacobian matrix and determinants
double Ji[3][3];
// get the time step size
double dt = tp.timeIncrement;
// number of solutes
const int nsol = m_pMat->Solutes();
const int nreact = m_pMat->Reactions();
// gradient of shape functions
int neln = el.Nodes();
vector<vec3d> gradN(neln);
// repeat for all integration points
int nint = el.GaussPoints();
double* gw = el.GaussWeights();
for (int n = 0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FESolutesMaterial::Point& spt = *(mp.ExtractData<FESolutesMaterial::Point>());
// calculate the jacobian
double detJ = invjac0(el, Ji, n)*gw[n];
vec3d g1(Ji[0][0], Ji[0][1], Ji[0][2]);
vec3d g2(Ji[1][0], Ji[1][1], Ji[1][2]);
vec3d g3(Ji[2][0], Ji[2][1], Ji[2][2]);
double* H = el.H(n);
double* Gr = el.Gr(n);
double* Gs = el.Gs(n);
double* Gt = el.Gt(n);
// evaluate spatial gradient of shape functions
for (int i = 0; i<neln; ++i)
{
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
}
vector<double> kappa(spt.m_k);
double osmc;
osmc = m_pMat->GetOsmoticCoefficient()->OsmoticCoefficient(mp);
// Miscellaneous constants
double R = m_pMat->m_Rgas;
double T = m_pMat->m_Tabs;
// evaluate the chat
vector<double> chat(nsol,0);
double phiwhat = 0;
// chemical reactions
for (int i=0; i<nreact; ++i) {
FEChemicalReaction* pri = m_pMat->GetReaction(i);
double zhat = pri->ReactionSupply(mp);
phiwhat += pri->m_Vbar*zhat;
for (int isol=0; isol<nsol; ++isol)
{
chat[isol] += zhat*pri->m_v[isol];
}
}
for (int i = 0; i<neln; ++i)
{
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
for (int isol = 0; isol<nsol; ++isol)
fe[nsol*i + isol] -= (spt.m_j[isol]*gradN[i] - H[i]*(spt.m_cdot[isol]*kappa[isol] - chat[isol]))*detJ;
}
}
}
//-----------------------------------------------------------------------------
//! Calculates element material stiffness element matrix
void FESolutesDomain::ElementStiffness(FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
const int nsol = m_pMat->Solutes();
const int nreact = m_pMat->Reactions();
// gradient of shape functions
vector<vec3d> gradN(neln);
double dt = tp.timeIncrement;
double ksi = tp.alpham / (tp.gamma*tp.alphaf);
// jacobian
double Ji[3][3];
// weights at gauss points
const double *gw = el.GaussWeights();
// calculate element stiffness matrix
for (int n = 0; n<nint; ++n)
{
// calculate jacobian
double detJ = invjac0(el, Ji, n)*gw[n];
vec3d g1(Ji[0][0], Ji[0][1], Ji[0][2]);
vec3d g2(Ji[1][0], Ji[1][1], Ji[1][2]);
vec3d g3(Ji[2][0], Ji[2][1], Ji[2][2]);
double* H = el.H(n);
double* Gr = el.Gr(n);
double* Gs = el.Gs(n);
double* Gt = el.Gt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FESolutesMaterial::Point& spt = *(mp.ExtractData<FESolutesMaterial::Point>());
double R = m_pMat->m_Rgas;
double T = m_pMat->m_Tabs;
double osmc;
osmc = m_pMat->GetOsmoticCoefficient()->OsmoticCoefficient(mp);
double dodJ = m_pMat->GetOsmoticCoefficient()->Tangent_OsmoticCoefficient_Strain(mp);
vector<double> dodc(nsol);
for (int isol=0; isol<nsol; ++isol)
dodc[isol] = m_pMat->GetOsmoticCoefficient()->Tangent_OsmoticCoefficient_Concentration(mp,isol);
// evaluate the chat
vector<vector<double>> dchatdc(nsol,vector<double>(nsol,0));
vector<double> dphiwhatdc(nsol,0);
// chemical reactions
for (int i=0; i<nreact; ++i) {
for (int isol = 0; isol < nsol; ++isol){
dphiwhatdc[isol] += m_pMat->GetReaction(i)->m_Vbar
*m_pMat->GetReaction(i)->Tangent_ReactionSupply_Concentration(mp,isol);
for (int jsol = 0; jsol < nsol; ++jsol){
dchatdc[isol][jsol] += m_pMat->GetReaction(i)->m_v[isol]
*m_pMat->GetReaction(i)->Tangent_ReactionSupply_Concentration(mp,jsol);
}
}
}
// evaluate spatial gradient of shape functions
for (int i = 0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate stiffness matrix
for (int i = 0; i<neln; ++i)
{
for (int j = 0; j<neln; ++j)
{
for (int isol = 0; isol<nsol; ++isol) {
for(int jsol=0; jsol<nsol; ++jsol){
double kcc = 0;
double d0p = m_pMat->GetSolute(isol)->m_pDiff->Tangent_Free_Diffusivity_Concentration(mp, jsol);
double d0 = m_pMat->GetSolute(isol)->m_pDiff->Free_Diffusivity(mp);
double kappa = spt.m_k[isol];
if (isol == jsol)
//TODO: add partition coeff terms
kcc = -(ksi/dt*m_btrans*kappa-dchatdc[isol][jsol])*H[i]*H[j]-gradN[i]*spt.m_gradc[isol]*H[j]*d0p+gradN[i]*(-gradN[j]*d0+spt.m_vft*H[j]);
else
kcc = H[i]*H[j]*dchatdc[isol][jsol] + (-gradN[i]*spt.m_gradc[isol]*d0p)*H[j];
ke[i*nsol + isol][j*nsol + jsol] += kcc*detJ;
}
}
}
}
}
}
//-----------------------------------------------------------------------------
void FESolutesDomain::StiffnessMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel = 0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int nsol = m_pMat->Solutes();
int ndof = nsol*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate material stiffness
ElementStiffness(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FESolutesDomain::Update(const FETimeInfo& tp)
{
bool berr = false;
int NE = (int)m_Elem.size();
#pragma omp parallel for shared(NE, berr)
for (int i = 0; i<NE; ++i)
{
try
{
UpdateElementStress(i, tp);
}
catch (NegativeJacobian e)
{
#pragma omp critical
{
// reset the logfile mode
berr = true;
if (NegativeJacobian::DoOutput()) feLogError(e.what());
}
}
}
if (berr) throw NegativeJacobianDetected();
}
//-----------------------------------------------------------------------------
//! Update element state data (mostly stresses, but some other stuff as well)
void FESolutesDomain::UpdateElementStress(int iel, const FETimeInfo& tp)
{
// time constants
double alphaf = tp.alphaf;
double alpham = tp.alpham;
// get the solid element
FESolidElement& el = m_Elem[iel];
// number of nodes
int neln = el.Nodes();
// number of solutes
const int nsol = m_pMat->Solutes();
// nodal coordinates
const int NELN = FEElement::MAX_NODES;
vector< vector<double> > ct(nsol, vector<double>(NELN));
vector< vector<double> > cp(nsol, vector<double>(NELN));
vector< vector<double> > act(nsol, vector<double>(NELN));
vector< vector<double> > acp(nsol, vector<double>(NELN));
vector<int> sid(nsol);
for (int j = 0; j<nsol; ++j) sid[j] = m_pMat->GetSolute(j)->GetSoluteDOF();
for (int j = 0; j<neln; ++j) {
FENode& node = m_pMesh->Node(el.m_node[j]);
for (int k = 0; k<nsol; ++k) {
ct[k][j] = node.get(m_dofC + sid[k]);
cp[k][j] = node.get_prev(m_dofC + sid[k]);
act[k][j] = node.get(m_dofAC + sid[k]);
acp[k][j] = node.get_prev(m_dofAC + sid[k]);
}
}
// loop over the integration points and update
// velocity, velocity gradient, acceleration
// stress and pressure at the integration point
int nint = el.GaussPoints();
for (int n = 0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FESolutesMaterial::Point& spt = *(mp.ExtractData<FESolutesMaterial::Point>());
// material point data
for (int isol = 0; isol < nsol; ++isol) {
spt.m_c[isol] = el.Evaluate(ct[isol], n)*alphaf + el.Evaluate(cp[isol], n)*(1 - alphaf);
spt.m_gradc[isol] = gradient(el, ct[isol], n)*alphaf + gradient(el, cp[isol], n)*(1 - alphaf);
spt.m_cdot[isol] = 0.0;
if (m_btrans) spt.m_cdot[isol] += el.Evaluate(act[isol], n)*alpham + el.Evaluate(acp[isol], n)*(1-alpham);
}
m_pMat->PartitionCoefficientFunctions(mp, spt.m_k, spt.m_dkdJ, spt.m_dkdc);
double R = m_pMat->m_Rgas;
double T = m_pMat->m_Tabs;
// calculate the solute flux
for (int isol = 0; isol < nsol; ++isol){
spt.m_j[isol] = m_pMat->SoluteFlux(mp, isol);
spt.m_ca[isol] = m_pMat->ConcentrationActual(mp, isol);
}
// update chemical reaction element data
for (int j=0; j<m_pMat->Reactions(); ++j)
m_pMat->GetReaction(j)->UpdateElementData(mp);
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEPolarFluidDomain3D.cpp | .cpp | 33,985 | 1,039 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2022 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEPolarFluidDomain3D.h"
#include "FEPolarFluidMaterialPoint.h"
#include "FEFluidSolver.h"
#include "FECore/log.h"
#include "FECore/DOFS.h"
#include <FECore/FEModel.h>
#include <FECore/FEAnalysis.h>
#include <FECore/sys.h>
#include "FEBioPolarFluid.h"
#include <FECore/FELinearSystem.h>
#include "FEBodyMoment.h"
//-----------------------------------------------------------------------------
//! constructor
//! Some derived classes will pass 0 to the pmat, since the pmat variable will be
//! to initialize another material. These derived classes will set the m_pMat variable as well.
FEPolarFluidDomain3D::FEPolarFluidDomain3D(FEModel* pfem) : FESolidDomain(pfem), FEPolarFluidDomain(pfem), m_dofW(pfem), m_dofAW(pfem), m_dofG(pfem), m_dofAG(pfem), m_dof(pfem)
{
m_pMat = 0;
m_btrans = true;
if (pfem)
{
m_dofW.AddVariable(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::RELATIVE_FLUID_VELOCITY));
m_dofAW.AddVariable(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::RELATIVE_FLUID_ACCELERATION));
m_dofG.AddVariable(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::FLUID_ANGULAR_VELOCITY));
m_dofAG.AddVariable(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::FLUID_ANGULAR_ACCELERATION));
m_dofEF = pfem->GetDOFIndex(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::FLUID_DILATATION), 0);
m_dofAEF = pfem->GetDOFIndex(FEBioPolarFluid::GetVariableName(FEBioPolarFluid::FLUID_DILATATION_TDERIV), 0);
FEDofList dofs(pfem);
dofs.AddDofs(m_dofW);
dofs.AddDofs(m_dofG);
dofs.AddDof(m_dofEF);
m_dof = dofs;
}
}
//-----------------------------------------------------------------------------
// \todo I don't think this is being used
FEPolarFluidDomain3D& FEPolarFluidDomain3D::operator = (FEPolarFluidDomain3D& d)
{
m_Elem = d.m_Elem;
m_pMesh = d.m_pMesh;
return (*this);
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::Serialize(DumpStream& ar)
{
FESolidDomain::Serialize(ar);
if (ar.IsShallow()) return;
ar & m_pMat;
ar & m_dofW & m_dofAW;
ar & m_dofG & m_dofAG;
ar & m_dof;
ar & m_dofEF & m_dofAEF;
}
//-----------------------------------------------------------------------------
// get total dof list
const FEDofList& FEPolarFluidDomain3D::GetDOFList() const
{
return m_dof;
}
//-----------------------------------------------------------------------------
//! Assign material
void FEPolarFluidDomain3D::SetMaterial(FEMaterial* pmat)
{
FEDomain::SetMaterial(pmat);
if (pmat)
{
m_pMat = dynamic_cast<FEPolarFluid*>(pmat);
assert(m_pMat);
}
else m_pMat = 0;
}
//-----------------------------------------------------------------------------
//! Initialize element data
void FEPolarFluidDomain3D::PreSolveUpdate(const FETimeInfo& timeInfo)
{
const int NE = FEElement::MAX_NODES;
vec3d x0[NE], r0, v;
FEMesh& m = *GetMesh();
for (size_t i=0; i<m_Elem.size(); ++i)
{
FESolidElement& el = m_Elem[i];
int neln = el.Nodes();
for (int i=0; i<neln; ++i)
{
x0[i] = m.Node(el.m_node[i]).m_r0;
}
int n = el.GaussPoints();
for (int j=0; j<n; ++j)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
pt.m_r0 = el.Evaluate(x0, j);
if (pt.m_ef <= -1) {
throw NegativeJacobianDetected();
}
mp.Update(timeInfo);
}
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::InternalForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i=0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInternalForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the internal equivalent nodal forces for solid elements
void FEPolarFluidDomain3D::ElementInternalForce(FESolidElement& el, vector<double>& fe)
{
int i, n;
// jacobian matrix, inverse jacobian matrix and determinants
double Ji[3][3], detJ;
const double *H, *Gr, *Gs, *Gt;
int nint = el.GaussPoints();
int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double* gw = el.GaussWeights();
FEViscousFluid* Viscous = m_pMat->GetViscous();
FEViscousPolarFluid* ViscPol = m_pMat->GetViscousPolar();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
// calculate the jacobian
detJ = invjac0(el, Ji, n)*gw[n];
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
// get the viscous stress tensor for this integration point
vec3d th = ViscPol->SkewStressDualVector(mp);
mat3d sva = mat3da(th);
mat3d sv = sva + Viscous->Stress(mp);
mat3d M = ViscPol->CoupleStress(mp);
// get the gradient of the elastic pressure
vec3d gradp = pt.m_gradef*m_pMat->Tangent_Pressure_Strain(mp);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
{
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
}
// Jdot/J
double dJoJ = pt.m_efdot/(pt.m_ef+1);
for (i=0; i<neln; ++i)
{
vec3d fv = sv*gradN[i] + gradp*H[i];
vec3d fg = M*gradN[i] - th*(2*H[i]);
double fJ = dJoJ*H[i] + gradN[i]*pt.m_vft;
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[7*i ] -= fv.x*detJ;
fe[7*i+1] -= fv.y*detJ;
fe[7*i+2] -= fv.z*detJ;
fe[7*i+3] -= fg.x*detJ;
fe[7*i+4] -= fg.y*detJ;
fe[7*i+5] -= fg.z*detJ;
fe[7*i+6] -= fJ*detJ;
}
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::BodyForce(FEGlobalVector& R, FEBodyForce& BF)
{
int NE = (int)m_Elem.size();
for (int i=0; i<NE; ++i)
{
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// apply body forces
ElementBodyForce(BF, el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the body forces
void FEPolarFluidDomain3D::ElementBodyForce(FEBodyForce& BF, FESolidElement& el, vector<double>& fe)
{
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d f;
// number of nodes
int neln = el.Nodes();
// nodal coordinates
vec3d r0[FEElement::MAX_NODES];
for (int i=0; i<neln; ++i)
r0[i] = m_pMesh->Node(el.m_node[i]).m_r0;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
double dens = m_pMat->Density(mp);
pt.m_r0 = el.Evaluate(r0, n);
detJ = detJ0(el, n)*gw[n];
// get the force
f = BF.force(mp);
H = el.H(n);
for (int i=0; i<neln; ++i)
{
fe[7*i ] -= H[i]*dens*f.x*detJ;
fe[7*i+1] -= H[i]*dens*f.y*detJ;
fe[7*i+2] -= H[i]*dens*f.z*detJ;
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the stiffness due to body forces
void FEPolarFluidDomain3D::ElementBodyForceStiffness(FEBodyForce& BF, FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int neln = el.Nodes();
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d f, k;
// gradient of shape functions
vec3d gradN;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
// calculate the jacobian
detJ = detJ0(el, n)*gw[n]*tp.alphaf;
H = el.H(n);
double dens = m_pMat->Density(mp);
// get the force
f = BF.force(mp);
H = el.H(n);
for (int i=0; i<neln; ++i) {
for (int j=0; j<neln; ++j)
{
k = f*(-H[i]*H[j]*dens/(pt.m_ef+1)*detJ);
ke[7*i ][7*j+6] += k.x;
ke[7*i+1][7*j+6] += k.y;
ke[7*i+2][7*j+6] += k.z;
}
}
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::BodyMoment(FEGlobalVector& R, FEBodyMoment& bm)
{
int NE = (int)m_Elem.size();
for (int i=0; i<NE; ++i)
{
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// apply body forces
ElementBodyMoment(bm, el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
//! calculates the body forces
void FEPolarFluidDomain3D::ElementBodyMoment(FEBodyMoment& bm, FESolidElement& el, vector<double>& fe)
{
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d m;
// number of nodes
int neln = el.Nodes();
// nodal coordinates
vec3d r0[FEElement::MAX_NODES];
for (int i=0; i<neln; ++i)
r0[i] = m_pMesh->Node(el.m_node[i]).m_r0;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
double dens = m_pMat->Density(mp);
pt.m_r0 = el.Evaluate(r0, n);
detJ = detJ0(el, n)*gw[n];
// get the moment
m = bm.moment(mp);
H = el.H(n);
for (int i=0; i<neln; ++i)
{
fe[7*i+3] -= H[i]*dens*m.x*detJ;
fe[7*i+4] -= H[i]*dens*m.y*detJ;
fe[7*i+5] -= H[i]*dens*m.z*detJ;
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the stiffness due to body moments
void FEPolarFluidDomain3D::ElementBodyMomentStiffness(FEBodyMoment& bm, FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int neln = el.Nodes();
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d m, k;
// gradient of shape functions
vec3d gradN;
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
// calculate the jacobian
detJ = detJ0(el, n)*gw[n]*tp.alphaf;
H = el.H(n);
double dens = m_pMat->Density(mp);
// get the force
m = bm.moment(mp);
H = el.H(n);
for (int i=0; i<neln; ++i) {
for (int j=0; j<neln; ++j)
{
k = m*(-H[i]*H[j]*dens/(pt.m_ef+1)*detJ);
ke[7*i+3][7*j+6] += k.x;
ke[7*i+4][7*j+6] += k.y;
ke[7*i+5][7*j+6] += k.z;
}
}
}
}
//-----------------------------------------------------------------------------
//! Calculates element material stiffness element matrix
void FEPolarFluidDomain3D::ElementStiffness(FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i7, j, j7, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double dt = tp.timeIncrement;
double ksi = tp.alpham/(tp.gamma*tp.alphaf);
double *H, *Gr, *Gs, *Gt;
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
FEViscousFluid* Viscous = m_pMat->GetViscous();
FEViscousPolarFluid* ViscPol = m_pMat->GetViscousPolar();
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjac0(el, Ji, n)*gw[n]*tp.alphaf;
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
double Jf = 1 + pt.m_ef;
// get the tangents
mat3d svJ = Viscous->Tangent_Strain(mp) + ViscPol->SkewTangent_Strain(mp);
vec3d thJ = ViscPol->SkewTangent_Strain(mp).vec();
tens4ds cvs = m_pMat->Tangent_RateOfDeformation(mp);
mat3d cva = ViscPol->SkewTangent_RateOfRotation(mp);
tens4d m = ViscPol->CoupleTangent_RateOfRotation(mp);
mat3d mJ = ViscPol->CoupleTangent_Strain(mp);
double dp = m_pMat->Tangent_Pressure_Strain(mp);
double d2p = m_pMat->Tangent_Pressure_Strain_Strain(mp);
// Jdot/J
double dJoJ = pt.m_efdot/Jf;
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate stiffness matrix
for (i=0, i7=0; i<neln; ++i, i7 += 7)
{
for (j=0, j7 = 0; j<neln; ++j, j7 += 7)
{
mat3da gNa(gradN[i]), gNb(gradN[j]);
mat3d Kvv = vdotTdotv(gradN[i], cvs, gradN[j]) + gNa*cva*gNb/2;
mat3d Kgv = cva*gNb*H[i];
vec3d kJv = (pt.m_gradef*(H[i]/Jf) + gradN[i])*H[j];
mat3d Kvg = -gNa*cva*H[j];
//! TODO: There may be a mistake in vdotTdotv when using tens4d object, evaluates as b.T.a instead of a.T.b
// mat3d Kgg = vdotTdotv(gradN[i], m, gradN[j])-cva*(2*H[i]*H[j]);
mat3d Kgg = vdotTdotv(gradN[j], m, gradN[i])-cva*(2*H[i]*H[j]);
vec3d kvJ = (svJ*gradN[i])*H[j] + (gradN[j]*dp+pt.m_gradef*(H[j]*d2p))*H[i];
vec3d kgJ = mJ*gradN[i]*H[j] - thJ*(2*H[i]*H[j]);
double kJJ = (H[j]*(ksi/dt - dJoJ) + gradN[j]*pt.m_vft)*H[i]/Jf;
ke[i7 ][j7 ] += Kvv(0,0)*detJ;
ke[i7 ][j7+1] += Kvv(0,1)*detJ;
ke[i7 ][j7+2] += Kvv(0,2)*detJ;
ke[i7 ][j7+3] += Kvg(0,0)*detJ;
ke[i7 ][j7+4] += Kvg(0,1)*detJ;
ke[i7 ][j7+5] += Kvg(0,2)*detJ;
ke[i7 ][j7+6] += kvJ.x*detJ;
ke[i7+1][j7 ] += Kvv(1,0)*detJ;
ke[i7+1][j7+1] += Kvv(1,1)*detJ;
ke[i7+1][j7+2] += Kvv(1,2)*detJ;
ke[i7+1][j7+3] += Kvg(1,0)*detJ;
ke[i7+1][j7+4] += Kvg(1,1)*detJ;
ke[i7+1][j7+5] += Kvg(1,2)*detJ;
ke[i7+1][j7+6] += kvJ.y*detJ;
ke[i7+2][j7 ] += Kvv(2,0)*detJ;
ke[i7+2][j7+1] += Kvv(2,1)*detJ;
ke[i7+2][j7+2] += Kvv(2,2)*detJ;
ke[i7+2][j7+3] += Kvg(2,0)*detJ;
ke[i7+2][j7+4] += Kvg(2,1)*detJ;
ke[i7+2][j7+5] += Kvg(2,2)*detJ;
ke[i7+2][j7+6] += kvJ.z*detJ;
ke[i7+3][j7 ] += Kgv(0,0)*detJ;
ke[i7+3][j7+1] += Kgv(0,1)*detJ;
ke[i7+3][j7+2] += Kgv(0,2)*detJ;
ke[i7+3][j7+3] += Kgg(0,0)*detJ;
ke[i7+3][j7+4] += Kgg(0,1)*detJ;
ke[i7+3][j7+5] += Kgg(0,2)*detJ;
ke[i7+3][j7+6] += kgJ.x*detJ;
ke[i7+4][j7 ] += Kgv(1,0)*detJ;
ke[i7+4][j7+1] += Kgv(1,1)*detJ;
ke[i7+4][j7+2] += Kgv(1,2)*detJ;
ke[i7+4][j7+3] += Kgg(1,0)*detJ;
ke[i7+4][j7+4] += Kgg(1,1)*detJ;
ke[i7+4][j7+5] += Kgg(1,2)*detJ;
ke[i7+4][j7+6] += kgJ.y*detJ;
ke[i7+5][j7 ] += Kgv(2,0)*detJ;
ke[i7+5][j7+1] += Kgv(2,1)*detJ;
ke[i7+5][j7+2] += Kgv(2,2)*detJ;
ke[i7+5][j7+3] += Kgg(2,0)*detJ;
ke[i7+5][j7+4] += Kgg(2,1)*detJ;
ke[i7+5][j7+5] += Kgg(2,2)*detJ;
ke[i7+5][j7+6] += kgJ.z*detJ;
ke[i7+6][j7 ] += kJv.x*detJ;
ke[i7+6][j7+1] += kJv.y*detJ;
ke[i7+6][j7+2] += kJv.z*detJ;
ke[i7+6][j7+6] += kJJ*detJ;
}
}
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::StiffnessMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate material stiffness
ElementStiffness(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::MassMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementMassMatrix(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementBodyForceStiffness(bf, el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::BodyMomentStiffness(FELinearSystem& LS, FEBodyMoment& bm)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementBodyMomentStiffness(bm, el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
//-----------------------------------------------------------------------------
//! calculates element inertial stiffness matrix
void FEPolarFluidDomain3D::ElementMassMatrix(FESolidElement& el, matrix& ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i7, j, j7, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double *H;
double *Gr, *Gs, *Gt;
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
double dt = tp.timeIncrement;
double ksi = tp.alpham/(tp.gamma*tp.alphaf)*m_btrans;
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjac0(el, Ji, n)*gw[n]*tp.alphaf;
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEPolarFluidMaterialPoint& pf = *(mp.ExtractData<FEPolarFluidMaterialPoint>());
double dens = m_pMat->Density(mp);
double kg = m_pMat->m_kg;
double moi = dens*kg*kg;
double J = 1+pt.m_ef;
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate stiffness matrix
for (i=0, i7=0; i<neln; ++i, i7 += 7)
{
for (j=0, j7 = 0; j<neln; ++j, j7 += 7)
{
mat3d Mv = ((mat3dd(ksi/dt) + pt.m_Lf)*H[j] + mat3dd(gradN[j]*pt.m_vft))*(H[i]*dens*detJ);
mat3d Jgg = mat3dd(ksi/dt*H[j] + gradN[j]*pt.m_vft)*(H[i]*moi*detJ);
mat3d Jgv = pf.m_Psi*(H[i]*H[j]*moi*detJ);
vec3d mJ = pt.m_aft*(-H[i]*H[j]*dens/J*detJ);
vec3d jJ = pf.m_gfdot*(-H[i]*H[j]*moi/J*detJ);
ke[i7 ][j7 ] += Mv(0,0);
ke[i7 ][j7+1] += Mv(0,1);
ke[i7 ][j7+2] += Mv(0,2);
ke[i7 ][j7+6] += mJ.x;
ke[i7+1][j7 ] += Mv(1,0);
ke[i7+1][j7+1] += Mv(1,1);
ke[i7+1][j7+2] += Mv(1,2);
ke[i7+1][j7+6] += mJ.y;
ke[i7+2][j7 ] += Mv(2,0);
ke[i7+2][j7+1] += Mv(2,1);
ke[i7+2][j7+2] += Mv(2,2);
ke[i7+2][j7+6] += mJ.z;
ke[i7+3][j7 ] += Jgv(0,0);
ke[i7+3][j7+1] += Jgv(0,1);
ke[i7+3][j7+2] += Jgv(0,2);
ke[i7+3][j7+3] += Jgg(0,0);
ke[i7+3][j7+4] += Jgg(0,1);
ke[i7+3][j7+5] += Jgg(0,2);
ke[i7+3][j7+6] += jJ.x;
ke[i7+4][j7 ] += Jgv(1,0);
ke[i7+4][j7+1] += Jgv(1,1);
ke[i7+4][j7+2] += Jgv(1,2);
ke[i7+4][j7+3] += Jgg(1,0);
ke[i7+4][j7+4] += Jgg(1,1);
ke[i7+4][j7+5] += Jgg(1,2);
ke[i7+4][j7+6] += jJ.y;
ke[i7+5][j7 ] += Jgv(2,0);
ke[i7+5][j7+1] += Jgv(2,1);
ke[i7+5][j7+2] += Jgv(2,2);
ke[i7+5][j7+3] += Jgg(2,0);
ke[i7+5][j7+4] += Jgg(2,1);
ke[i7+5][j7+5] += Jgg(2,2);
ke[i7+5][j7+6] += jJ.z;
}
}
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::Update(const FETimeInfo& tp)
{
bool berr = false;
int NE = (int) m_Elem.size();
#pragma omp parallel for shared(NE, berr)
for (int i=0; i<NE; ++i)
{
try
{
UpdateElementStress(i, tp);
}
catch (NegativeJacobian e)
{
#pragma omp critical
{
// reset the logfile mode
berr = true;
if (NegativeJacobian::DoOutput()) feLogError(e.what());
}
}
}
if (berr) throw NegativeJacobianDetected();
}
//-----------------------------------------------------------------------------
//! Update element state data (mostly stresses, but some other stuff as well)
void FEPolarFluidDomain3D::UpdateElementStress(int iel, const FETimeInfo& tp)
{
double alphaf = tp.alphaf;
double alpham = tp.alpham;
// get the solid element
FESolidElement& el = m_Elem[iel];
// get the number of integration points
int nint = el.GaussPoints();
// number of nodes
int neln = el.Nodes();
// nodal coordinates
const int NELN = FEElement::MAX_NODES;
vec3d vt[NELN], vp[NELN];
vec3d at[NELN], ap[NELN];
vec3d gt[NELN], gp[NELN];
vec3d agt[NELN], agp[NELN];
double et[NELN], ep[NELN];
double aet[NELN], aep[NELN];
for (int j=0; j<neln; ++j) {
FENode& node = m_pMesh->Node(el.m_node[j]);
vt[j] = node.get_vec3d(m_dofW[0], m_dofW[1], m_dofW[2]);
vp[j] = node.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2]);
at[j] = node.get_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
ap[j] = node.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
gt[j] = node.get_vec3d(m_dofG[0], m_dofG[1], m_dofG[2]);
gp[j] = node.get_vec3d_prev(m_dofG[0], m_dofG[1], m_dofG[2]);
agt[j] = node.get_vec3d(m_dofAG[0], m_dofAG[1], m_dofAG[2]);
agp[j] = node.get_vec3d_prev(m_dofAG[0], m_dofAG[1], m_dofAG[2]);
et[j] = node.get(m_dofEF);
ep[j] = node.get_prev(m_dofEF);
aet[j] = node.get(m_dofAEF);
aep[j] = node.get_prev(m_dofAEF);
}
// loop over the integration points and update
// velocity, velocity gradient, acceleration
// stress and pressure at the integration point
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEPolarFluidMaterialPoint& pf = *(mp.ExtractData<FEPolarFluidMaterialPoint>());
// material point data
pt.m_vft = el.Evaluate(vt, n)*alphaf + el.Evaluate(vp, n)*(1-alphaf);
pt.m_Lf = gradient(el, vt, n)*alphaf + gradient(el, vp, n)*(1-alphaf);
pt.m_aft = pt.m_Lf*pt.m_vft;
if (m_btrans) pt.m_aft += el.Evaluate(at, n)*alpham + el.Evaluate(ap, n)*(1-alpham);
pf.m_gf = el.Evaluate(gt, n)*alphaf + el.Evaluate(gp, n)*(1-alphaf);
pf.m_Psi = gradient(el, gt, n)*alphaf + gradient(el, gp, n)*(1-alphaf);
pf.m_gfdot = pf.m_Psi*pt.m_vft;
if (m_btrans) pf.m_gfdot += el.Evaluate(agt, n)*alpham + el.Evaluate(agp, n)*(1-alpham);
pt.m_ef = el.Evaluate(et, n)*alphaf + el.Evaluate(ep, n)*(1-alphaf);
pt.m_gradef = gradient(el, et, n)*alphaf + gradient(el, ep, n)*(1-alphaf);
pt.m_efdot = pt.m_gradef*pt.m_vft;
if (m_btrans) pt.m_efdot += el.Evaluate(aet, n)*alpham + el.Evaluate(aep, n)*(1-alpham);
// calculate the stress at this material point
pt.m_sf = m_pMat->Stress(mp);
pf.m_sfa = m_pMat->GetViscousPolar()->SkewStress(mp);
// calculate the fluid pressure
pt.m_pf = m_pMat->Pressure(mp);
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::InertialForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i=0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInertialForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
//-----------------------------------------------------------------------------
void FEPolarFluidDomain3D::ElementInertialForce(FESolidElement& el, vector<double>& fe)
{
int i, n;
// jacobian determinant
double detJ;
const double* H;
int nint = el.GaussPoints();
int neln = el.Nodes();
double* gw = el.GaussWeights();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEPolarFluidMaterialPoint& pf = *(mp.ExtractData<FEPolarFluidMaterialPoint>());
double dens = m_pMat->Density(mp);
double kg = m_pMat->m_kg;
// calculate the jacobian
detJ = detJ0(el, n)*gw[n];
H = el.H(n);
for (i=0; i<neln; ++i)
{
vec3d fv = pt.m_aft*(dens*H[i]);
vec3d fg = pf.m_gfdot*(dens*kg*kg*H[i]);
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[7*i ] -= fv.x*detJ;
fe[7*i+1] -= fv.y*detJ;
fe[7*i+2] -= fv.z*detJ;
fe[7*i+3] -= fg.x*detJ;
fe[7*i+4] -= fg.y*detJ;
fe[7*i+5] -= fg.z*detJ;
}
}
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FENewtonianRealVapor.h | .h | 3,472 | 87 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEViscousFluid.h"
#include <FECore/FEFunction1D.h>
//-----------------------------------------------------------------------------
// This class evaluates the viscous stress in a Newtonian viscous real vapor
class FEBIOFLUID_API FENewtonianRealVapor : public FEViscousFluid
{
public:
enum { MAX_NVC = 4 };
public:
//! constructor
FENewtonianRealVapor(FEModel* pfem);
//! initialization
bool Init() override;
//! Serialization
void Serialize(DumpStream& ar) override;
//! viscous stress
mat3ds Stress(FEMaterialPoint& pt) override;
//! tangent of stress with respect to strain J
mat3ds Tangent_Strain(FEMaterialPoint& mp) override;
//! tangent of stress with respect to rate of deformation tensor D
tens4ds Tangent_RateOfDeformation(FEMaterialPoint& mp) override;
//! tangent of stress with respect to temperature
mat3ds Tangent_Temperature(FEMaterialPoint& mp) override;
//! dynamic viscosity
double ShearViscosity(FEMaterialPoint& mp) override;
double TangentShearViscosityTemperature(FEMaterialPoint& mp);
double TangentShearViscosityStrain(FEMaterialPoint& mp);
//! bulk viscosity
double BulkViscosity(FEMaterialPoint& mp) override;
double TangentBulkViscosityTemperature(FEMaterialPoint& mp);
double TangentBulkViscosityStrain(FEMaterialPoint& mp);
public:
double m_kappa; //!< bulk viscosity
double m_mu; //!< shear viscosity
double m_Tr; //!< referential temperature
double m_Tc; //!< normalized critical temperature (Tc/Tr)
double m_alpha; //!< exponent alpha used for calculating temperature map
int m_nvc; //!< number of virial coefficients for isochoric specific heat capacity
FEFunction1D* m_esat; //!< dilatation on saturation curve
FEFunction1D* m_musat; //!< normalized shear viscosity vs normalized temperature on saturation curve
FEFunction1D* m_C[MAX_NVC]; //!< non-dimensional pressure coefficient (multiply by m_Pr to get actual value)
// declare parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEThermoFluidSolver.cpp | .cpp | 42,935 | 1,287 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEBioThermoFluid.h"
#include "FEFluidHeatSupply.h"
#include "FEFluidResistanceBC.h"
#include "FEBackFlowStabilization.h"
#include "FEFluidNormalVelocity.h"
#include "FEFluidVelocity.h"
#include "FEFluidRotationalVelocity.h"
#include "FETiedFluidInterface.h"
#include "FEThermoFluidSolver.h"
#include "FEThermoFluidDomain3D.h"
#include "FEFluidDomain.h"
#include <assert.h>
#include "FEFluidResidualVector.h"
#include <FEBioMech/FEResidualVector.h>
#include <FECore/FEModel.h>
#include <FECore/log.h>
#include <FECore/DOFS.h>
#include <FECore/FEGlobalMatrix.h>
#include <FECore/sys.h>
#include <FEBioMech/FEBodyForce.h>
#include <FECore/FEBoundaryCondition.h>
#include <FECore/FENodalLoad.h>
#include <FECore/FESurfaceLoad.h>
#include <FECore/FEModelLoad.h>
#include <FECore/FEAnalysis.h>
#include <FECore/FELinearConstraintManager.h>
#include <FECore/FELinearSystem.h>
#include <FECore/FENLConstraint.h>
#include "FEThermoFluidAnalysis.h"
//-----------------------------------------------------------------------------
// define the parameter list
BEGIN_FECORE_CLASS(FEThermoFluidSolver, FENewtonSolver)
ADD_PARAMETER(m_Vtol , "vtol" );
ADD_PARAMETER(m_Ftol , "ftol" );
ADD_PARAMETER(m_Ttol , "ttol" );
ADD_PARAMETER(m_Etol, FE_RANGE_GREATER_OR_EQUAL(0.0), "etol");
ADD_PARAMETER(m_Rtol, FE_RANGE_GREATER_OR_EQUAL(0.0), "rtol");
ADD_PARAMETER(m_rhoi , "rhoi" );
ADD_PARAMETER(m_pred , "predictor" );
ADD_PARAMETER(m_minJf, "min_volume_ratio");
ADD_PARAMETER(m_minT , "min_abs_temperature");
ADD_PARAMETER(m_solve_strategy, "solve_strategy")->setEnums("coupled\0sequential\0");
ADD_PARAMETER(m_Tmin , "min_T_drop");
ADD_PARAMETER(m_Tmax , "min_T_rise");
ADD_PARAMETER(m_Tnum , "min_T_num");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
//! FEThermoFluidSolver Construction
//
FEThermoFluidSolver::FEThermoFluidSolver(FEModel* pfem) : FENewtonSolver(pfem), m_dofW(pfem), m_dofAW(pfem), m_dofEF(pfem), m_dofT(pfem)
{
// default values
m_Rtol = 0.001;
m_Etol = 0.01;
m_Vtol = 0.001;
m_Ftol = 0.001;
m_Ttol = 0.001;
m_Rmin = 1.0e-20;
m_Rmax = 0; // not used if zero
m_minJf = 0; // not used if zero
m_minT = 0; // not used if zero
m_Tmin = 0; // not used if zero
m_Tmax = 0; // not used if zero
m_Tnum = 1;
m_nveq = 0;
m_ndeq = 0;
m_nteq = 0;
m_niter = 0;
// assume non-symmetric stiffness
m_msymm = REAL_UNSYMMETRIC;
m_solve_strategy = SOLVE_COUPLED;
m_rhoi = 0;
m_pred = 0;
m_sudden_T_change = false;
// Preferred strategy is Broyden's method
SetDefaultStrategy(QN_BROYDEN);
// turn off checking for a zero diagonal
CheckZeroDiagonal(false);
// get the dof indices
// TODO: Can this be done in Init, since there is no error checking
if (pfem)
{
m_dofW.AddVariable(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::RELATIVE_FLUID_VELOCITY));
m_dofAW.AddVariable(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::RELATIVE_FLUID_ACCELERATION));
m_dofEF.AddVariable(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::FLUID_DILATATION));
m_dofAEF = pfem->GetDOFIndex(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::FLUID_DILATATION_TDERIV), 0);
m_dofT.AddVariable(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::TEMPERATURE));
m_dofAT = pfem->GetDOFIndex(FEBioThermoFluid::GetVariableName(FEBioThermoFluid::TEMPERATURE_TDERIV), 0);
}
}
//-----------------------------------------------------------------------------
FEThermoFluidSolver::~FEThermoFluidSolver()
{
}
//-----------------------------------------------------------------------------
//! Allocates and initializes the data structures used by the FEThermoFluidSolver
//
bool FEThermoFluidSolver::Init()
{
// initialize base class
if (FENewtonSolver::Init() == false) return false;
// check parameters
if (m_Vtol < 0.0) { feLogError("vtol must be nonnegative."); return false; }
if (m_Ftol < 0.0) { feLogError("dtol must be nonnegative."); return false; }
if (m_Ttol < 0.0) { feLogError("ttol must be nonnegative."); return false; }
if (m_Etol < 0.0) { feLogError("etol must be nonnegative."); return false; }
if (m_Rtol < 0.0) { feLogError("rtol must be nonnegative."); return false; }
if (m_rhoi == -1) {
m_alphaf = m_alpham = m_gammaf = 1.0;
}
else if ((m_rhoi >= 0) && (m_rhoi <= 1)) {
m_alphaf = 1.0/(1+m_rhoi);
m_alpham = (3-m_rhoi)/(1+m_rhoi)/2;
m_gammaf = 0.5 + m_alpham - m_alphaf;
}
else { feLogError("rhoi must be -1 or between 0 and 1."); return false; }
// allocate vectors
int neq = m_neq;
m_Fr.assign(neq, 0);
m_Ui.assign(neq, 0);
m_Ut.assign(neq, 0);
m_vi.assign(m_nveq,0);
m_Vi.assign(m_nveq,0);
m_di.assign(m_ndeq,0);
m_Di.assign(m_ndeq,0);
m_ti.assign(m_nteq,0);
m_Ti.assign(m_nteq,0);
// we need to fill the total DOF vector m_Ut
// TODO: I need to find an easier way to do this
FEModel& fem = *GetFEModel();
FEMesh& mesh = fem.GetMesh();
gather(m_Ut, mesh, m_dofW[0]);
gather(m_Ut, mesh, m_dofW[1]);
gather(m_Ut, mesh, m_dofW[2]);
gather(m_Ut, mesh, m_dofEF[0]);
gather(m_Ut, mesh, m_dofT[0]);
// set flag for transient or steady-state analyses
FEAnalysis* pstep = fem.GetCurrentStep();
for (int i = 0; i<mesh.Domains(); ++i)
{
FEDomain& dom = mesh.Domain(i);
if (dom.IsActive()) {
FEFluidDomain* fdom = dynamic_cast<FEFluidDomain*>(&dom);
if (pstep->m_nanalysis == FEThermoFluidAnalysis::STEADY_STATE)
fdom->SetSteadyStateAnalysis();
else
fdom->SetTransientAnalysis();
}
}
return true;
}
//-----------------------------------------------------------------------------
//! Initialize equations
bool FEThermoFluidSolver::InitEquations()
{
// Add the solution variables
AddSolutionVariable(&m_dofW , 1, "velocity" , m_Vtol);
AddSolutionVariable(&m_dofEF, 1, "dilatation" , m_Ftol);
AddSolutionVariable(&m_dofT , 1, "temperature", m_Ttol);
// base class initialization
if (FENewtonSolver::InitEquations() == false) return false;
// determined the nr of velocity and dilatation equations
FEMesh& mesh = GetFEModel()->GetMesh();
m_nveq = m_ndeq = m_nteq = 0;
for (int i=0; i<mesh.Nodes(); ++i)
{
FENode& n = mesh.Node(i);
if (n.m_ID[m_dofW[0]] != -1) m_nveq++;
if (n.m_ID[m_dofW[1]] != -1) m_nveq++;
if (n.m_ID[m_dofW[2]] != -1) m_nveq++;
if (n.m_ID[m_dofEF[0]] != -1) m_ndeq++;
if (n.m_ID[m_dofT[0]] != -1) m_nteq++;
}
// check that we are using a block scheme for sequential solves
if ((m_solve_strategy == SOLVE_SEQUENTIAL) && (m_eq_scheme != EQUATION_SCHEME::BLOCK))
{
feLogWarning("You need a block solver when using the sequential solve strategy.");
return false;
}
// Next, we add any Lagrange Multipliers
FEModel& fem = *GetFEModel();
for (int i = 0; i < fem.NonlinearConstraints(); ++i)
{
FENLConstraint* lmc = fem.NonlinearConstraint(i);
if (lmc->IsActive())
{
m_neq += lmc->InitEquations(m_neq);
}
}
for (int i = 0; i < fem.SurfacePairConstraints(); ++i)
{
FESurfacePairConstraint* spc = fem.SurfacePairConstraint(i);
if (spc->IsActive())
{
m_neq += spc->InitEquations(m_neq);
}
}
if (m_eq_scheme == EQUATION_SCHEME::BLOCK)
{
// repartition the equations so that we only have two partitions,
// one for the fluid-dilatation, and one for the temperature.
// fluid equations is all the rest
int nfeq = m_neq - m_nteq;
// create the new partitions
// Note that this assumes that the temperature equations are always last!
vector<int> p = { nfeq, m_nteq };
SetPartitions(p);
}
return true;
}
//-----------------------------------------------------------------------------
//! Initialize equations
bool FEThermoFluidSolver::InitEquations2()
{
// Add the solution variables
AddSolutionVariable(&m_dofW , 1, "velocity" , m_Vtol);
AddSolutionVariable(&m_dofEF, 1, "dilatation" , m_Ftol);
AddSolutionVariable(&m_dofT , 1, "temperature", m_Ttol);
// base class initialization
if (FENewtonSolver::InitEquations2() == false) return false;
// determined the nr of velocity and dilatation equations
FEMesh& mesh = GetFEModel()->GetMesh();
m_nveq = m_ndeq = m_nteq = 0;
for (int i=0; i<mesh.Nodes(); ++i)
{
FENode& n = mesh.Node(i);
if (n.m_ID[m_dofW[0]] != -1) m_nveq++;
if (n.m_ID[m_dofW[1]] != -1) m_nveq++;
if (n.m_ID[m_dofW[2]] != -1) m_nveq++;
if (n.m_ID[m_dofEF[0]] != -1) m_ndeq++;
if (n.m_ID[m_dofT[0]] != -1) m_nteq++;
}
// Next, we add any Lagrange Multipliers
FEModel& fem = *GetFEModel();
for (int i = 0; i < fem.NonlinearConstraints(); ++i)
{
FENLConstraint* lmc = fem.NonlinearConstraint(i);
if (lmc->IsActive())
{
m_neq += lmc->InitEquations(m_neq);
}
}
for (int i = 0; i < fem.SurfacePairConstraints(); ++i)
{
FESurfacePairConstraint* spc = fem.SurfacePairConstraint(i);
if (spc->IsActive())
{
m_neq += spc->InitEquations(m_neq);
}
}
return true;
}
//-----------------------------------------------------------------------------
void FEThermoFluidSolver::GetVelocityData(vector<double> &vi, vector<double> &ui)
{
FEModel& fem = *GetFEModel();
int N = fem.GetMesh().Nodes(), nid, m = 0;
zero(vi);
for (int i=0; i<N; ++i)
{
FENode& n = fem.GetMesh().Node(i);
nid = n.m_ID[m_dofW[0]];
if (nid != -1)
{
nid = (nid < -1 ? -nid-2 : nid);
vi[m++] = ui[nid];
assert(m <= (int) vi.size());
}
nid = n.m_ID[m_dofW[1]];
if (nid != -1)
{
nid = (nid < -1 ? -nid-2 : nid);
vi[m++] = ui[nid];
assert(m <= (int) vi.size());
}
nid = n.m_ID[m_dofW[2]];
if (nid != -1)
{
nid = (nid < -1 ? -nid-2 : nid);
vi[m++] = ui[nid];
assert(m <= (int) vi.size());
}
}
}
//-----------------------------------------------------------------------------
void FEThermoFluidSolver::GetDilatationData(vector<double> &ei, vector<double> &ui)
{
FEModel& fem = *GetFEModel();
int N = fem.GetMesh().Nodes(), nid, m = 0;
zero(ei);
for (int i=0; i<N; ++i)
{
FENode& n = fem.GetMesh().Node(i);
nid = n.m_ID[m_dofEF[0]];
if (nid != -1)
{
nid = (nid < -1 ? -nid-2 : nid);
ei[m++] = ui[nid];
assert(m <= (int) ei.size());
}
}
}
//-----------------------------------------------------------------------------
void FEThermoFluidSolver::GetTemperatureData(vector<double> &ti, vector<double> &ui)
{
FEModel& fem = *GetFEModel();
int N = fem.GetMesh().Nodes(), nid, m = 0;
zero(ti);
for (int i=0; i<N; ++i)
{
FENode& n = fem.GetMesh().Node(i);
nid = n.m_ID[m_dofT[0]];
if (nid != -1)
{
nid = (nid < -1 ? -nid-2 : nid);
ti[m++] = ui[nid];
assert(m <= (int) ti.size());
}
}
}
//-----------------------------------------------------------------------------
//! Update the kinematics of the model, such as nodal positions, velocities,
//! accelerations, etc.
void FEThermoFluidSolver::UpdateKinematics(vector<double>& ui)
{
// get the mesh
FEModel& fem = *GetFEModel();
FEMesh& mesh = fem.GetMesh();
// update nodes
vector<double> U(m_Ut.size());
for (size_t i=0; i<m_Ut.size(); ++i) U[i] = ui[i] + m_Ui[i] + m_Ut[i];
scatter(U, mesh, m_dofW[0]);
scatter(U, mesh, m_dofW[1]);
scatter(U, mesh, m_dofW[2]);
scatter(U, mesh, m_dofEF[0]);
// scatter(U, mesh, m_dofT[0]);
// update temperature data
int nssd = 0, nssr = 0;
for (int i=0; i<mesh.Nodes(); ++i)
{
FENode& node = mesh.Node(i);
// update nodal temperature
int n = node.m_ID[m_dofT[0]];
// Force the temperature to remain positive
if (n >= 0) {
double Tt = 0 + m_Ut[n] + m_Ui[n] + ui[n];
double Tp = node.get_prev(m_dofT[0]);
if ((m_Tmin > 0) && (node.get_bc(m_dofT[0]) == DOF_OPEN) && (Tp - Tt >= m_Tmin))
nssd++;
if ((m_Tmax > 0) && (node.get_bc(m_dofT[0]) == DOF_OPEN) && (Tt - Tp >= m_Tmax))
nssr++;
node.set(m_dofT[0], Tt);
}
}
if (nssd >= m_Tnum) m_sudden_T_change = true;
if (nssr >= m_Tnum) m_sudden_T_change = true;
// force dilatations to remain greater than -1
if (m_minJf > 0) {
const int NN = mesh.Nodes();
for (int i=0; i<NN; ++i)
{
FENode& node = mesh.Node(i);
if (node.get(m_dofEF[0]) <= -1.0)
node.set(m_dofEF[0], m_minJf - 1.0);
}
}
// force absolute temperature to remain greater than 0
double Tr = fem.GetGlobalConstant("T");
if (m_minT > 0) {
const int NN = mesh.Nodes();
for (int i=0; i<NN; ++i)
{
FENode& node = mesh.Node(i);
if (node.get(m_dofT[0]) <= -Tr)
node.set(m_dofT[0], m_minT - Tr);
}
}
// make sure the prescribed velocities are fulfilled
int nvel = fem.BoundaryConditions();
for (int i=0; i<nvel; ++i)
{
FEBoundaryCondition& bc = *fem.BoundaryCondition(i);
if (bc.IsActive() && HasActiveDofs(bc.GetDofList())) bc.Update();
}
// enforce the linear constraints
// TODO: do we really have to do this? Shouldn't the algorithm
// already guarantee that the linear constraints are satisfied?
FELinearConstraintManager& LCM = fem.GetLinearConstraintManager();
if (LCM.LinearConstraints() > 0)
{
LCM.Update();
}
// update time derivatives of velocity and dilatation
// for dynamic simulations
FEAnalysis* pstep = fem.GetCurrentStep();
if (pstep->m_nanalysis == FEThermoFluidAnalysis::DYNAMIC)
{
int N = mesh.Nodes();
double dt = fem.GetTime().timeIncrement;
double cgi = 1 - 1.0/m_gammaf;
for (int i=0; i<N; ++i)
{
FENode& n = mesh.Node(i);
// velocity time derivative
vec3d vft = n.get_vec3d(m_dofW[0], m_dofW[1], m_dofW[2]);
vec3d vfp = n.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2]);
vec3d aft = n.get_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
vec3d afp = n.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
aft = afp*cgi + (vft - vfp)/(m_gammaf*dt);
n.set_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2], aft);
// dilatation time derivative
double eft = n.get(m_dofEF[0]);
double efp = n.get_prev(m_dofEF[0]);
double aefp = n.get_prev(m_dofAEF);
double aeft = aefp*cgi + (eft - efp)/(m_gammaf*dt);
n.set(m_dofAEF, aeft);
// temperature time derivative
double Tt = n.get(m_dofT[0]);
double Tp = n.get_prev(m_dofT[0]);
double aTp = n.get_prev(m_dofAT);
double aTt = aTp*cgi + (Tt - Tp)/(m_gammaf*dt);
n.set(m_dofAT, aTt);
}
}
// update nonlinear constraints (needed for updating Lagrange Multiplier)
for (int i = 0; i < fem.NonlinearConstraints(); ++i)
{
FENLConstraint* nlc = fem.NonlinearConstraint(i);
if (nlc->IsActive()) nlc->Update(m_Ui, ui);
}
for (int i = 0; i < fem.SurfacePairConstraints(); ++i)
{
FESurfacePairConstraint* spc = fem.SurfacePairConstraint(i);
if (spc->IsActive()) spc->Update(m_Ui, ui);
}
}
//-----------------------------------------------------------------------------
void FEThermoFluidSolver::Update2(const vector<double>& ui)
{
// get the mesh
FEModel& fem = *GetFEModel();
FEMesh& mesh = fem.GetMesh();
// update nodes
vector<double> U(m_Ut.size());
for (size_t i = 0; i<m_Ut.size(); ++i) U[i] = ui[i] + m_Ui[i] + m_Ut[i];
scatter(U, mesh, m_dofW[0]);
scatter(U, mesh, m_dofW[1]);
scatter(U, mesh, m_dofW[2]);
scatter(U, mesh, m_dofEF[0]);
scatter(U, mesh, m_dofT[0]);
// Update the prescribed nodes
for (int i = 0; i<mesh.Nodes(); ++i)
{
FENode& node = mesh.Node(i);
if (node.m_rid == -1)
{
vec3d dv(0, 0, 0);
for (int j = 0; j < node.m_ID.size(); ++j)
{
int nj = -node.m_ID[j] - 2; if (nj >= 0) node.set(j, node.get(j) + ui[nj]);
}
}
}
// update model state
GetFEModel()->Update();
}
//-----------------------------------------------------------------------------
//! Updates the current state of the model
void FEThermoFluidSolver::Update(vector<double>& ui)
{
FEModel& fem = *GetFEModel();
FETimeInfo& tp = fem.GetTime();
tp.currentIteration = m_niter;
// update kinematics
UpdateKinematics(ui);
// update model state
// GetFEModel()->Update();
UpdateModel();
}
//-----------------------------------------------------------------------------
//! Update DOF increments
void FEThermoFluidSolver::UpdateIncrements(vector<double>& Ui, vector<double>& ui, bool emap)
{
FEModel& fem = *GetFEModel();
// get the mesh
FEMesh& mesh = fem.GetMesh();
// extract the velocity and dilatation increments
GetVelocityData(m_vi, ui);
GetDilatationData(m_di, ui);
GetTemperatureData(m_ti, ui);
// update all degrees of freedom
for (int i=0; i<m_neq; ++i) Ui[i] += ui[i];
// update velocities
for (int i = 0; i<m_nveq; ++i) m_Vi[i] += m_vi[i];
// update dilatations
for (int i = 0; i<m_ndeq; ++i) m_Di[i] += m_di[i];
// update temperatures
for (int i = 0; i<m_nteq; ++i) m_Ti[i] += m_ti[i];
for (int i = 0; i < fem.NonlinearConstraints(); ++i)
{
FENLConstraint* plc = fem.NonlinearConstraint(i);
if (plc && plc->IsActive()) plc->UpdateIncrements(Ui, ui);
}
for (int i = 0; i < fem.SurfacePairConstraints(); ++i)
{
FESurfacePairConstraint* psc = fem.SurfacePairConstraint(i);
if (psc && psc->IsActive()) psc->UpdateIncrements(Ui, ui);
}
// TODO: This is a hack!
// The problem is that I only want to call the domain's IncrementalUpdate during
// the quasi-Newtoon loop. However, this function is also called after the loop
// converges. The emap parameter is used here to detect wether we are inside the
// loop (emap == false), or not (emap == true).
if (emap == false)
{
for (int i = 0; i < mesh.Domains(); ++i)
{
FEDomain& dom = mesh.Domain(i);
dom.IncrementalUpdate(ui, true);
}
}
}
//-----------------------------------------------------------------------------
//! Update nonlinear constraints
void FEThermoFluidSolver::UpdateConstraints()
{
FEModel& fem = *GetFEModel();
FETimeInfo& tp = fem.GetTime();
tp.currentIteration = m_niter;
// Update all nonlinear constraints
for (int i = 0; i<fem.NonlinearConstraints(); ++i)
{
FENLConstraint* pci = fem.NonlinearConstraint(i);
if (pci->IsActive()) pci->Update();
}
}
//-----------------------------------------------------------------------------
bool FEThermoFluidSolver::InitStep(double time)
{
FEModel& fem = *GetFEModel();
// set time integration parameters
FETimeInfo& tp = fem.GetTime();
tp.alphaf = m_alphaf;
tp.alpham = m_alpham;
tp.gamma = m_gammaf;
// evaluate load curve values at current (or intermediate) time
double t = tp.currentTime;
double dt = tp.timeIncrement;
double ta = (t > 0) ? t - (1-m_alphaf)*dt : m_alphaf*dt;
return FESolver::InitStep(ta);
}
//-----------------------------------------------------------------------------
//! Prepares the data for the first BFGS-iteration.
void FEThermoFluidSolver::PrepStep()
{
FEModel& fem = *GetFEModel();
FETimeInfo& tp = fem.GetTime();
double dt = tp.timeIncrement;
tp.currentIteration = m_niter;
// zero total DOFs
zero(m_Ui);
zero(m_Vi);
zero(m_Di);
zero(m_Ti);
// store previous mesh state
// we need them for strain and acceleration calculations
FEMesh& mesh = fem.GetMesh();
for (int i=0; i<mesh.Nodes(); ++i)
{
FENode& ni = mesh.Node(i);
ni.m_rp = ni.m_rt = ni.m_r0;
ni.UpdateValues();
switch (m_pred) {
case 0:
{
// initial guess at start of new time step (default)
vec3d afp = ni.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
ni.set_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2], afp*(m_gammaf-1)/m_gammaf);
ni.set(m_dofAEF, ni.get_prev(m_dofAEF)*(m_gammaf-1)/m_gammaf);
ni.set(m_dofAT, ni.get_prev(m_dofAT)*(m_gammaf-1)/m_gammaf);
}
break;
case 1:
{
// initial guess at start of new time step (Zero Ydot)
ni.set_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2], vec3d(0,0,0));
ni.set(m_dofAEF, 0);
ni.set(m_dofAT, 0);
vec3d vfp = ni.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2]);
vec3d afp = ni.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
ni.set_vec3d(m_dofW[0], m_dofW[1], m_dofW[2], vfp + afp*dt*(1-m_gammaf)*m_alphaf);
ni.set(m_dofEF[0], ni.get_prev(m_dofEF[0]) + ni.get_prev(m_dofAEF)*dt*(1-m_gammaf)*m_alphaf);
ni.set(m_dofT[0] , ni.get_prev(m_dofT[0]) + ni.get_prev(m_dofAT )*dt*(1-m_gammaf)*m_alphaf);
}
break;
case 2:
{
// initial guess at start of new time step (Same Ydot)
vec3d afp = ni.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2]);
ni.set_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2], afp);
ni.set(m_dofAEF, ni.get_prev(m_dofAEF));
ni.set(m_dofAT, ni.get_prev(m_dofAT));
vec3d vfp = ni.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2]);
ni.set_vec3d(m_dofW[0], m_dofW[1], m_dofW[2], vfp + afp*dt);
ni.set(m_dofEF[0], ni.get_prev(m_dofEF[0]) + ni.get_prev(m_dofAEF)*dt);
ni.set(m_dofT[0] , ni.get_prev(m_dofT[0]) + ni.get_prev(m_dofAT)*dt);
}
break;
default:
break;
}
}
// apply prescribed velocities
// we save the prescribed velocity increments in the ui vector
vector<double>& ui = m_ui;
zero(ui);
int nbc = fem.BoundaryConditions();
for (int i=0; i<nbc; ++i)
{
FEBoundaryCondition& bc = *fem.BoundaryCondition(i);
if (bc.IsActive() && HasActiveDofs(bc.GetDofList())) bc.PrepStep(ui);
}
// do the linear constraints
fem.GetLinearConstraintManager().PrepStep();
// initialize material point data
// NOTE: do this before the stresses are updated
// TODO: does it matter if the stresses are updated before
// the material point data is initialized
// update domain data
for (int i=0; i<mesh.Domains(); ++i) mesh.Domain(i).PreSolveUpdate(tp);
// update model state
UpdateModel();
for (int i = 0; i < fem.NonlinearConstraints(); ++i)
{
FENLConstraint* plc = fem.NonlinearConstraint(i);
if (plc && plc->IsActive()) plc->PrepStep();
}
for (int i = 0; i < fem.SurfacePairConstraints(); ++i)
{
FESurfacePairConstraint* psc = fem.SurfacePairConstraint(i);
if (psc && psc->IsActive()) psc->PrepStep();
}
// apply prescribed DOFs for specialized surface loads
int nsl = fem.ModelLoads();
for (int i = 0; i < nsl; ++i)
{
FEModelLoad& pml = *fem.ModelLoad(i);
if (pml.IsActive()) pml.PrepStep();
}
// see if we need to do contact augmentations
m_baugment = false;
for (int i = 0; i<fem.SurfacePairConstraints(); ++i)
{
FEContactInterface& ci = dynamic_cast<FEContactInterface&>(*fem.SurfacePairConstraint(i));
if (ci.IsActive() && (ci.m_laugon == FECore::AUGLAG_METHOD)) m_baugment = true;
}
// see if we have to do nonlinear constraint augmentations
if (fem.NonlinearConstraints() != 0) m_baugment = true;
}
//-----------------------------------------------------------------------------
bool FEThermoFluidSolver::Quasin()
{
FEModel& fem = *GetFEModel();
// convergence norms
double normR1; // residual norm
double normE1; // energy norm
double normV; // velocity norm
double normv; // velocity increment norm
double normRi = 0; // initial residual norm
double normVi = 0; // initial velocity norm
double normEi = 0; // initial energy norm
double normEm = 0; // max energy norm
double normDi = 0; // initial dilatation norm
double normD; // current dilatation norm
double normd; // incremement dilatation norm
double normTi = 0; // initial temperature norm
double normT; // current temperature norm
double normt; // incremement temperature norm
// prepare for the first iteration
const FETimeInfo& tp = fem.GetTime();
PrepStep();
// Init QN method
if (QNInit() == false) return false;
// this flag indicates whether the velocity has converged for a sequential solve
// (This is not used for a coupled solve.)
bool vel_converged = false;
// loop until converged or when max nr of reformations reached
bool bconv = false; // convergence flag
do
{
feLog(" %d\n", m_niter+1);
// assume we'll converge.
bconv = true;
// for sequential solve, we set one of the residual components to zero
if (m_solve_strategy == SOLVE_SEQUENTIAL)
{
int veq = m_neq - m_nteq;
if (vel_converged == false)
{
// zero the solute residual
for (int i = veq; i < m_neq; ++i) m_R0[i] = 0.0;
}
else
{
// zero the velocity residual
for (int i = 0; i < veq; ++i) m_R0[i] = 0.0;
}
}
// solve the equations
SolveEquations(m_ui, m_R0);
// do the line search
double s = DoLineSearch();
// for sequential solve, we set one of the residual components to zero
if (m_solve_strategy == SOLVE_SEQUENTIAL)
{
int veq = m_neq - m_nteq;
if (vel_converged == false)
{
// zero the solute residual
for (int i = veq; i < m_neq; ++i) m_R1[i] = 0.0;
// zero the solute solution
for (int i = veq; i < m_neq; ++i) m_ui[i] = 0.0;
}
else
{
// zero the velocity residual
for (int i = 0; i < veq; ++i) m_R1[i] = 0.0;
}
}
// set initial convergence norms
if (m_niter == 0)
{
normRi = fabs(m_R0*m_R0);
normEi = fabs(m_ui*m_R0);
normVi = fabs(m_vi*m_vi);
normDi = fabs(m_di*m_di);
normTi = fabs(m_ti*m_ti);
normEm = normEi;
}
// calculate actual increment
// NOTE: We don't apply the line search directly to m_ui since we need the unscaled search direction for the QN update below
int neq = (int)m_Ui.size();
vector<double> ui(m_ui);
for (int i = 0; i<neq; ++i) ui[i] *= s;
// update other increments (e.g., Lagrange multipliers)
UpdateIncrements(m_Ui, ui, false);
// calculate the norms
normR1 = m_R1*m_R1;
normv = m_vi*m_vi;
normV = m_Vi*m_Vi;
normd = m_di*m_di;
normD = m_Di*m_Di;
normt = m_ti*m_ti;
normT = m_Ti*m_Ti;
normE1 = fabs(m_ui*m_R1);
// check for nans
if (ISNAN(normR1)) throw NANInResidualDetected();
// check residual norm
if ((m_Rtol > 0) && (normR1 > m_Rtol*normRi)) bconv = false;
// check velocity norm
if ((m_Vtol > 0) && (normv > (m_Vtol*m_Vtol)*normV )) bconv = false;
// check dilatation norm
if ((m_Ftol > 0) && (normd > (m_Ftol*m_Ftol)*normD )) bconv = false;
// check temperature norm
if ((m_Ttol > 0) && (normt > (m_Ttol*m_Ttol)*normT )) bconv = false;
// check energy norm
if ((m_Etol > 0) && (normE1 > m_Etol*normEi)) bconv = false;
// check linestep size
if ((m_lineSearch->m_LStol > 0) && (s < m_lineSearch->m_LSmin)) bconv = false;
// check energy divergence
if (normE1 > normEm) bconv = false;
// print convergence summary
feLog(" Nonlinear solution status: time= %lg\n", tp.currentTime);
feLog("\tstiffness updates = %d\n", m_qnstrategy->m_nups);
feLog("\tright hand side evaluations = %d\n", m_nrhs);
feLog("\tstiffness matrix reformations = %d\n", m_nref);
if (m_lineSearch->m_LStol > 0) feLog("\tstep from line search = %lf\n", s);
feLog("\tconvergence norms : INITIAL CURRENT REQUIRED\n");
feLog("\t residual %15le %15le %15le \n", normRi, normR1, m_Rtol*normRi);
feLog("\t energy %15le %15le %15le \n", normEi, normE1, m_Etol*normEi);
feLog("\t velocity %15le %15le %15le \n", normVi, normv ,(m_Vtol*m_Vtol)*normV );
feLog("\t dilatation %15le %15le %15le \n", normDi, normd ,(m_Ftol*m_Ftol)*normD );
feLog("\t temperature %15le %15le %15le \n", normTi, normt ,(m_Ttol*m_Ttol)*normT );
// see if we may have a small residual
if ((bconv == false) && (normR1 < m_Rmin))
{
// check for almost zero-residual on the first iteration
// this might be an indication that there is no force on the system
feLogWarning("No force acting on the system.");
bconv = true;
}
// see if we have exceeded the max residual
if ((bconv == false) && (m_Rmax > 0) && (normR1 >= m_Rmax))
{
// doesn't look like we're getting anywhere, so let's retry the time step
throw MaxResidualError();
}
// check if we have converged.
// If not, calculate the BFGS update vectors
if (bconv == false)
{
if (s < m_lineSearch->m_LSmin)
{
// check for zero linestep size
feLogWarning("Zero linestep size. Stiffness matrix will now be reformed");
QNForceReform(true);
}
else if ((normE1 > normEm) && m_bdivreform)
{
// check for diverging
feLogWarning("Problem is diverging. Stiffness matrix will now be reformed");
normEm = normE1;
normEi = normE1;
normRi = normR1;
normVi = normv;
normDi = normd;
normTi = normt;
QNForceReform(true);
}
// Do the QN update (This may also do a stiffness reformation if necessary)
bool bret = QNUpdate();
// something went wrong with the update, so we'll need to break
if (bret == false) break;
}
else if (m_baugment)
{
// Do augmentations
bconv = DoAugmentations();
}
if (bconv && (m_solve_strategy == SOLVE_SEQUENTIAL))
{
if (vel_converged == false)
{
vel_converged = true;
bconv = false;
m_qnstrategy->m_nups = 0;
m_niter = -1;
Residual(m_R0);
feLog("\n*** Velocity converged. Now solving for temperature.\n");
}
}
// check for sudden temperature change
if (bconv && m_sudden_T_change) {
m_sudden_T_change = false;
throw ConcentrationChangeDetected();
}
else m_sudden_T_change = false;
// increase iteration number
m_niter++;
// do minor iterations callbacks
fem.DoCallback(CB_MINOR_ITERS);
}
while (bconv == false);
// if converged we update the total velocities
if (bconv)
{
UpdateIncrements(m_Ut, m_Ui, true);
zero(m_Ui);
zero(m_Di); zero(m_Vi); zero(m_Ti);
}
return bconv;
}
//-----------------------------------------------------------------------------
//! Calculates global stiffness matrix.
bool FEThermoFluidSolver::StiffnessMatrix(FELinearSystem& LS)
{
FEModel& fem = *GetFEModel();
const FETimeInfo& tp = fem.GetTime();
// get the mesh
FEMesh& mesh = fem.GetMesh();
// calculate the stiffness matrix for each domain
for (int i=0; i<mesh.Domains(); ++i)
{
FEFluidDomain& dom = dynamic_cast<FEFluidDomain&>(mesh.Domain(i));
dom.StiffnessMatrix(LS);
}
// calculate the body force stiffness matrix for each domain
int NML = fem.ModelLoads();
for (int j = 0; j<NML; ++j)
{
FEModelLoad* pml = fem.ModelLoad(j);
FEBodyForce* pbf = dynamic_cast<FEBodyForce*>(pml);
FEFluidHeatSupply* phs = dynamic_cast<FEFluidHeatSupply*>(pml);
if (pbf && pbf->IsActive())
{
for (int i = 0; i<pbf->Domains(); ++i)
{
FEFluidDomain& dom = dynamic_cast<FEFluidDomain&>(*pbf->Domain(i));
dom.BodyForceStiffness(LS, *pbf);
}
}
else if (phs && phs->IsActive())
{
for (int i = 0; i<phs->Domains(); ++i)
{
FEThermoFluidDomain3D* tdom = dynamic_cast<FEThermoFluidDomain3D*>(phs->Domain(i));
if (tdom) tdom->HeatSupplyStiffness(LS, *phs);
}
}
}
// calculate contact stiffness
ContactStiffness(LS);
// calculate stiffness matrix due to model loads
int nsl = fem.ModelLoads();
for (int i=0; i<nsl; ++i)
{
FEModelLoad* pml = fem.ModelLoad(i);
if (pml->IsActive()) pml->StiffnessMatrix(LS);
}
// Add mass matrix
// loop over all domains
for (int i=0; i<mesh.Domains(); ++i)
{
FEFluidDomain& dom = dynamic_cast<FEFluidDomain&>(mesh.Domain(i));
dom.MassMatrix(LS);
}
// calculate nonlinear constraint stiffness
// note that this is the contribution of the
// constraints enforced with augmented lagrangian
NonLinearConstraintStiffness(LS, tp);
return true;
}
//-----------------------------------------------------------------------------
//! Calculate the stiffness contribution due to nonlinear constraints
void FEThermoFluidSolver::NonLinearConstraintStiffness(FELinearSystem& LS, const FETimeInfo& tp)
{
FEModel& fem = *GetFEModel();
int N = fem.NonlinearConstraints();
for (int i=0; i<N; ++i)
{
FENLConstraint* plc = fem.NonlinearConstraint(i);
if (plc->IsActive()) plc->StiffnessMatrix(LS, tp);
}
}
//-----------------------------------------------------------------------------
//! This function calculates the contact stiffness matrix
void FEThermoFluidSolver::ContactStiffness(FELinearSystem& LS)
{
FEModel& fem = *GetFEModel();
const FETimeInfo& tp = fem.GetTime();
for (int i = 0; i<fem.SurfacePairConstraints(); ++i)
{
FEContactInterface* pci = dynamic_cast<FEContactInterface*>(fem.SurfacePairConstraint(i));
if (pci->IsActive()) pci->StiffnessMatrix(LS, tp);
}
}
//-----------------------------------------------------------------------------
//! Calculates the contact forces
void FEThermoFluidSolver::ContactForces(FEGlobalVector& R)
{
FEModel& fem = *GetFEModel();
const FETimeInfo& tp = fem.GetTime();
for (int i = 0; i<fem.SurfacePairConstraints(); ++i)
{
FEContactInterface* pci = dynamic_cast<FEContactInterface*>(fem.SurfacePairConstraint(i));
if (pci->IsActive()) pci->LoadVector(R, tp);
}
}
//-----------------------------------------------------------------------------
//! calculates the residual vector
//! Note that the concentrated nodal forces are not calculated here.
//! This is because they do not depend on the geometry
//! so we only calculate them once (in Quasin) and then add them here.
bool FEThermoFluidSolver::Residual(vector<double>& R)
{
FEModel& fem = *GetFEModel();
// get the time information
const FETimeInfo& tp = fem.GetTime();
// initialize residual with concentrated nodal loads
zero(R);
// zero nodal reaction forces
zero(m_Fr);
// setup the global vector
// FEFluidResidualVector RHS(fem, R, m_Fr);
FEResidualVector RHS(fem, R, m_Fr);
// get the mesh
FEMesh& mesh = fem.GetMesh();
// calculate the internal (stress) forces
for (int i=0; i<mesh.Domains(); ++i)
{
FEFluidDomain& dom = dynamic_cast<FEFluidDomain&>(mesh.Domain(i));
dom.InternalForces(RHS);
}
// calculate the model loads
for (int j = 0; j<fem.ModelLoads(); ++j)
{
FEModelLoad* pml = fem.ModelLoad(j);
FEBodyForce* pbf = dynamic_cast<FEBodyForce*>(pml);
FEFluidHeatSupply* phs = dynamic_cast<FEFluidHeatSupply*>(pml);
if (pbf && pbf->IsActive())
{
for (int i = 0; i<pbf->Domains(); ++i)
{
FEFluidDomain* fdom = dynamic_cast<FEFluidDomain*>(pbf->Domain(i));
fdom->BodyForce(RHS, *pbf);
}
}
else if (phs && phs->IsActive())
{
for (int i = 0; i<phs->Domains(); ++i)
{
FEThermoFluidDomain3D* tdom = dynamic_cast<FEThermoFluidDomain3D*>(phs->Domain(i));
if (tdom) tdom->HeatSupply(RHS, *phs);
}
}
}
// calculate inertial forces
for (int i=0; i<mesh.Domains(); ++i)
{
FEFluidDomain& fdom = dynamic_cast<FEFluidDomain&>(mesh.Domain(i));
fdom.InertialForces(RHS);
}
// calculate contact forces
ContactForces(RHS);
// calculate nonlinear constraint forces
// note that these are the linear constraints
// enforced using the augmented lagrangian
NonLinearConstraintForces(RHS, tp);
// add model loads
int NML = fem.ModelLoads();
for (int i=0; i<NML; ++i)
{
FEModelLoad& mli = *fem.ModelLoad(i);
if (mli.IsActive())
{
mli.LoadVector(RHS);
}
}
// set the nodal reaction forces
// TODO: Is this a good place to do this?
for (int i=0; i<mesh.Nodes(); ++i)
{
FENode& node = mesh.Node(i);
node.set_load(m_dofW[0], 0);
node.set_load(m_dofW[1], 0);
node.set_load(m_dofW[2], 0);
int n;
if ((n = -node.m_ID[m_dofW[0]] - 2) >= 0) node.set_load(m_dofW[0], -m_Fr[n]);
if ((n = -node.m_ID[m_dofW[1]] - 2) >= 0) node.set_load(m_dofW[1], -m_Fr[n]);
if ((n = -node.m_ID[m_dofW[2]] - 2) >= 0) node.set_load(m_dofW[2], -m_Fr[n]);
}
// increase RHS counter
m_nrhs++;
return true;
}
//-----------------------------------------------------------------------------
//! calculate the nonlinear constraint forces
void FEThermoFluidSolver::NonLinearConstraintForces(FEGlobalVector& R, const FETimeInfo& tp)
{
FEModel& fem = *GetFEModel();
int N = fem.NonlinearConstraints();
for (int i=0; i<N; ++i)
{
FENLConstraint* plc = fem.NonlinearConstraint(i);
if (plc->IsActive()) plc->LoadVector(R, tp);
}
}
//-----------------------------------------------------------------------------
//! Serialization
void FEThermoFluidSolver::Serialize(DumpStream& ar)
{
FENewtonSolver::Serialize(ar);
ar & m_nrhs;
ar & m_niter;
ar & m_nref & m_ntotref;
ar & m_nveq & m_ndeq & m_nteq;
ar & m_Fr & m_Ui &m_Ut;
ar & m_Vi & m_Di & m_Ti;
if (ar.IsLoading())
{
m_Fr.assign(m_neq, 0);
m_Vi.assign(m_nveq,0);
m_Di.assign(m_ndeq,0);
m_Ti.assign(m_nteq,0);
}
if (ar.IsShallow()) return;
ar & m_rhoi & m_alphaf & m_alpham;
ar & m_gammaf;
ar & m_pred;
ar & m_dofW & m_dofEF & m_dofAEF & m_dofT & m_dofAT;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidPressureLoad.cpp | .cpp | 3,985 | 120 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2020 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFluidPressureLoad.h"
#include "FECore/FECoreKernel.h"
#include "FEBioFluid.h"
#include <FECore/FEModel.h>
//-----------------------------------------------------------------------------
BEGIN_FECORE_CLASS(FEFluidPressureLoad, FESurfaceLoad)
ADD_PARAMETER(m_p0 , "pressure");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEFluidPressureLoad::FEFluidPressureLoad(FEModel* pfem) : FESurfaceLoad(pfem)
{
m_pfluid = nullptr;
m_p0 = 0;
m_dofEF = pfem->GetDOFIndex(FEBioFluid::GetVariableName(FEBioFluid::FLUID_DILATATION), 0);
m_dof.Clear();
m_dof.AddDof(m_dofEF);
}
//-----------------------------------------------------------------------------
bool FEFluidPressureLoad::Init()
{
if (FESurfaceLoad::Init() == false) return false;
// get fluid from first surface element
// assuming the entire surface bounds the same fluid
FESurfaceElement& el = m_psurf->Element(0);
FEElement* pe = el.m_elem[0].pe;
if (pe == nullptr) return false;
// get the material
FEMaterial* pm = GetFEModel()->GetMaterial(pe->GetMatID());
m_pfluid = pm->ExtractProperty<FEFluidMaterial>();
if (m_pfluid == nullptr) return false;
return true;
}
//-----------------------------------------------------------------------------
//! Activate the degrees of freedom for this BC
void FEFluidPressureLoad::Activate()
{
FESurface* ps = &GetSurface();
for (int i=0; i<ps->Nodes(); ++i)
{
FENode& node = ps->Node(i);
// mark node as having prescribed DOF
node.set_bc(m_dofEF, DOF_PRESCRIBED);
}
FESurfaceLoad::Activate();
}
//-----------------------------------------------------------------------------
//! Evaluate and prescribe the resistance pressure
void FEFluidPressureLoad::Update()
{
// prescribe this dilatation at the nodes
FESurface* ps = &GetSurface();
for (int i=0; i<ps->Nodes(); ++i)
{
if (ps->Node(i).m_ID[m_dofEF] < -1)
{
FENode& node = ps->Node(i);
// calculate the dilatation
double e = node.get(m_dofEF);
bool good = m_pfluid->Dilatation(0,m_p0,e);
assert(good);
// set node as having prescribed DOF
node.set(m_dofEF, e);
}
}
GetFEModel()->SetMeshUpdateFlag(true);
}
//-----------------------------------------------------------------------------
//! serialization
void FEFluidPressureLoad::Serialize(DumpStream& ar)
{
FESurfaceLoad::Serialize(ar);
if (ar.IsShallow()) return;
ar & m_dofEF;
ar & m_pfluid;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEThermoFluid.h | .h | 4,467 | 112 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FEBioMech/FEBodyForce.h>
#include "FEFluidMaterial.h"
#include "FEElasticFluid.h"
#include "FEFluidThermalConductivity.h"
#include "FEFluidMaterialPoint.h"
#include "FEThermoFluidMaterialPoint.h"
//-----------------------------------------------------------------------------
//! Base class for fluid materials.
class FEBIOFLUID_API FEThermoFluid : public FEFluidMaterial
{
public:
FEThermoFluid(FEModel* pfem);
// returns a pointer to a new material point object
FEMaterialPointData* CreateMaterialPointData() override;
//! Serialization
void Serialize(DumpStream& ar) override;
public:
//! calculate stress at material point
mat3ds Stress(FEMaterialPoint& pt) override;
//! tangent of stress with respect to strain J
mat3ds Tangent_Strain(FEMaterialPoint& mp) override;
//! tangent of stress with respect to temperature T
mat3ds Tangent_Temperature(FEMaterialPoint& mp);
//! Elastic pressure
double Pressure(FEMaterialPoint& mp) override { return m_pElastic->Pressure(mp); }
//! tangent of elastic pressure with respect to strain J
double Tangent_Pressure_Strain(FEMaterialPoint& mp) override { return m_pElastic->Tangent_Strain(mp); }
//! 2nd tangent of elastic pressure with respect to strain J
double Tangent_Pressure_Strain_Strain(FEMaterialPoint& mp) override { return m_pElastic->Tangent_Strain_Strain(mp); }
//! tangent of elastic pressure with respect to temperature T
double Tangent_Pressure_Temperature(FEMaterialPoint& mp) { return m_pElastic->Tangent_Temperature(mp); }
//! 2nd tangent of elastic pressure with respect to temperature T
double Tangent_Pressure_Temperature_Temperature(FEMaterialPoint& mp) { return m_pElastic->Tangent_Temperature_Temperature(mp); }
//! tangent of elastic pressure with respect to strain J and temperature T
double Tangent_Pressure_Strain_Temperature(FEMaterialPoint& mp) { return m_pElastic->Tangent_Strain_Temperature(mp); }
public:
//! bulk modulus
double BulkModulus(FEMaterialPoint& mp) override;
//! heat flux
vec3d HeatFlux(FEMaterialPoint& mp);
//! strain energy density
double StrainEnergyDensity(FEMaterialPoint& mp) override;
//! invert pressure-dilatation relation
bool Dilatation(const double T, const double p, double& e) override { return GetElastic()->Dilatation(T,p,e); }
//! fluid pressure from state variables
double Pressure(const double ef, const double T) override { return GetElastic()->Pressure(ef, T); };
//! evaluate temperature
double Temperature(FEMaterialPoint& mp) override;
public:
//! return elastic part
FEElasticFluid* GetElastic() { return m_pElastic; }
//! return thermal conductivity part
FEFluidThermalConductivity* GetConduct() { return m_pConduct; }
private: // material properties
FEElasticFluid* m_pElastic; //!< pointer to elastic part of fluid material
FEFluidThermalConductivity* m_pConduct; //!< pointer to fluid thermal conductivity material
// declare parameter list
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEThermoFluidPressureLoad.h | .h | 3,367 | 99 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include "FEThermoFluid.h"
#include <FECore/FESurfaceConstraint.h>
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! The FEConstraintNormalFlow class implements a fluid surface with zero
//! tangential velocity as a linear constraint.
class FEBIOFLUID_API FEThermoFluidPressureLoad : public FESurfaceConstraint
{
public:
//! constructor
FEThermoFluidPressureLoad(FEModel* pfem);
//! destructor
~FEThermoFluidPressureLoad() {}
//! calculate traction stiffness (there is none for this load)
void StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) override;
//! calculate load vector (there is none for this load)
void LoadVector(FEGlobalVector& R, const FETimeInfo& tp) override;
//! initialize
bool Init() override;
// allocate equations
int InitEquations(int neq) override;
//! serialization
void Serialize(DumpStream& ar) override;
//! augmentation
bool Augment(int naug, const FETimeInfo& tp) override;
// return the surface
FESurface* GetSurface() override { return &m_surf; }
protected:
void UnpackLM(vector<int>& lm, int n);
// Build the matrix profile
void BuildMatrixProfile(FEGlobalMatrix& M) override;
void Update(const std::vector<double>& Ui, const std::vector<double>& ui) override;
void UpdateIncrements(std::vector<double>& Ui, const std::vector<double>& ui) override;
void PrepStep() override;
protected:
int m_dofT;
int m_dofEF;
vector<int> m_EQ;
vector<double> m_Lm, m_Lmp;
FESurface m_surf;
vector<double> m_pn; //!< prescribed fluid pressure at nodes
FEThermoFluid* m_pfluid; //!< pointer to thermo-fluid material
public:
FEParamDouble m_p; // prescribed pressure
int m_laugon;
double m_tol;
double m_eps;
int m_naugmin;
int m_naugmax;
DECLARE_FECORE_CLASS();
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEThermoFluidDomain3D.h | .h | 4,902 | 142 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESolidDomain.h>
#include "FEFluidDomain.h"
#include "FEThermoFluid.h"
#include "FEFluidHeatSupply.h"
//-----------------------------------------------------------------------------
//! domain described by 3D volumetric elements
//!
class FEBIOFLUID_API FEThermoFluidDomain3D : public virtual FESolidDomain, public FEFluidDomain
{
public:
//! constructor
FEThermoFluidDomain3D(FEModel* pfem);
~FEThermoFluidDomain3D() {}
//! assignment operator
FEThermoFluidDomain3D& operator = (FEThermoFluidDomain3D& d);
//! initialize
bool Init() override;
//! serialize
void Serialize(DumpStream& ar) override;
//! initialize elements
void PreSolveUpdate(const FETimeInfo& timeInfo) override;
public: // overrides from FEDomain
//! get the material
FEMaterial* GetMaterial() override { return m_pMat; }
//! set the material
void SetMaterial(FEMaterial* pm) override;
// get total dof list
const FEDofList& GetDOFList() const override;
public: // overrides from FEElasticDomain
// update stresses
void Update(const FETimeInfo& tp) override;
// update the element stress
void UpdateElementStress(int iel, const FETimeInfo& tp);
//! internal stress forces
void InternalForces(FEGlobalVector& R) override;
//! body forces
void BodyForce(FEGlobalVector& R, FEBodyForce& BF) override;
//! Calculate the heat supply
void HeatSupply(FEGlobalVector& R, FEFluidHeatSupply& r);
//! inertial forces for dynamic problems
void InertialForces(FEGlobalVector& R) override;
//! calculates the global stiffness matrix for this domain
void StiffnessMatrix(FELinearSystem& LS) override;
//! Calculate stiffness contribution of heat supplies
void HeatSupplyStiffness(FELinearSystem& LS, FEFluidHeatSupply& bf);
//! calculates inertial stiffness
void MassMatrix(FELinearSystem& LS) override;
//! body force stiffness
void BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf) override;
public:
// --- S T I F F N E S S ---
//! calculates the solid element stiffness matrix
void ElementStiffness(FESolidElement& el, matrix& ke);
//! calculates the solid element mass matrix
void ElementMassMatrix(FESolidElement& el, matrix& ke);
//! calculates the stiffness matrix due to body forces
void ElementBodyForceStiffness(FEBodyForce& bf, FESolidElement& el, matrix& ke);
//! calculates the stiffness matrix due to heat supplies
void ElementHeatSupplyStiffness(FEFluidHeatSupply& bf, FESolidElement& el, matrix& ke);
// --- R E S I D U A L ---
//! Calculates the internal stress vector for solid elements
void ElementInternalForce(FESolidElement& el, vector<double>& fe);
//! Calculates external body forces for solid elements
void ElementBodyForce(FEBodyForce& BF, FESolidElement& elem, vector<double>& fe);
//! Calculates external supplies for solid elements
void ElementHeatSupply(FEFluidHeatSupply& BF, FESolidElement& elem, vector<double>& fe);
//! Calculates the inertial force vector for solid elements
void ElementInertialForce(FESolidElement& el, vector<double>& fe);
protected:
FEThermoFluid* m_pMat;
double m_Tr; // referential absolute temperature
protected:
FEDofList m_dofW;
FEDofList m_dofAW;
FEDofList m_dof;
int m_dofEF;
int m_dofAEF;
int m_dofT;
int m_dofAT;
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEBiphasicFSIDomain3D.cpp | .cpp | 45,453 | 1,117 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEBiphasicFSIDomain3D.h"
#include <FECore/log.h>
#include <FECore/FEModel.h>
#include "FEBioFSI.h"
#include "FEFluidFSI.h"
#include <FECore/FELinearSystem.h>
//-----------------------------------------------------------------------------
//! constructor
//! Some derived classes will pass 0 to the pmat, since the pmat variable will be
//! to initialize another material. These derived classes will set the m_pMat variable as well.
FEBiphasicFSIDomain3D::FEBiphasicFSIDomain3D(FEModel* pfem) : FESolidDomain(pfem), FEBiphasicFSIDomain(pfem), m_dofU(pfem), m_dofV(pfem), m_dofW(pfem), m_dofAW(pfem), m_dofSU(pfem), m_dofR(pfem), m_dof(pfem)
{
m_pMat = 0;
m_btrans = true;
m_sseps = 0;
// TODO: Can this be done in Init, since there is no error checking
if (pfem)
{
m_dofU.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::DISPLACEMENT));
m_dofV.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::VELOCITY));
m_dofW.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::RELATIVE_FLUID_VELOCITY));
m_dofAW.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::RELATIVE_FLUID_ACCELERATION));
m_dofSU.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::SHELL_DISPLACEMENT));
m_dofR.AddVariable(FEBioFSI::GetVariableName(FEBioFSI::RIGID_ROTATION));
m_dofEF = pfem->GetDOFIndex(FEBioFSI::GetVariableName(FEBioFSI::FLUID_DILATATION), 0);
m_dofAEF = pfem->GetDOFIndex(FEBioFSI::GetVariableName(FEBioFSI::FLUID_DILATATION_TDERIV), 0);
}
}
//-----------------------------------------------------------------------------
// \todo I don't think this is being used
FEBiphasicFSIDomain3D& FEBiphasicFSIDomain3D::operator = (FEBiphasicFSIDomain3D& d)
{
m_Elem = d.m_Elem;
m_pMesh = d.m_pMesh;
return (*this);
}
//-----------------------------------------------------------------------------
// get the total dof
const FEDofList& FEBiphasicFSIDomain3D::GetDOFList() const
{
return m_dof;
}
//-----------------------------------------------------------------------------
//! Assign material
void FEBiphasicFSIDomain3D::SetMaterial(FEMaterial* pmat)
{
FEDomain::SetMaterial(pmat);
if (pmat)
{
m_pMat = dynamic_cast<FEBiphasicFSI*>(pmat);
assert(m_pMat);
}
else m_pMat = 0;
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::Activate()
{
for (int i=0; i<Nodes(); ++i)
{
FENode& node = Node(i);
if (node.HasFlags(FENode::EXCLUDE) == false)
{
if (node.m_rid < 0)
{
node.set_active(m_dofU[0]);
node.set_active(m_dofU[1]);
node.set_active(m_dofU[2]);
}
node.set_active(m_dofW[0]);
node.set_active(m_dofW[1]);
node.set_active(m_dofW[2]);
node.set_active(m_dofEF);
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::Reset()
{
// reset base class data
FESolidDomain::Reset();
// initialize all element data
ForEachMaterialPoint([=](FEMaterialPoint& mp) {
FEBiphasicFSIMaterialPoint& pt = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
// initialize referential solid volume fraction
pt.m_phi0 = m_pMat->m_phi0(mp);
});
}
//-----------------------------------------------------------------------------
//! Initialize element data
void FEBiphasicFSIDomain3D::PreSolveUpdate(const FETimeInfo& timeInfo)
{
const int NE = FEElement::MAX_NODES;
vec3d x0[NE], xt[NE], r0, rt, v;
FEMesh& m = *GetMesh();
for (size_t i=0; i<m_Elem.size(); ++i)
{
FESolidElement& el = m_Elem[i];
if (el.isActive())
{
int neln = el.Nodes();
for (int i=0; i<neln; ++i)
{
x0[i] = m.Node(el.m_node[i]).m_r0;
xt[i] = m.Node(el.m_node[i]).m_rt;
}
int n = el.GaussPoints();
for (int j=0; j<n; ++j)
{
r0 = el.Evaluate(x0, j);
rt = el.Evaluate(xt, j);
FEMaterialPoint& mp = *el.GetMaterialPoint(j);
FEElasticMaterialPoint& et = *mp.ExtractData<FEElasticMaterialPoint>();
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
et.m_Wp = et.m_Wt;
if ((pt.m_ef <= -1) || (et.m_J <= 0)) {
throw NegativeJacobianDetected();
}
mp.Update(timeInfo);
}
}
}
}
//-----------------------------------------------------------------------------
//! Unpack the element LM data.
void FEBiphasicFSIDomain3D::UnpackLM(FEElement& el, vector<int>& lm)
{
int N = el.Nodes();
lm.resize(N*10);
for (int i=0; i<N; ++i)
{
FENode& node = m_pMesh->Node(el.m_node[i]);
vector<int>& id = node.m_ID;
// first the displacement dofs
lm[7*i ] = id[m_dofU[0]];
lm[7*i+1] = id[m_dofU[1]];
lm[7*i+2] = id[m_dofU[2]];
lm[7*i+3] = id[m_dofW[0]];
lm[7*i+4] = id[m_dofW[1]];
lm[7*i+5] = id[m_dofW[2]];
lm[7*i+6] = id[m_dofEF];
// rigid rotational dofs
lm[7*N + 3*i ] = id[m_dofR[0]];
lm[7*N + 3*i+1] = id[m_dofR[1]];
lm[7*N + 3*i+2] = id[m_dofR[2]];
}
// substitute interface dofs for solid-shell interfaces
FESolidElement& sel = static_cast<FESolidElement&>(el);
for (int i = 0; i<sel.m_bitfc.size(); ++i)
{
if (sel.m_bitfc[i]) {
FENode& node = m_pMesh->Node(el.m_node[i]);
vector<int>& id = node.m_ID;
// first the displacement dofs
lm[7*i ] = id[m_dofSU[0]];
lm[7*i+1] = id[m_dofSU[1]];
lm[7*i+2] = id[m_dofSU[2]];
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::InternalForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i=0; i<NE; ++i)
{
// element force vector
vector<double> fe;
vector<int> lm;
// get the element
FESolidElement& el = m_Elem[i];
if (el.isActive()) {
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInternalForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
}
//-----------------------------------------------------------------------------
//! calculates the internal equivalent nodal forces for solid elements
void FEBiphasicFSIDomain3D::ElementInternalForce(FESolidElement& el, vector<double>& fe)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, n;
// jacobian matrix, inverse jacobian matrix and determinants
double Ji[3][3], detJ;
mat3ds sv, se, pi;
vec3d gradp, divTe;
mat3ds km1;
const double *H, *Gr, *Gs, *Gt;
int nint = el.GaussPoints();
int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
double* gw = el.GaussWeights();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEElasticMaterialPoint& et = *(mp.ExtractData<FEElasticMaterialPoint>());
FEFSIMaterialPoint& ft = *(mp.ExtractData<FEFSIMaterialPoint>());
FEBiphasicFSIMaterialPoint& bt = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
// calculate the jacobian
detJ = invjact(el, Ji, n, tp.alphaf)*gw[n];
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
// get the viscous stress tensor for this integration point
sv = m_pMat->Fluid()->GetViscous()->Stress(mp);
se = m_pMat->Solid()->Stress(mp);
// get the gradient of the elastic pressure
gradp = pt.m_gradef*m_pMat->Fluid()->Tangent_Pressure_Strain(mp);
// get inverse of permeability tensor
km1 = m_pMat->InvPermeability(mp);
//get pI
pi = mat3dd(m_pMat->Fluid()->Pressure(mp));
// get fluid supply (if present)
double phifhat = 0;
if (m_pMat->FluidSupply()) phifhat = m_pMat->FluidSupply()->Supply(mp);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
{
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
}
// Jfdot wrt fluid
double phif = m_pMat->Porosity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
double dJfdotf = pt.m_efdot + pt.m_gradef*ft.m_w/phif;
double Jf = 1 + pt.m_ef;
// Jsdot/Js
double dJsoJ = ft.m_Jdot/et.m_J;
for (i=0; i<neln; ++i)
{
vec3d fs = ((se-sv*phis)*gradN[i] + (sv*bt.m_gradJ/(phif*et.m_J)*phis - km1*ft.m_w)*H[i])*detJ;
vec3d ff = (sv*gradN[i] + (gradp + km1*ft.m_w - sv*bt.m_gradJ*phis/(phif*et.m_J))*H[i])*detJ;
double fJ = (H[i]*(dJfdotf*phif/Jf - dJsoJ + phifhat) + gradN[i]*ft.m_w)*detJ;
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[7*i ] -= fs.x;
fe[7*i+1] -= fs.y;
fe[7*i+2] -= fs.z;
fe[7*i+3] -= ff.x;
fe[7*i+4] -= ff.y;
fe[7*i+5] -= ff.z;
fe[7*i+6] -= fJ;
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::BodyForce(FEGlobalVector& R, FEBodyForce& BF)
{
int NE = (int)m_Elem.size();
for (int i=0; i<NE; ++i)
{
// get the element
FESolidElement& el = m_Elem[i];
if (el.isActive()) {
vector<double> fe;
vector<int> lm;
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// apply body forces
ElementBodyForce(BF, el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
}
//-----------------------------------------------------------------------------
//! calculates the body forces
void FEBiphasicFSIDomain3D::ElementBodyForce(FEBodyForce& BF, FESolidElement& el, vector<double>& fe)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
// jacobian
double detJ;
double *H;
double* gw = el.GaussWeights();
vec3d ff, f;
// number of nodes
int neln = el.Nodes();
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
double densTs = m_pMat->TrueSolidDensity(mp);
double densTf = m_pMat->TrueFluidDensity(mp);
detJ = detJt(el, n, tp.alphaf)*gw[n];
// get the force
double phis = m_pMat->SolidVolumeFrac(mp);
f = BF.force(mp)*((-densTf+densTs)*phis*detJ);
ff = BF.force(mp)*(densTf*detJ);
H = el.H(n);
for (int i=0; i<neln; ++i)
{
fe[7*i+0] -= H[i]*f.x;
fe[7*i+1] -= H[i]*f.y;
fe[7*i+2] -= H[i]*f.z;
fe[7*i+3] -= H[i]*ff.x;
fe[7*i+4] -= H[i]*ff.y;
fe[7*i+5] -= H[i]*ff.z;
}
}
}
//-----------------------------------------------------------------------------
//! This function calculates the stiffness due to body forces
//! For now, we assume that the body force is constant
void FEBiphasicFSIDomain3D::ElementBodyForceStiffness(FEBodyForce& BF, FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int neln = el.Nodes();
int ndof = ke.columns()/neln;
// jacobian
double Ji[3][3], detJ;
double *H, *Gr, *Gs, *Gt;
double* gw = el.GaussWeights();
vec3d f, ff, fs, ffs, kwJ, kuJ;
mat3d Kwu, Kuu;
// gradient of shape functions
vector<vec3d> gradN(neln);
// loop over integration points
int nint = el.GaussPoints();
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *mp.ExtractData<FEFluidMaterialPoint>();
double Jf = 1 + pt.m_ef;
// calculate the jacobian
detJ = invjact(el, Ji, n, tp.alphaf)*gw[n]*tp.alphaf;
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
double densf = m_pMat->FluidDensity(mp);
double densTf = m_pMat->TrueFluidDensity(mp);
double denss = m_pMat->SolidDensity(mp);
double densTs = m_pMat->TrueSolidDensity(mp);
// get the force
ff = BF.force(mp)*(densTf*detJ);
f = BF.force(mp)*(densf*detJ);
fs = BF.force(mp)*(densTs*detJ);
double phif = m_pMat->Porosity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
ffs = BF.force(mp)*((phis/phif*(densf+denss) - densTf*phis + denss)*detJ);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// evaluate spatial gradient of shape functions
for (int i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
for (int i=0; i<neln; ++i) {
for (int j=0; j<neln; ++j)
{
kwJ = ff*(-H[i]*H[j]/Jf);
kuJ = ff*(H[i]*H[j]*phis/Jf);
Kwu = (ff & gradN[j])*H[i];
Kuu = mat3d(0.0);
ke[ndof*i+0][ndof*j ] += Kuu(0,0); ke[ndof*i+0][ndof*j+1] += Kuu(0,1); ke[ndof*i+0][ndof*j+2] += Kuu(0,2);
ke[ndof*i+1][ndof*j ] += Kuu(1,0); ke[ndof*i+1][ndof*j+1] += Kuu(1,1); ke[ndof*i+1][ndof*j+2] += Kuu(1,2);
ke[ndof*i+2][ndof*j ] += Kuu(2,0); ke[ndof*i+2][ndof*j+1] += Kuu(2,1); ke[ndof*i+2][ndof*j+2] += Kuu(2,2);
ke[ndof*i+3][ndof*j ] += Kwu(0,0); ke[ndof*i+3][ndof*j+1] += Kwu(0,1); ke[ndof*i+3][ndof*j+2] += Kwu(0,2);
ke[ndof*i+4][ndof*j ] += Kwu(1,0); ke[ndof*i+4][ndof*j+1] += Kwu(1,1); ke[ndof*i+4][ndof*j+2] += Kwu(1,2);
ke[ndof*i+5][ndof*j ] += Kwu(2,0); ke[ndof*i+5][ndof*j+1] += Kwu(2,1); ke[ndof*i+5][ndof*j+2] += Kwu(2,2);
ke[ndof*i+0][ndof*j+6] += kuJ.x;
ke[ndof*i+1][ndof*j+6] += kuJ.y;
ke[ndof*i+2][ndof*j+6] += kuJ.z;
ke[ndof*i+3][ndof*j+6] += kwJ.x;
ke[ndof*i+4][ndof*j+6] += kwJ.y;
ke[ndof*i+5][ndof*j+6] += kwJ.z;
}
}
}
}
//-----------------------------------------------------------------------------
//! Calculates element material stiffness element matrix
void FEBiphasicFSIDomain3D::ElementStiffness(FESolidElement &el, matrix &ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i7, j, j7, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
// gradient of shape functions
vector<vec3d> gradN(neln);
vector<mat3d> gradgradN(neln);
double dt = tp.timeIncrement;
double a = tp.gamma/(tp.beta*dt);
double c = tp.alpham/(tp.alphaf*tp.gamma*dt);
double dtrans = m_btrans ? 1 : m_sseps;
double *H, *Gr, *Gs, *Gt;
vec3d g[3], dg[3][3];
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjact(el, Ji, n, tp.alphaf)*gw[n]*tp.alphaf;
ContraBaseVectors(el, n, g, tp.alphaf);
ContraBaseVectorDerivatives(el, n, dg, tp.alphaf);
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// get the shape function derivatives
double* Grr = el.Grr(n); double* Grs = el.Grs(n); double* Grt = el.Grt(n);
double* Gsr = el.Gsr(n); double* Gss = el.Gss(n); double* Gst = el.Gst(n);
double* Gtr = el.Gtr(n); double* Gts = el.Gts(n); double* Gtt = el.Gtt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMaterialPoint& et = *(mp.ExtractData<FEElasticMaterialPoint>());
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEFSIMaterialPoint& fpt = *(mp.ExtractData<FEFSIMaterialPoint>());
FEBiphasicFSIMaterialPoint& bpt = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
double Jf = 1 + pt.m_ef;
// get the tangents
mat3ds se = m_pMat->Solid()->Stress(mp);
tens4ds cs = m_pMat->Solid()->Tangent(mp);
mat3ds sv = m_pMat->Fluid()->GetViscous()->Stress(mp);
mat3ds svJ = m_pMat->Fluid()->GetViscous()->Tangent_Strain(mp);
tens4ds cv = m_pMat->Fluid()->Tangent_RateOfDeformation(mp);
double dp = m_pMat->Fluid()->Tangent_Pressure_Strain(mp);
double d2p = m_pMat->Fluid()->Tangent_Pressure_Strain_Strain(mp);
vec3d gradp = pt.m_gradef*dp;
// Jsdot/Js = div(vs)
double dJsoJ = fpt.m_Jdot/et.m_J;
mat3ds km1 = m_pMat->InvPermeability(mp);
//Include dependence of permeability on displacement
tens4dmm K = m_pMat->Permeability_Tangent(mp);
// include contributions from fluid supply (if present)
double phifhat = 0;
mat3d dphifhatdE(mat3dd(0));
double dphifhatdef = 0;
mat3ds dphifhatdD(0);
if (m_pMat->FluidSupply()) {
phifhat = m_pMat->FluidSupply()->Supply(mp);
dphifhatdE = m_pMat->FluidSupply()->Tangent_Supply_Strain(mp);
dphifhatdef = m_pMat->FluidSupply()->Tangent_Supply_Dilatation(mp);
dphifhatdD = m_pMat->FluidSupply()->Tangent_Supply_RateOfDeformation(mp);
}
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate spatial gradgrad of shape functions
for (i=0; i<neln; ++i) {
gradgradN[i] = (((dg[0][0] & g[0]) + (dg[0][1] & g[1]) + (dg[0][2] & g[2]))*Gr[i]
+ ((dg[1][0] & g[0]) + (dg[1][1] & g[1]) + (dg[1][2] & g[2]))*Gs[i]
+ ((dg[2][0] & g[0]) + (dg[2][1] & g[1]) + (dg[2][2] & g[2]))*Gt[i]
+ (g[0] & g[0])*Grr[i] + (g[0] & g[1])*Gsr[i] + (g[0] & g[2])*Gtr[i]
+ (g[1] & g[0])*Grs[i] + (g[1] & g[1])*Gss[i] + (g[1] & g[2] )*Gts[i]
+ (g[2] & g[0])*Grt[i] + (g[2] & g[1])*Gst[i] + (g[2] & g[2])*Gtt[i]);
}
double phif = m_pMat->Porosity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
vec3d gradphif = m_pMat->gradPorosity(mp);
// evaluate stiffness matrix
for (i=0, i7=0; i<neln; ++i, i7 += 7)
{
for (j=0, j7 = 0; j<neln; ++j, j7 += 7)
{
mat3d M = mat3dd(a*dtrans) - et.m_L;
tens4d km1km1 = dyad2(km1,km1);
tens4d Kfull = tens4d(K);
mat3d Kuu = (sv*((gradN[j]&gradN[i])*phis) - (-((sv*gradN[i])&gradN[j])*phis/phif + vdotTdotv(gradN[i], cv, gradN[j])*(-bpt.m_Lw.sym()*phis/(phif*phif) + M))*phis - vdotTdotv(gradN[i], cv, fpt.m_w*phis/(phif*phif)) * ((gradphif&gradN[j])*2.0*phis/phif + (gradN[j]&gradphif)) + vdotTdotv(gradN[i], cv, fpt.m_w*phis*phis/(phif*phif)) * ((-bpt.m_gradJ&gradN[j])/et.m_J + gradgradN[j]) + mat3dd((se*gradN[i])*gradN[j]) + vdotTdotv(gradN[i], cs, gradN[j]) - (((sv*bpt.m_gradJ)*phis/(et.m_J*phif*phif))&gradN[j])*H[i] + (-((sv*bpt.m_gradJ)&gradN[j])*phis/phif + vdotTdotv(bpt.m_gradJ, cv, gradN[j])*(-bpt.m_Lw.sym()*phis/(phif*phif) + M))*phis/(phif*et.m_J)*H[i] + vdotTdotv(bpt.m_gradJ, cv, fpt.m_w*phis/(phif*phif*phif*et.m_J)*H[i]) * ((gradphif&gradN[j])*2.0*phis/phif + (gradN[j]&gradphif)) - vdotTdotv(bpt.m_gradJ, cv, fpt.m_w*phis*phis/(phif*phif*phif*et.m_J)*H[i]) * ((-bpt.m_gradJ&gradN[j])/et.m_J + gradgradN[j]) + sv*((bpt.m_gradJ&gradN[j]) - (gradN[j]&bpt.m_gradJ) + gradgradN[j]*et.m_J)*H[i]*phis/(phif*et.m_J) + (-((km1*fpt.m_w)&gradN[j])*2.0 + (gradN[j]&(km1*fpt.m_w)) + km1*(gradN[j]*fpt.m_w) + ddot(ddot(km1km1,Kfull),mat3dd(gradN[j]*fpt.m_w)))*H[i])*detJ; //mixture 3 adjusted viscous stress
mat3d Kuw = (vdotTdotv(gradN[i], cv, (gradphif*H[j]/phif-gradN[j]))*phis/phif + vdotTdotv((-gradphif*H[j]/phif + gradN[j]), cv, bpt.m_gradJ)*H[i]*phis/(phif*phif*et.m_J) - km1*H[i]*H[j])*detJ; //mixture 3 adjusted stress
vec3d kuJ = ((-svJ*gradN[i])*H[j]*phis + svJ*bpt.m_gradJ*H[j]*H[i]*phis/(phif*et.m_J))*detJ; //mixture 3 adjusted stress
mat3d Kwu = (((gradp&gradN[j])-(gradN[j]&gradp))*H[i] + sv*((bpt.m_gradJ&gradN[j])*(phis/phif)+(gradN[j]&bpt.m_gradJ) - gradgradN[j]*et.m_J)*(phis*H[i]/(et.m_J*phif)) - (-((sv*bpt.m_gradJ)&gradN[j])*phis/phif + vdotTdotv(bpt.m_gradJ, cv, gradN[j])*(-bpt.m_Lw.sym()*phis/(phif*phif) + M))*H[i]*phis/(phif*et.m_J) - vdotTdotv(bpt.m_gradJ*H[i]*phis/(et.m_J*phif*phif*phif), cv, fpt.m_w) * ((gradphif&gradN[j])*2.0*phis/phif + (gradN[j]&gradphif)) + vdotTdotv(bpt.m_gradJ*H[i]*phis*phis/(et.m_J*phif*phif*phif), cv, fpt.m_w) * (-(bpt.m_gradJ&gradN[j])/et.m_J + gradgradN[j]) + sv*((gradN[i]&gradN[j])-(gradN[j]&gradN[i])) + (-((sv*gradN[i])&gradN[j])*phis/phif + vdotTdotv(gradN[i], cv, gradN[j])*(-bpt.m_Lw.sym()*phis/(phif*phif) + M)) + vdotTdotv(gradN[i], cv, fpt.m_w/(phif*phif)) * ((gradphif&gradN[j])*2.0*phis/phif + (gradN[j]&gradphif)) + vdotTdotv(gradN[i], cv, fpt.m_w*phis/(phif*phif)) * ((bpt.m_gradJ&gradN[j])/et.m_J - gradgradN[j]) + (((km1*fpt.m_w)&gradN[j])*2.0 - (gradN[j]&(km1*fpt.m_w)) - km1*(gradN[j]*fpt.m_w) - ddot(ddot(km1km1,Kfull),mat3dd(gradN[j]*fpt.m_w)))*H[i])*detJ; //fluid adjusted visc stress
mat3d Kww = ((vdotTdotv(bpt.m_gradJ, cv, (gradphif*H[j]/phif-gradN[j]))*phis/(phif*phif*et.m_J) + km1*H[j])*H[i] + vdotTdotv(gradN[i], cv, (-gradphif*H[j]/phif+gradN[j]))/phif)*detJ; //fluid adjusted visc stress
vec3d kwJ = ((svJ*gradN[i])*H[j] +(gradN[j]*dp+(pt.m_gradef*d2p - svJ*bpt.m_gradJ*phis/(phif*et.m_J))*H[j])*H[i])*detJ; //fluid adjusted visc stress
vec3d kJu = (((gradN[j]&fpt.m_w) - mat3dd(gradN[j]*fpt.m_w)) * gradN[i] + ((gradN[j]*pt.m_efdot + ((gradN[j]&fpt.m_w) - mat3dd(gradN[j]*fpt.m_w))*pt.m_gradef)/Jf - gradN[j]*(dJsoJ + a*dtrans) + et.m_L.transpose()*gradN[j]*dtrans
+ (dphifhatdE+mat3dd(phifhat))*gradN[j])*H[i])*detJ;
vec3d kJw = ((pt.m_gradef*(H[i]/Jf) + gradN[i])*H[j] + dphifhatdD*(gradN[j]-gradphif*(H[j]/phif))*(H[i]/phif))*detJ;
double kJJ = (((c*phif*dtrans - (pt.m_efdot*phif + pt.m_gradef*fpt.m_w)/Jf)*H[j] + gradN[j]*fpt.m_w)*H[i]/Jf
+H[i]*H[j]*dphifhatdef)*detJ;
ke[i7 ][j7 ] += Kuu(0,0); ke[i7 ][j7+1] += Kuu(0,1); ke[i7 ][j7+2] += Kuu(0,2);
ke[i7+1][j7 ] += Kuu(1,0); ke[i7+1][j7+1] += Kuu(1,1); ke[i7+1][j7+2] += Kuu(1,2);
ke[i7+2][j7 ] += Kuu(2,0); ke[i7+2][j7+1] += Kuu(2,1); ke[i7+2][j7+2] += Kuu(2,2);
ke[i7 ][j7+3] += Kuw(0,0); ke[i7 ][j7+4] += Kuw(0,1); ke[i7 ][j7+5] += Kuw(0,2);
ke[i7+1][j7+3] += Kuw(1,0); ke[i7+1][j7+4] += Kuw(1,1); ke[i7+1][j7+5] += Kuw(1,2);
ke[i7+2][j7+3] += Kuw(2,0); ke[i7+2][j7+4] += Kuw(2,1); ke[i7+2][j7+5] += Kuw(2,2);
ke[i7+3][j7 ] += Kwu(0,0); ke[i7+3][j7+1] += Kwu(0,1); ke[i7+3][j7+2] += Kwu(0,2);
ke[i7+4][j7 ] += Kwu(1,0); ke[i7+4][j7+1] += Kwu(1,1); ke[i7+4][j7+2] += Kwu(1,2);
ke[i7+5][j7 ] += Kwu(2,0); ke[i7+5][j7+1] += Kwu(2,1); ke[i7+5][j7+2] += Kwu(2,2);
ke[i7+3][j7+3] += Kww(0,0); ke[i7+3][j7+4] += Kww(0,1); ke[i7+3][j7+5] += Kww(0,2);
ke[i7+4][j7+3] += Kww(1,0); ke[i7+4][j7+4] += Kww(1,1); ke[i7+4][j7+5] += Kww(1,2);
ke[i7+5][j7+3] += Kww(2,0); ke[i7+5][j7+4] += Kww(2,1); ke[i7+5][j7+5] += Kww(2,2);
ke[i7+0][j7+6] += kuJ.x;
ke[i7+1][j7+6] += kuJ.y;
ke[i7+2][j7+6] += kuJ.z;
ke[i7+3][j7+6] += kwJ.x;
ke[i7+4][j7+6] += kwJ.y;
ke[i7+5][j7+6] += kwJ.z;
ke[i7+6][j7 ] += kJu.x;
ke[i7+6][j7+1] += kJu.y;
ke[i7+6][j7+2] += kJu.z;
ke[i7+6][j7+3] += kJw.x;
ke[i7+6][j7+4] += kJw.y;
ke[i7+6][j7+5] += kJw.z;
ke[i7+6][j7+6] += kJJ;
}
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::StiffnessMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
if (el.isActive()) {
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate material stiffness
ElementStiffness(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::MassMatrix(FELinearSystem& LS)
{
// repeat over all solid elements
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
if (el.isActive()) {
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementMassMatrix(el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::BodyForceStiffness(FELinearSystem& LS, FEBodyForce& bf)
{
FEBiphasicFSI* pme = dynamic_cast<FEBiphasicFSI*>(GetMaterial()); assert(pme);
// repeat over all solid elements
int NE = (int)m_Elem.size();
for (int iel=0; iel<NE; ++iel)
{
FESolidElement& el = m_Elem[iel];
if (el.isActive()) {
// element stiffness matrix
FEElementMatrix ke(el);
// create the element's stiffness matrix
int ndof = 7*el.Nodes();
ke.resize(ndof, ndof);
ke.zero();
// calculate inertial stiffness
ElementBodyForceStiffness(bf, el, ke);
// get the element's LM vector
vector<int> lm;
UnpackLM(el, lm);
ke.SetIndices(lm);
// assemble element matrix in global stiffness matrix
LS.Assemble(ke);
}
}
}
//-----------------------------------------------------------------------------
//! calculates element inertial stiffness matrix
void FEBiphasicFSIDomain3D::ElementMassMatrix(FESolidElement& el, matrix& ke)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, i7, j, j7, n;
// Get the current element's data
const int nint = el.GaussPoints();
const int neln = el.Nodes();
double dtrans = m_btrans ? 1 : m_sseps;
// gradient of shape functions
vector<vec3d> gradN(neln);
vector<mat3d> gradgradN(neln);
double *H;
double *Gr, *Gs, *Gt;
vec3d g[3], dg[3][3];
// jacobian
double Ji[3][3], detJ;
// weights at gauss points
const double *gw = el.GaussWeights();
double dt = tp.timeIncrement;
double a = tp.gamma/(tp.beta*dt);
double b = tp.alpham/(tp.alphaf*tp.beta*dt*dt);
double c = tp.alpham/(tp.alphaf*tp.gamma*dt);
// calculate element stiffness matrix
for (n=0; n<nint; ++n)
{
// calculate jacobian
detJ = invjact(el, Ji, n, tp.alphaf)*gw[n]*tp.alphaf;
ContraBaseVectors(el, n, g, tp.alphaf);
ContraBaseVectorDerivatives(el, n, dg, tp.alphaf);
vec3d g1(Ji[0][0],Ji[0][1],Ji[0][2]);
vec3d g2(Ji[1][0],Ji[1][1],Ji[1][2]);
vec3d g3(Ji[2][0],Ji[2][1],Ji[2][2]);
H = el.H(n);
Gr = el.Gr(n);
Gs = el.Gs(n);
Gt = el.Gt(n);
// get the shape function derivatives
double* Grr = el.Grr(n); double* Grs = el.Grs(n); double* Grt = el.Grt(n);
double* Gsr = el.Gsr(n); double* Gss = el.Gss(n); double* Gst = el.Gst(n);
double* Gtr = el.Gtr(n); double* Gts = el.Gts(n); double* Gtt = el.Gtt(n);
// setup the material point
// NOTE: deformation gradient and determinant have already been evaluated in the stress routine
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEElasticMaterialPoint& et = *(mp.ExtractData<FEElasticMaterialPoint>());
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEFSIMaterialPoint& fpt = *(mp.ExtractData<FEFSIMaterialPoint>());
FEBiphasicFSIMaterialPoint& bpt = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
double Jf = 1 + pt.m_ef;
double denss = m_pMat->SolidDensity(mp);
double densTf = m_pMat->TrueFluidDensity(mp);
// Jsdot/Js = div(vs)
double dJsoJ = fpt.m_Jdot/et.m_J;
// evaluate spatial gradient of shape functions
for (i=0; i<neln; ++i)
gradN[i] = g1*Gr[i] + g2*Gs[i] + g3*Gt[i];
// evaluate spatial gradgrad of shape functions
for (i=0; i<neln; ++i) {
gradgradN[i] = (((dg[0][0] & g[0]) + (dg[0][1] & g[1]) + (dg[0][2] & g[2]))*Gr[i]
+ ((dg[1][0] & g[0]) + (dg[1][1] & g[1]) + (dg[1][2] & g[2]))*Gs[i]
+ ((dg[2][0] & g[0]) + (dg[2][1] & g[1]) + (dg[2][2] & g[2]))*Gt[i]
+ (g[0] & g[0])*Grr[i] + (g[0] & g[1])*Gsr[i] + (g[0] & g[2])*Gtr[i]
+ (g[1] & g[0])*Grs[i] + (g[1] & g[1])*Gss[i] + (g[1] & g[2] )*Gts[i]
+ (g[2] & g[0])*Grt[i] + (g[2] & g[1])*Gst[i] + (g[2] & g[2])*Gtt[i]);
}
double phif = m_pMat->Porosity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
vec3d gradphif = m_pMat->gradPorosity(mp);
// evaluate stiffness matrix
for (i=0, i7=0; i<neln; ++i, i7 += 7)
{
for (j=0, j7 = 0; j<neln; ++j, j7 += 7)
{
mat3d Kuu = ((mat3dd(b*H[j]*dtrans))*denss*H[i] + (((et.m_a*phis)&gradN[j]) + mat3dd(b*phif*H[j]*dtrans) - ((fpt.m_w&gradN[j]) * (-1.0/phif*dJsoJ + a*dtrans) - (fpt.m_w&(et.m_L.transpose()*gradN[j]*dtrans)))*phis/phif + mat3dd(gradN[j]*fpt.m_w*a*dtrans) - ((bpt.m_Lw*fpt.m_w)&gradN[j])*phis/(phif*phif) + ((fpt.m_w&gradN[j])*((gradphif*2.0/phif + bpt.m_gradJ/et.m_J)*fpt.m_w) - (fpt.m_w&(gradgradN[j].transpose()*fpt.m_w)))*phis/(phif*phif) - pt.m_Lf*(mat3dd(gradN[j]*fpt.m_w)) - (pt.m_aft&gradN[j])*phis)*(-H[i]*densTf*phis/phif))*detJ; //mixture 2
mat3d Kuw = ((mat3dd(c*dtrans-phis/phif*dJsoJ-(gradphif*fpt.m_w)/(phif*phif))+pt.m_Lf)*H[j] + mat3dd(gradN[j]*fpt.m_w)/phif)*(-H[i]*densTf/phif*phis*detJ); //mixture 2
vec3d kuJ = pt.m_aft*(densTf/Jf*H[i]*H[j]*phis*detJ); //mixture 2
mat3d Kwu = (((et.m_a&gradN[j])*phis + mat3dd(b*phif*H[j]*dtrans) - ((fpt.m_w&gradN[j]) * (-1.0/phif*dJsoJ + a*dtrans) - (fpt.m_w&(et.m_L.transpose()*gradN[j]*dtrans)))*phis/phif + mat3dd(gradN[j]*fpt.m_w*a*dtrans) - ((bpt.m_Lw*fpt.m_w)&gradN[j])*phis/(phif*phif) + ((fpt.m_w&gradN[j])*((gradphif*2.0/phif + bpt.m_gradJ/et.m_J)*fpt.m_w) - (fpt.m_w&(gradgradN[j].transpose()*fpt.m_w)))*phis/(phif*phif) - pt.m_Lf*mat3dd(gradN[j]*fpt.m_w))*(H[i]*densTf/phif) + (pt.m_aft&gradN[j])*H[i]*densTf*(1.0-phis/phif))*detJ;
mat3d Kww = ((mat3dd(c*dtrans-phis/phif*dJsoJ-(gradphif*fpt.m_w)/(phif*phif))+pt.m_Lf)*H[j] + mat3dd(gradN[j]*fpt.m_w)/phif)*(H[i]*densTf/phif*detJ);
vec3d kwJ = pt.m_aft*(-densTf/Jf*H[i]*H[j]*detJ);
ke[i7+0][j7 ] += Kuu(0,0); ke[i7+0][j7+1] += Kuu(0,1); ke[i7+0][j7+2] += Kuu(0,2);
ke[i7+1][j7 ] += Kuu(1,0); ke[i7+1][j7+1] += Kuu(1,1); ke[i7+1][j7+2] += Kuu(1,2);
ke[i7+2][j7 ] += Kuu(2,0); ke[i7+2][j7+1] += Kuu(2,1); ke[i7+2][j7+2] += Kuu(2,2);
ke[i7+0][j7+3] += Kuw(0,0); ke[i7+0][j7+4] += Kuw(0,1); ke[i7+0][j7+5] += Kuw(0,2);
ke[i7+1][j7+3] += Kuw(1,0); ke[i7+1][j7+4] += Kuw(1,1); ke[i7+1][j7+5] += Kuw(1,2);
ke[i7+2][j7+3] += Kuw(2,0); ke[i7+2][j7+4] += Kuw(2,1); ke[i7+2][j7+5] += Kuw(2,2);
ke[i7+3][j7 ] += Kwu(0,0); ke[i7+3][j7+1] += Kwu(0,1); ke[i7+3][j7+2] += Kwu(0,2);
ke[i7+4][j7 ] += Kwu(1,0); ke[i7+4][j7+1] += Kwu(1,1); ke[i7+4][j7+2] += Kwu(1,2);
ke[i7+5][j7 ] += Kwu(2,0); ke[i7+5][j7+1] += Kwu(2,1); ke[i7+5][j7+2] += Kwu(2,2);
ke[i7+3][j7+3] += Kww(0,0); ke[i7+3][j7+4] += Kww(0,1); ke[i7+3][j7+5] += Kww(0,2);
ke[i7+4][j7+3] += Kww(1,0); ke[i7+4][j7+4] += Kww(1,1); ke[i7+4][j7+5] += Kww(1,2);
ke[i7+5][j7+3] += Kww(2,0); ke[i7+5][j7+4] += Kww(2,1); ke[i7+5][j7+5] += Kww(2,2);
ke[i7+0][j7+6] += kuJ.x;
ke[i7+1][j7+6] += kuJ.y;
ke[i7+2][j7+6] += kuJ.z;
ke[i7+3][j7+6] += kwJ.x;
ke[i7+4][j7+6] += kwJ.y;
ke[i7+5][j7+6] += kwJ.z;
}
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::Update(const FETimeInfo& tp)
{
bool berr = false;
int NE = (int) m_Elem.size();
#pragma omp parallel for shared(NE, berr)
for (int i=0; i<NE; ++i)
{
try
{
FESolidElement& el = Element(i);
if (el.isActive())
{
UpdateElementStress(i, tp);
}
}
catch (NegativeJacobian e)
{
#pragma omp critical
{
// reset the logfile mode
berr = true;
if (e.DoOutput()) feLogError(e.what());
}
}
}
if (berr) throw NegativeJacobianDetected();
}
//-----------------------------------------------------------------------------
//! Update element state data (mostly stresses, but some other stuff as well)
void FEBiphasicFSIDomain3D::UpdateElementStress(int iel, const FETimeInfo& tp)
{
double alphaf = tp.alphaf;
double alpham = tp.alpham;
double dt = GetFEModel()->GetTime().timeIncrement;
double dtrans = m_btrans ? 1 : m_sseps;
// get the solid element
FESolidElement& el = m_Elem[iel];
// get the number of integration points
int nint = el.GaussPoints();
// number of nodes
int neln = el.Nodes();
// nodal coordinates
const int NELN = FEElement::MAX_NODES;
vec3d r0[NELN], r[NELN];
vec3d vs[NELN];
vec3d a[NELN];
vec3d w[NELN];
vec3d aw[NELN];
double e[NELN];
double ae[NELN];
for (int j=0; j<neln; ++j) {
FENode& node = m_pMesh->Node(el.m_node[j]);
r0[j] = node.m_r0;
r[j] = node.m_rt*alphaf + node.m_rp*(1-alphaf);
vs[j] = node.get_vec3d(m_dofV[0], m_dofV[1], m_dofV[2])*alphaf + node.m_vp*(1-alphaf);
w[j] = node.get_vec3d(m_dofW[0], m_dofW[1], m_dofW[2])*alphaf + node.get_vec3d_prev(m_dofW[0], m_dofW[1], m_dofW[2])*(1-alphaf);
e[j] = node.get(m_dofEF)*alphaf + node.get_prev(m_dofEF)*(1-alphaf);
a[j] = node.m_at*alpham + node.m_ap*(1-alpham);
aw[j] = node.get_vec3d(m_dofAW[0], m_dofAW[1], m_dofAW[2])*alpham + node.get_vec3d_prev(m_dofAW[0], m_dofAW[1], m_dofAW[2])*(1-alpham);
ae[j] = node.get(m_dofAEF)*alpham + node.get_prev(m_dofAEF)*(1-alpham);
}
// loop over the integration points and update
// velocity, velocity gradient, acceleration
// stress and pressure at the integration point
for (int n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEElasticMaterialPoint& ept = *(mp.ExtractData<FEElasticMaterialPoint>());
FEFSIMaterialPoint& ft = *(mp.ExtractData<FEFSIMaterialPoint>());
FEBiphasicFSIMaterialPoint& bt = *(mp.ExtractData<FEBiphasicFSIMaterialPoint>());
// elastic material point data
mp.m_r0 = el.Evaluate(r0, n);
mp.m_rt = el.Evaluate(r, n);
mat3d Ft, Fp;
double Jt, Jp;
Jt = defgrad(el, Ft, n);
Jp = defgradp(el, Fp, n);
ept.m_F = Ft*alphaf + Fp*(1 - alphaf);
ept.m_J = ept.m_F.det();
mat3d Fi = ept.m_F.inverse();
ept.m_L = (Ft - Fp)*Fi*(dtrans / dt);
ept.m_v = m_btrans ? el.Evaluate(vs, n) : vec3d(0, 0, 0);
ept.m_a = m_btrans ? el.Evaluate(a, n) : vec3d(0, 0, 0);
//NOTE: Made these new function. Converts from GradJ to gradJ
vec3d GradJ = FESolidDomain::GradJ(el,n);
vec3d GradJp = FESolidDomain::GradJp(el, n);
//calculate gradJ gradphif
bt.m_gradJ = Fi.transpose()*(GradJ*alphaf + GradJp*(1-alphaf));
// FSI material point data
ft.m_w = el.Evaluate(w, n);
ft.m_Jdot = (Jt - Jp) / dt*dtrans;
ft.m_aw = el.Evaluate(aw, n)*dtrans;
// fluid material point data
bt.m_phi0 = m_pMat->SolidReferentialVolumeFraction(mp);
double phif = m_pMat->Porosity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
vec3d gradphif = m_pMat->gradPorosity(mp);
pt.m_efdot = el.Evaluate(ae, n)*dtrans;
pt.m_vft = ept.m_v + ft.m_w/phif;
mat3d Gradw = Gradient(el, w, n);
bt.m_Lw = Gradw*Fi;
pt.m_Lf = ept.m_L + bt.m_Lw/phif - (ft.m_w & gradphif)/(phif*phif);
pt.m_ef = el.Evaluate(e, n);
vec3d GradJf = Gradient(el, e, n);
pt.m_gradef = Fi.transpose()*GradJf;
// fluid acceleration
pt.m_aft = (ft.m_aw + ept.m_a*phif - ft.m_w*ft.m_Jdot*phis/phif/ept.m_J + pt.m_Lf*ft.m_w)/phif;
// calculate the fluid stress at this material point
pt.m_sf = m_pMat->Fluid()->Stress(mp);
// calculate the solid stress at this material point
ft.m_ss = m_pMat->Solid()->Stress(mp) - m_pMat->Fluid()->GetViscous()->Stress(mp)*phis;
// calculate the mixture stress at this material point
ept.m_s = ft.m_ss + pt.m_sf;
// calculate the fluid pressure
pt.m_pf = m_pMat->Fluid()->Pressure(mp);
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::InertialForces(FEGlobalVector& R)
{
int NE = (int)m_Elem.size();
#pragma omp parallel for shared (NE)
for (int i=0; i<NE; ++i)
{
// get the element
FESolidElement& el = m_Elem[i];
if (el.isActive()) {
// element force vector
vector<double> fe;
vector<int> lm;
// get the element force vector and initialize it to zero
int ndof = 7*el.Nodes();
fe.assign(ndof, 0);
// calculate internal force vector
ElementInertialForce(el, fe);
// get the element's LM vector
UnpackLM(el, lm);
// assemble element 'fe'-vector into global R vector
R.Assemble(el.m_node, lm, fe);
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::ElementInertialForce(FESolidElement& el, vector<double>& fe)
{
const FETimeInfo& tp = GetFEModel()->GetTime();
int i, n;
// jacobian determinant
double detJ;
const double* H;
int nint = el.GaussPoints();
int neln = el.Nodes();
double* gw = el.GaussWeights();
// repeat for all integration points
for (n=0; n<nint; ++n)
{
FEMaterialPoint& mp = *el.GetMaterialPoint(n);
FEFluidMaterialPoint& pt = *(mp.ExtractData<FEFluidMaterialPoint>());
FEElasticMaterialPoint& ept = *(mp.ExtractData<FEElasticMaterialPoint>());
double densTf = m_pMat->TrueFluidDensity(mp);
double densTs = m_pMat->TrueSolidDensity(mp);
double phis = m_pMat->SolidVolumeFrac(mp);
// calculate the jacobian
detJ = detJt(el, n, tp.alphaf)*gw[n];
H = el.H(n);
for (i=0; i<neln; ++i)
{
vec3d f = pt.m_aft*(densTf*H[i]*detJ);
vec3d fs = (-pt.m_aft*densTf + ept.m_a*densTs)*H[i]*phis*detJ; //mixture 2
// calculate internal force
// the '-' sign is so that the internal forces get subtracted
// from the global residual vector
fe[7*i+0] -= fs.x;
fe[7*i+1] -= fs.y;
fe[7*i+2] -= fs.z;
fe[7*i+3] -= f.x;
fe[7*i+4] -= f.y;
fe[7*i+5] -= f.z;
}
}
}
//-----------------------------------------------------------------------------
void FEBiphasicFSIDomain3D::Serialize(DumpStream& ar)
{
FESolidDomain::Serialize(ar);
ar & m_sseps & m_btrans;
}
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FESolutesDomain.h | .h | 3,196 | 107 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#pragma once
#include <FECore/FESolidDomain.h>
#include "FESolutesMaterial.h"
#include "febiofluid_api.h"
//-----------------------------------------------------------------------------
//! domain described by 3D volumetric elements
//!
class FEBIOFLUID_API FESolutesDomain : public virtual FESolidDomain
{
public:
//! constructor
FESolutesDomain(FEModel* pfem);
~FESolutesDomain() {}
//! initialize elements
void PreSolveUpdate(const FETimeInfo& timeInfo) override;
void SetSteadyStateAnalysis() { m_btrans = false; }
void SetTransientAnalysis() { m_btrans = true; }
public: // overrides from FEDomain
//! get the material
FEMaterial* GetMaterial() override { return m_pMat; }
//! set the material
void SetMaterial(FEMaterial* pm) override;
//! get the total dofs
const FEDofList& GetDOFList() const override;
public: // overrides from FEElasticDomain
//! initialize class
bool Init() override;
//! serialize data to archive
void Serialize(DumpStream& ar) override;
//! Reset data
void Reset() override;
//! activate
void Activate() override;
//! initialize material points in the domain
void InitMaterialPoints() override;
// update stresses
void Update(const FETimeInfo& tp) override;
// update the element stress
void UpdateElementStress(int iel, const FETimeInfo& tp);
//! internal stress forces
void InternalForces(FEGlobalVector& R);
//! calculates the global stiffness matrix for this domain
void StiffnessMatrix(FELinearSystem& LS);
public:
// --- S T I F F N E S S ---
//! calculates the solid element stiffness matrix
void ElementStiffness(FESolidElement& el, matrix& ke);
// --- R E S I D U A L ---
//! Calculates the internal stress vector for solid elements
void ElementInternalForce(FESolidElement& el, vector<double>& fe);
protected:
bool m_btrans;
int m_dofC;
int m_dofAC;
FEDofList m_dof;
FESolutesMaterial* m_pMat;
};
| Unknown |
3D | febiosoftware/FEBio | FEBioFluid/FEConstraintNormalFlow.cpp | .cpp | 6,175 | 135 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEConstraintNormalFlow.h"
#include "FECore/FECoreKernel.h"
#include <FECore/FEMesh.h>
BEGIN_FECORE_CLASS(FEConstraintNormalFlow, FESurfaceConstraint)
ADD_PARAMETER(m_lc.m_laugon, "laugon");
ADD_PARAMETER(m_lc.m_tol, "tol");
ADD_PARAMETER(m_lc.m_eps, "penalty");
ADD_PARAMETER(m_lc.m_rhs, "rhs");
ADD_PARAMETER(m_lc.m_naugmin, "minaug");
ADD_PARAMETER(m_lc.m_naugmax, "maxaug");
END_FECORE_CLASS();
//-----------------------------------------------------------------------------
FEConstraintNormalFlow::FEConstraintNormalFlow(FEModel* pfem) : FESurfaceConstraint(pfem), m_surf(pfem), m_lc(pfem)
{
m_binit = false;
}
//-----------------------------------------------------------------------------
//! Initializes data structures.
void FEConstraintNormalFlow::Activate()
{
// don't forget to call base class
FESurfaceConstraint::Activate();
if (m_binit == false)
{
m_surf.UpdateNodeNormals();
// get the dof indices
int dof_wx = GetDOFIndex("wx");
int dof_wy = GetDOFIndex("wy");
int dof_wz = GetDOFIndex("wz");
// create linear constraints
// for a surface with zero tangential velocity the constraints
// on (vx, vy, vz) are
// (1-nx^2)*vx - nx*ny*vy - nx*nz*vz = 0
// -nx*ny*vx + (1-ny^2)*vy - ny*nz*vz = 0
// -nx*nz*vx - ny*nz*vy + (1-nz^2)*vz = 0
for (int i=0; i<m_surf.Nodes(); ++i) {
FENode& node = m_surf.Node(i);
if ((node.HasFlags(FENode::EXCLUDE) == false) && (node.m_rid == -1)) {
vec3d nn = m_surf.NodeNormal(i);
// (1-nx^2)*vx - nx*ny*vy - nx*nz*vz = 0
FEAugLagLinearConstraint* pLC0 = fecore_alloc(FEAugLagLinearConstraint, GetFEModel());
pLC0->AddDOF(node.GetID(), dof_wx, 1.0 - nn.x * nn.x);
pLC0->AddDOF(node.GetID(), dof_wy, - nn.x * nn.y);
pLC0->AddDOF(node.GetID(), dof_wz, - nn.x * nn.z);
// add the linear constraint to the system
if ((pLC0->m_dof[0]->m_val != 0) || (pLC0->m_dof[1]->m_val != 0) || (pLC0->m_dof[2]->m_val != 0))
m_lc.add(pLC0);
// -nx*ny*vx + (1-ny^2)*vy - ny*nz*vz = 0
FEAugLagLinearConstraint* pLC1 = fecore_alloc(FEAugLagLinearConstraint, GetFEModel());
pLC1->AddDOF(node.GetID(), dof_wx, -nn.y * nn.x);
pLC1->AddDOF(node.GetID(), dof_wy, 1.0 -nn.y * nn.y);
pLC1->AddDOF(node.GetID(), dof_wz, -nn.y * nn.z);
// add the linear constraint to the system
if ((pLC1->m_dof[0]->m_val != 0) || (pLC1->m_dof[1]->m_val != 0) || (pLC1->m_dof[2]->m_val != 0))
m_lc.add(pLC1);
// -nx*nz*vx - ny*nz*vy + (1-nz^2)*vz = 0
FEAugLagLinearConstraint* pLC2 = fecore_alloc(FEAugLagLinearConstraint, GetFEModel());
pLC2->AddDOF(node.GetID(), dof_wx, -nn.z * nn.x);
pLC2->AddDOF(node.GetID(), dof_wy, -nn.z * nn.y);
pLC2->AddDOF(node.GetID(), dof_wz, 1.0-nn.z * nn.z);
// add the linear constraint to the system
if ((pLC2->m_dof[0]->m_val != 0) || (pLC2->m_dof[1]->m_val != 0) || (pLC2->m_dof[2]->m_val != 0))
m_lc.add(pLC2);
}
}
m_lc.Init();
m_lc.Activate();
m_binit = true;
}
}
//-----------------------------------------------------------------------------
bool FEConstraintNormalFlow::Init()
{
// initialize surface
return m_surf.Init();
}
//-----------------------------------------------------------------------------
void FEConstraintNormalFlow::Serialize(DumpStream& ar)
{
FESurfaceConstraint::Serialize(ar);
m_lc.Serialize(ar);
if (ar.IsShallow()) return;
ar & m_surf;
}
//-----------------------------------------------------------------------------
void FEConstraintNormalFlow::LoadVector(FEGlobalVector& R, const FETimeInfo& tp) { m_lc.LoadVector(R, tp); }
void FEConstraintNormalFlow::StiffnessMatrix(FELinearSystem& LS, const FETimeInfo& tp) { m_lc.StiffnessMatrix(LS, tp); }
bool FEConstraintNormalFlow::Augment(int naug, const FETimeInfo& tp) { return m_lc.Augment(naug, tp); }
void FEConstraintNormalFlow::BuildMatrixProfile(FEGlobalMatrix& M) { m_lc.BuildMatrixProfile(M); }
int FEConstraintNormalFlow::InitEquations(int neq) { return m_lc.InitEquations(neq); }
void FEConstraintNormalFlow::Update(const std::vector<double>& Ui, const std::vector<double>& ui) { m_lc.Update(Ui, ui); }
void FEConstraintNormalFlow::UpdateIncrements(std::vector<double>& Ui, const std::vector<double>& ui) { m_lc.UpdateIncrements(Ui, ui); }
void FEConstraintNormalFlow::PrepStep() { m_lc.PrepStep(); }
| C++ |
3D | febiosoftware/FEBio | FEBioFluid/FEFluidResidualVector.cpp | .cpp | 2,886 | 90 | /*This file is part of the FEBio source code and is licensed under the MIT license
listed below.
See Copyright-FEBio.txt for details.
Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
the City of New York, and others.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.*/
#include "stdafx.h"
#include "FEFluidResidualVector.h"
#include "FECore/DOFS.h"
#include "FECore/FEModel.h"
#include <FECore/FELinearConstraintManager.h>
using namespace std;
//-----------------------------------------------------------------------------
FEFluidResidualVector::FEFluidResidualVector(FEModel& fem, vector<double>& R, vector<double>& Fr) : FEGlobalVector(fem, R, Fr)
{
}
//-----------------------------------------------------------------------------
FEFluidResidualVector::~FEFluidResidualVector()
{
}
//-----------------------------------------------------------------------------
void FEFluidResidualVector::Assemble(vector<int>& en, vector<int>& elm, vector<double>& fe)
{
vector<double>& R = m_R;
int i, I;
vec3d a, d;
//#pragma omp critical
{
// assemble the element residual into the global residual
int ndof = (int)fe.size();
for (i=0; i<ndof; ++i)
{
I = elm[i];
if ( I >= 0){
#pragma omp atomic
R[I] += fe[i];
}
// TODO: Find another way to store reaction forces
else if (-I-2 >= 0){
#pragma omp atomic
m_Fr[-I-2] -= fe[i];
}
}
int ndn = ndof / (int)en.size();
// if there are linear constraints we need to apply them
// process linear constraints
FELinearConstraintManager& LCM = m_fem.GetLinearConstraintManager();
if (LCM.LinearConstraints())
{
LCM.AssembleResidual(R, en, elm, fe);
}
}
}
| C++ |
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