CFEM_LinearElasticity::CFEM_LinearElasticity(unsigned short val_nDim, unsigned short val_nVar,
CConfig *config) : CFEM_Elasticity(val_nDim, val_nVar, config) {
unsigned short iVar;
if (nDim == 2){
nodalDisplacement = new su2double* [4]; /*--- As of now, 4 is the maximum number of nodes for 2D problems ---*/
for (iVar = 0; iVar < 4; iVar++) nodalDisplacement[iVar] = new su2double[nDim];
}
else if (nDim == 3){
nodalDisplacement = new su2double* [8]; /*--- As of now, 8 is the maximum number of nodes for 3D problems ---*/
for (iVar = 0; iVar < 8; iVar++) nodalDisplacement[iVar] = new su2double[nDim];
}
/*--- If it is linear elasticity, D is constant along the calculations ---*/
Compute_Constitutive_Matrix();
}
void CFEM_NonlinearElasticity::Compute_Tangent_Matrix(CElement *element, CConfig *config){
unsigned short iVar, jVar, kVar;
unsigned short iGauss, nGauss;
unsigned short iNode, jNode, nNode;
unsigned short iDim, bDim;
su2double Ks_Aux_ab;
su2double Weight, Jac_x;
su2double AuxMatrixKc[3][6];
su2double AuxMatrixKs[3];
/*--- Initialize auxiliary matrices ---*/
if (nDim == 2) bDim = 3;
else bDim = 6;
for (iVar = 0; iVar < bDim; iVar++){
for (jVar = 0; jVar < nDim; jVar++){
Ba_Mat[iVar][jVar] = 0.0;
Bb_Mat[iVar][jVar] = 0.0;
}
}
for (iVar = 0; iVar < 3; iVar++){
for (jVar = 0; jVar < 6; jVar++){
AuxMatrixKc[iVar][jVar] = 0.0;
}
}
for (iVar = 0; iVar < 3; iVar++){
AuxMatrixKs[iVar] = 0.0;
}
element->clearElement(); /*--- Restarts the element: avoids adding over previous results in other elements --*/
element->ComputeGrad_NonLinear();
nNode = element->GetnNodes();
nGauss = element->GetnGaussPoints();
/*--- Full integration of the constitutive and stress term ---*/
for (iGauss = 0; iGauss < nGauss; iGauss++){
Weight = element->GetWeight(iGauss);
Jac_x = element->GetJ_x(iGauss);
/*--- Initialize the deformation gradient for each Gauss Point ---*/
for (iVar = 0; iVar < 3; iVar++){
for (jVar = 0; jVar < 3; jVar++){
F_Mat[iVar][jVar] = 0.0;
b_Mat[iVar][jVar] = 0.0;
}
}
/*--- Retrieve the values of the gradients of the shape functions for each node ---*/
/*--- This avoids repeated operations ---*/
for (iNode = 0; iNode < nNode; iNode++){
for (iDim = 0; iDim < nDim; iDim++){
GradNi_Ref_Mat[iNode][iDim] = element->GetGradNi_X(iNode,iGauss,iDim);
GradNi_Curr_Mat[iNode][iDim] = element->GetGradNi_x(iNode,iGauss,iDim);
currentCoord[iNode][iDim] = element->GetCurr_Coord(iNode, iDim);
}
/*--- Compute the deformation gradient ---*/
for (iVar = 0; iVar < nDim; iVar++){
for (jVar = 0; jVar < nDim; jVar++){
F_Mat[iVar][jVar] += currentCoord[iNode][iVar]*GradNi_Ref_Mat[iNode][jVar];
}
}
/*--- This implies plane strain --> Consider the possible implementation for plane stress --*/
if (nDim == 2){
F_Mat[2][2] = 1.0;
}
}
if (nDim == 2) {
if (plane_stress){
// Compute the value of the term 33 for the deformation gradient
Compute_Plane_Stress_Term(element, config);
F_Mat[2][2] = f33;
}
else{
F_Mat[2][2] = 1.0;
}
}
/*--- Determinant of F --> Jacobian of the transformation ---*/
J_F = F_Mat[0][0]*F_Mat[1][1]*F_Mat[2][2]+
F_Mat[0][1]*F_Mat[1][2]*F_Mat[2][0]+
F_Mat[0][2]*F_Mat[1][0]*F_Mat[2][1]-
F_Mat[0][2]*F_Mat[1][1]*F_Mat[2][0]-
F_Mat[1][2]*F_Mat[2][1]*F_Mat[0][0]-
F_Mat[2][2]*F_Mat[0][1]*F_Mat[1][0];
/*--- Compute the left Cauchy deformation tensor ---*/
for (iVar = 0; iVar < 3; iVar++){
for (jVar = 0; jVar < 3; jVar++){
for (kVar = 0; kVar < 3; kVar++){
b_Mat[iVar][jVar] += F_Mat[iVar][kVar]*F_Mat[jVar][kVar];
}
}
}
/*--- Compute the constitutive matrix ---*/
Compute_Constitutive_Matrix(element, config);
Compute_Stress_Tensor(element, config);
for (iNode = 0; iNode < nNode; iNode++){
/*--------------------------------------------------------------------------------*/
/*---------------------------- NODAL STRESS TERM ---------------------------------*/
/*--------------------------------------------------------------------------------*/
/*--- Compute the nodal stress term for each gaussian point and for each node, ---*/
/*--- and add it to the element structure to be retrieved from the solver ---*/
for (iVar = 0; iVar < nDim; iVar++){
KAux_t_a[iVar] = 0.0;
for (jVar = 0; jVar < nDim; jVar++){
KAux_t_a[iVar] += Weight * Stress_Tensor[iVar][jVar] * GradNi_Curr_Mat[iNode][jVar] * Jac_x;
}
}
element->Add_Kt_a(KAux_t_a, iNode);
/*--------------------------------------------------------------------------------*/
/*----------------------- CONSTITUTIVE AND STRESS TERM ---------------------------*/
/*--------------------------------------------------------------------------------*/
if (nDim == 2){
Ba_Mat[0][0] = GradNi_Curr_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Curr_Mat[iNode][1];
Ba_Mat[2][0] = GradNi_Curr_Mat[iNode][1];
Ba_Mat[2][1] = GradNi_Curr_Mat[iNode][0];
}
else if (nDim ==3){
Ba_Mat[0][0] = GradNi_Curr_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Curr_Mat[iNode][1];
Ba_Mat[2][2] = GradNi_Curr_Mat[iNode][2];
Ba_Mat[3][0] = GradNi_Curr_Mat[iNode][1];
Ba_Mat[3][1] = GradNi_Curr_Mat[iNode][0];
Ba_Mat[4][0] = GradNi_Curr_Mat[iNode][2];
Ba_Mat[4][2] = GradNi_Curr_Mat[iNode][0];
Ba_Mat[5][1] = GradNi_Curr_Mat[iNode][2];
Ba_Mat[5][2] = GradNi_Curr_Mat[iNode][1];
}
/*--- Compute the BT.D Matrix ---*/
for (iVar = 0; iVar < nDim; iVar++){
for (jVar = 0; jVar < bDim; jVar++){
AuxMatrixKc[iVar][jVar] = 0.0;
for (kVar = 0; kVar < bDim; kVar++){
AuxMatrixKc[iVar][jVar] += Ba_Mat[kVar][iVar]*D_Mat[kVar][jVar];
}
}
}
/*--- Compute the BT.D Matrix ---*/
for (iVar = 0; iVar < nDim; iVar++){
AuxMatrixKs[iVar] = 0.0;
for (jVar = 0; jVar < nDim; jVar++){
AuxMatrixKs[iVar] += GradNi_Curr_Mat[iNode][jVar]*Stress_Tensor[jVar][iVar]; // DOUBLE CHECK
}
}
/*--- Assumming symmetry ---*/
for (jNode = iNode; jNode < nNode; jNode++){
if (nDim == 2){
Bb_Mat[0][0] = GradNi_Curr_Mat[jNode][0];
Bb_Mat[1][1] = GradNi_Curr_Mat[jNode][1];
Bb_Mat[2][0] = GradNi_Curr_Mat[jNode][1];
Bb_Mat[2][1] = GradNi_Curr_Mat[jNode][0];
}
else if (nDim ==3){
Bb_Mat[0][0] = GradNi_Curr_Mat[jNode][0];
Bb_Mat[1][1] = GradNi_Curr_Mat[jNode][1];
Bb_Mat[2][2] = GradNi_Curr_Mat[jNode][2];
Bb_Mat[3][0] = GradNi_Curr_Mat[jNode][1];
Bb_Mat[3][1] = GradNi_Curr_Mat[jNode][0];
Bb_Mat[4][0] = GradNi_Curr_Mat[jNode][2];
Bb_Mat[4][2] = GradNi_Curr_Mat[jNode][0];
Bb_Mat[5][1] = GradNi_Curr_Mat[jNode][2];
Bb_Mat[5][2] = GradNi_Curr_Mat[jNode][1];
}
/*--- KAux_ab is the term for the constitutive part of the tangent matrix ---*/
for (iVar = 0; iVar < nDim; iVar++){
for (jVar = 0; jVar < nDim; jVar++){
KAux_ab[iVar][jVar] = 0.0;
for (kVar = 0; kVar < bDim; kVar++){
KAux_ab[iVar][jVar] += Weight * AuxMatrixKc[iVar][kVar] * Bb_Mat[kVar][jVar] * Jac_x;
}
}
}
/*--- Ks_Aux_ab is the term for the constitutive part of the tangent matrix ---*/
Ks_Aux_ab = 0.0;
for (iVar = 0; iVar < nDim; iVar++){
Ks_Aux_ab += Weight * AuxMatrixKs[iVar] * GradNi_Curr_Mat[jNode][iVar] * Jac_x;
}
element->Add_Kab(KAux_ab,iNode, jNode);
element->Add_Ks_ab(Ks_Aux_ab,iNode, jNode);
/*--- Symmetric terms --*/
if (iNode != jNode){
element->Add_Kab_T(KAux_ab, jNode, iNode);
element->Add_Ks_ab(Ks_Aux_ab,jNode, iNode);
}
}
}
}
}
void CFEALinearElasticity::Compute_Tangent_Matrix(CElement *element, CConfig *config) {
unsigned short iVar, jVar, kVar;
unsigned short iGauss, nGauss;
unsigned short iNode, jNode, nNode;
unsigned short iDim;
unsigned short bDim;
su2double Weight, Jac_X;
su2double AuxMatrix[3][6], *res_aux = new su2double[nVar];
/*--- Set element properties and recompute the constitutive matrix, this is needed
for multiple material cases and for correct differentiation ---*/
SetElement_Properties(element, config);
/*--- Register pre-accumulation inputs, material props and nodal coords ---*/
AD::StartPreacc();
AD::SetPreaccIn(E);
AD::SetPreaccIn(Nu);
AD::SetPreaccIn(Rho_s);
AD::SetPreaccIn(Rho_s_DL);
element->SetPreaccIn_Coords();
/*--- Recompute Lame parameters as they depend on the material properties ---*/
Compute_Lame_Parameters();
Compute_Constitutive_Matrix(element, config);
/*--- Initialize auxiliary matrices ---*/
if (nDim == 2) bDim = 3;
else bDim = 6;
for (iVar = 0; iVar < bDim; iVar++) {
for (jVar = 0; jVar < nDim; jVar++) {
Ba_Mat[iVar][jVar] = 0.0;
Bb_Mat[iVar][jVar] = 0.0;
}
}
for (iVar = 0; iVar < 3; iVar++) {
for (jVar = 0; jVar < 6; jVar++) {
AuxMatrix[iVar][jVar] = 0.0;
}
}
element->clearElement(); /*--- Restarts the element: avoids adding over previous results in other elements --*/
element->ComputeGrad_Linear();
nNode = element->GetnNodes();
nGauss = element->GetnGaussPoints();
for (iGauss = 0; iGauss < nGauss; iGauss++) {
Weight = element->GetWeight(iGauss);
Jac_X = element->GetJ_X(iGauss);
/*--- Retrieve the values of the gradients of the shape functions for each node ---*/
/*--- This avoids repeated operations ---*/
for (iNode = 0; iNode < nNode; iNode++) {
for (iDim = 0; iDim < nDim; iDim++) {
GradNi_Ref_Mat[iNode][iDim] = element->GetGradNi_X(iNode,iGauss,iDim);
}
}
for (iNode = 0; iNode < nNode; iNode++) {
if (nDim == 2) {
Ba_Mat[0][0] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][0] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][1] = GradNi_Ref_Mat[iNode][0];
}
else if (nDim == 3) {
Ba_Mat[0][0] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][2] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[3][0] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[3][1] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[4][0] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[4][2] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[5][1] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[5][2] = GradNi_Ref_Mat[iNode][1];
}
/*--- Compute the BT.D Matrix ---*/
for (iVar = 0; iVar < nDim; iVar++) {
for (jVar = 0; jVar < bDim; jVar++) {
AuxMatrix[iVar][jVar] = 0.0;
for (kVar = 0; kVar < bDim; kVar++) {
AuxMatrix[iVar][jVar] += Ba_Mat[kVar][iVar]*D_Mat[kVar][jVar];
}
}
}
/*--- Assumming symmetry ---*/
for (jNode = iNode; jNode < nNode; jNode++) {
if (nDim == 2) {
Bb_Mat[0][0] = GradNi_Ref_Mat[jNode][0];
Bb_Mat[1][1] = GradNi_Ref_Mat[jNode][1];
Bb_Mat[2][0] = GradNi_Ref_Mat[jNode][1];
Bb_Mat[2][1] = GradNi_Ref_Mat[jNode][0];
}
else if (nDim ==3) {
Bb_Mat[0][0] = GradNi_Ref_Mat[jNode][0];
Bb_Mat[1][1] = GradNi_Ref_Mat[jNode][1];
Bb_Mat[2][2] = GradNi_Ref_Mat[jNode][2];
Bb_Mat[3][0] = GradNi_Ref_Mat[jNode][1];
Bb_Mat[3][1] = GradNi_Ref_Mat[jNode][0];
Bb_Mat[4][0] = GradNi_Ref_Mat[jNode][2];
Bb_Mat[4][2] = GradNi_Ref_Mat[jNode][0];
Bb_Mat[5][1] = GradNi_Ref_Mat[jNode][2];
Bb_Mat[5][2] = GradNi_Ref_Mat[jNode][1];
}
for (iVar = 0; iVar < nDim; iVar++) {
for (jVar = 0; jVar < nDim; jVar++) {
KAux_ab[iVar][jVar] = 0.0;
for (kVar = 0; kVar < bDim; kVar++) {
KAux_ab[iVar][jVar] += Weight * AuxMatrix[iVar][kVar] * Bb_Mat[kVar][jVar] * Jac_X;
}
}
}
element->Add_Kab(KAux_ab,iNode, jNode);
/*--- Symmetric terms --*/
if (iNode != jNode) {
element->Add_Kab_T(KAux_ab, jNode, iNode);
}
}
}
}
// compute residual
for(iNode = 0; iNode<nNode; ++iNode)
{
for(jNode = 0; jNode<nNode; ++jNode)
{
su2double *Kab = element->Get_Kab(iNode,jNode);
for (iVar = 0; iVar < nVar; iVar++) {
res_aux[iVar] = 0.0;
for (jVar = 0; jVar < nVar; jVar++)
res_aux[iVar] += Kab[iVar*nVar+jVar]*
(element->GetCurr_Coord(jNode,jVar)-element->GetRef_Coord(jNode,jVar));
}
element->Add_Kt_a(res_aux,iNode);
}
}
/*--- Register the stress residual as preaccumulation output ---*/
element->SetPreaccOut_Kt_a();
AD::EndPreacc();
delete[] res_aux;
}
void CFEALinearElasticity::Compute_Averaged_NodalStress(CElement *element, CConfig *config) {
unsigned short iVar, jVar;
unsigned short iGauss, nGauss;
unsigned short iNode, nNode;
unsigned short iDim, bDim;
/*--- Auxiliary vector ---*/
su2double Strain[6], Stress[6];
/*--- Set element properties and recompute the constitutive matrix, this is needed
for multiple material cases and for correct differentiation ---*/
SetElement_Properties(element, config);
Compute_Constitutive_Matrix(element, config);
/*--- Initialize auxiliary matrices ---*/
if (nDim == 2) bDim = 3;
else bDim = 6;
for (iVar = 0; iVar < bDim; iVar++) {
for (jVar = 0; jVar < nDim; jVar++) {
Ba_Mat[iVar][jVar] = 0.0;
}
}
element->clearStress(); /*--- Clears the stress in the element: avoids adding over previous results in other elements --*/
element->ComputeGrad_Linear();
nNode = element->GetnNodes();
nGauss = element->GetnGaussPoints();
for (iGauss = 0; iGauss < nGauss; iGauss++) {
/*--- Retrieve the values of the gradients of the shape functions for each node ---*/
/*--- This avoids repeated operations ---*/
for (iNode = 0; iNode < nNode; iNode++) {
for (iDim = 0; iDim < nDim; iDim++) {
GradNi_Ref_Mat[iNode][iDim] = element->GetGradNi_X(iNode,iGauss,iDim);
nodalDisplacement[iNode][iDim] = element->GetCurr_Coord(iNode, iDim) - element->GetRef_Coord(iNode, iDim);
}
}
for (iVar = 0; iVar < bDim; iVar++) {
Strain[iVar] = 0.0;
}
for (iNode = 0; iNode < nNode; iNode++) {
/*--- Set matrix B ---*/
if (nDim == 2) {
Ba_Mat[0][0] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][0] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][1] = GradNi_Ref_Mat[iNode][0];
}
else if (nDim ==3) {
Ba_Mat[0][0] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[1][1] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[2][2] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[3][0] = GradNi_Ref_Mat[iNode][1];
Ba_Mat[3][1] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[4][0] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[4][2] = GradNi_Ref_Mat[iNode][0];
Ba_Mat[5][1] = GradNi_Ref_Mat[iNode][2];
Ba_Mat[5][2] = GradNi_Ref_Mat[iNode][1];
}
/*--- Compute the Strain Vector as B*u ---*/
for (iVar = 0; iVar < bDim; iVar++) {
for (jVar = 0; jVar < nDim; jVar++) {
Strain[iVar] += Ba_Mat[iVar][jVar]*nodalDisplacement[iNode][jVar];
}
}
}
/*--- Compute the Stress Vector as D*epsilon ---*/
for (iVar = 0; iVar < bDim; iVar++) {
Stress[iVar] = 0.0;
for (jVar = 0; jVar < bDim; jVar++) {
Stress[iVar] += D_Mat[iVar][jVar]*Strain[jVar];
}
}
for (iNode = 0; iNode < nNode; iNode++) {
/*--- If nDim is 3 and we compute it this way, the 3rd component is the Szz, while in the ---*/
/*--- output it is the 4th component for practical reasons ---*/
if (nDim == 2) {
element->Add_NodalStress(Stress[0] * element->GetNi_Extrap(iNode, iGauss), iNode, 0);
element->Add_NodalStress(Stress[1] * element->GetNi_Extrap(iNode, iGauss), iNode, 1);
element->Add_NodalStress(Stress[2] * element->GetNi_Extrap(iNode, iGauss), iNode, 2);
}
else if (nDim == 3) {
element->Add_NodalStress(Stress[0] * element->GetNi_Extrap(iNode, iGauss), iNode, 0);
element->Add_NodalStress(Stress[1] * element->GetNi_Extrap(iNode, iGauss), iNode, 1);
element->Add_NodalStress(Stress[3] * element->GetNi_Extrap(iNode, iGauss), iNode, 2);
element->Add_NodalStress(Stress[2] * element->GetNi_Extrap(iNode, iGauss), iNode, 3);
element->Add_NodalStress(Stress[4] * element->GetNi_Extrap(iNode, iGauss), iNode, 4);
element->Add_NodalStress(Stress[5] * element->GetNi_Extrap(iNode, iGauss), iNode, 5);
}
}
}
}