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Thermo-elasticTopologyOptimization
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cflin 2 years ago
parent
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f5a826a54c
3 changed files with 33 additions and 55 deletions
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  1. 16
      examples/top-thermoelastic-regular-model/config.json
  2. 67
      src/ThermoelasticTop3d.cpp
  3. 5
      src/Top3d.cpp

16
examples/top-thermoelastic-regular-model/config.json
View File

@ -11,10 +11,10 @@
"penal": 3.0,
"r_min": 1.5,
"T_ref": 295,
"T_limit": 345,
"R_E": 12,
"T_limit": 325,
"R_E": 8,
"R_lambda": 8,
"R_beta": 0
"R_beta":0
},
"model": {
"regular_model": {
@ -29,7 +29,7 @@
{
"min": [0, 0.5, 0.5],
"max": [1, 0.5, 0.5],
"val": [0.0, 0.0, -1e15]
"val": [0.0, 0.0, -1.5e9]
}
],
@ -51,12 +51,12 @@
{
"min": [0, 0.2, 0.5],
"max": [1, 0.2, 0.5],
"heat_flux": 0.335, "unit": "W"
"heat_flux": 12.35, "unit": "W"
},
{
"min": [0, 0.8, 0.5],
"max": [1, 0.8, 0.5],
"heat_flux": 0.335, "unit": "W"
"heat_flux": 12.35, "unit": "W"
}
],
@ -64,12 +64,12 @@
{
"min": [0, 0, 0],
"max": [1, 1, 0],
"temperature": 325, "unit": "K"
"temperature": 312, "unit": "K"
},
{
"min": [0, 0, 1],
"max": [1, 1, 1],
"temperature": 325, "unit": "K"
"temperature": 312, "unit": "K"
}
]
}

67
src/ThermoelasticTop3d.cpp
View File

@ -34,7 +34,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::VectorXd dv(sp_mesh_->GetNumEles());
dv.setOnes();
dv = sp_mech_top3d_->H_ * (dv.array() / sp_mech_top3d_->Hs_.array()).matrix().eval();
dv = (sp_mech_top3d_->H_ * dv).array() / sp_mech_top3d_->Hs_.array();
Eigen::VectorXd ele_to_write =
Eigen::VectorXd::Zero(sp_mesh_->GetLx() * sp_mesh_->GetLy() * sp_mesh_->GetLz());
@ -77,10 +77,10 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
spdlog::warn("using Eigen built-in direct solver!");
#endif
// start iteration
while (change > sp_para_->tol_x * 1e-6 && loop < sp_para_->max_loop) {
while (change > sp_para_->tol_x && loop < sp_para_->max_loop) {
++loop;
// filter
xPhys_col = sp_mech_top3d_->H_ * (xPhys_col.array() / sp_mech_top3d_->Hs_.array()).matrix().eval();
xPhys_col = (sp_mech_top3d_->H_ * xPhys_col).array() / sp_mech_top3d_->Hs_.array();
auto CalR = [](double rho, double R) {
return rho / (1.0 + R * (1.0 - rho));
};
@ -93,7 +93,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
};
auto CalDRDrho_Vec = [](const Eigen::VectorXd &vec_rho, double R) -> Eigen::VectorXd {
auto down = 1 + R * (1 - vec_rho.array());
return (1 + R) / down.pow(2);
return (1 + R) / (down * down);
};
auto CalE_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd {
return E_min + CalR_Vec(vec_rho, sp_para_->R_E).array() * (E0_m - E_min);
@ -154,7 +154,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
double beta_rho = CalBeta(xPhys_col(i));
F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
}
if (loop ==1 || loop == sp_para_->max_loop)
if (loop == 1 || loop == sp_para_->max_loop)
spdlog::info("||Fth|| / ||Fm||: {}", F_th.norm() / sp_mech_top3d_->F_.norm());
Eigen::VectorXd F = Eigen::VectorXd(sp_mech_top3d_->F_) + F_th;
@ -169,9 +169,9 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
// compliance
Eigen::VectorXd ce(sp_mesh_->GetNumEles());
for (int i = 0; i < sp_mesh_->GetNumEles(); ++i) {
Eigen::VectorXi dofs_in_ele_i = sp_mesh_->MapEleId2Dofs(i);
Eigen::VectorXd ce(sp_mech_top3d_->sp_mesh_->GetNumEles());
for (int i = 0; i < sp_mech_top3d_->sp_mesh_->GetNumEles(); ++i) {
Eigen::VectorXi dofs_in_ele_i = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i);
Eigen::VectorXd Ue = sp_mech_top3d_->U_(dofs_in_ele_i);
ce(i) = Ue.transpose() * sp_mech_top3d_->Ke_ * Ue;
}
@ -190,13 +190,12 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::VectorXd v_dFth_drho(i_dFth_drho_.size());
for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) {
Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i);
Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i);
// Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i);
double Te = T(dofs_th).mean();
// double beta_rho = CalBeta(xPhys_col(i));
// F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
Eigen::VectorXd ele_dFth_drho =
(CalDBetaDrho(xPhys_col(i)) * (Te - sp_mech_top3d_->sp_para_->T_ref)
) * Inted_;// 24x1
CalDBetaDrho(xPhys_col(i)) * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;// 24x1
assert(ele_dFth_drho.size() == 24);
v_dFth_drho(Eigen::seqN(i * ele_dFth_drho.size(), ele_dFth_drho.size())) = ele_dFth_drho;
}
@ -209,27 +208,27 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
sp_mech_top3d_->sp_mesh_->GetNumDofs());
Eigen::VectorXd v_dFth_dT(i_dFth_dT_.size());
for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) {
Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i);
Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i);
// Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i);
// Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i);
double beta_rho = CalBeta(xPhys_col(i));
// F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
Eigen::MatrixXd ele_dFth_dT =
Eigen::VectorXd::Ones(dofs_th.size()) * 1.0 / 8.0 * beta_rho * Inted_.transpose();
Eigen::VectorXd::Ones(sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE()) * 1.0 /
sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE() * beta_rho * Inted_.transpose();
assert(ele_dFth_dT.rows() == 8 && ele_dFth_dT.cols() == 24);
v_dFth_dT(Eigen::seqN(i * ele_dFth_dT.size(), ele_dFth_dT.size())) = ele_dFth_dT.reshaped();
}
auto v_dFth_dT_tri = Vec2Triplet(i_dFth_dT_, j_dFth_dT_, v_dFth_dT);
dFth_dT.setFromTriplets(v_dFth_dT_tri.begin(), v_dFth_dT_tri.end());
Eigen::VectorXd rhs = dFth_dT *2* lambda_m;
Eigen::VectorXd rhs = dFth_dT * 2 * lambda_m;
for (auto dof_value: sp_thermal_top3d_->v_dofs_to_set) {
auto [dof, value] = dof_value;
rhs(dof) = sp_thermal_top3d_->K_.coeffRef(dof, dof) * value;
}
// lambda_t
Eigen::VectorXd lambda_t = solver_th.solve(rhs);
// dF_drho
Eigen::SparseMatrix<double> &dF_drho = dFth_drho;
// lambda_m_Mul_dKm_drho_Mul_U
Eigen::VectorXd lambda_m_Mul_dKm_drho_Mul_U =
-CalDEDrho_Vec(xPhys_col).array() * ce.array();
@ -251,8 +250,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
+
lambda_m_Mul_dKm_drho_Mul_U
+
2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_)
;
2 * Eigen::VectorXd(dFth_drho * sp_mech_top3d_->U_);
// dT_drho
auto CalDKth_Mul_T__For_DTi_Drhoj = [&](int rho_i) -> Eigen::SparseVector<double> {
Eigen::VectorXi dofs_in_ele = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(rho_i);
@ -266,7 +264,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
return sp_dKth_Mul_T;
};
auto CalDTi_Drhoj = [&](int Tdof, const Eigen::SparseVector<double> &sp_dKth_Mul_T) -> double {
Eigen::VectorXd Li=Eigen::VectorXd ::Zero(sp_dKth_Mul_T.rows());
Eigen::VectorXd Li = Eigen::VectorXd::Zero(sp_dKth_Mul_T.rows());
Li(Tdof) = -1;
for (auto dof_value: sp_thermal_top3d_->v_dofs_to_set) {
auto [dof, value] = dof_value;
@ -279,38 +277,19 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
sp_thermal_top3d_->set_dofs_to_load.size());
for (auto it = map_ele2Limit.begin(); it != map_ele2Limit.end(); ++it) {
auto [ele_id, v_limited] = *it;
auto sp_dKth_Mul_T=CalDKth_Mul_T__For_DTi_Drhoj(ele_id);
auto sp_dKth_Mul_T = CalDKth_Mul_T__For_DTi_Drhoj(ele_id);
for (auto &limited: v_limited) {
dT_drho(ele_id, limited.idx_of_load_dof) = CalDTi_Drhoj(limited.dof,sp_dKth_Mul_T);
dT_drho(ele_id, limited.idx_of_load_dof) = CalDTi_Drhoj(limited.dof, sp_dKth_Mul_T);
}
}
// for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) {
// Eigen::VectorXi dofs_in_ele_i = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i);
// Eigen::VectorXd dKe_th_Mul_T =
// CalDlambdaDrho(xPhys_col(i)) * sp_thermal_top3d_->Ke_ * T(dofs_in_ele_i);
// Eigen::MatrixXd Ke_th(sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE(),
// sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE());
// for (int j1 = 0; j1 < Ke_th.cols(); ++j1) {
// for (int i1 = 0; i1 < Ke_th.rows(); ++i1) {
// Ke_th(i1, j1) = sp_thermal_top3d_->K_.coeffRef(i1, j1);
// }
// }
// Eigen::VectorXd ele_dT_drho = Ke_th.llt().solve(-dKe_th_Mul_T);
// dT_drho(i, dofs_in_ele_i) = ele_dT_drho.transpose();
// }
// for (auto dof_value: sp_thermal_top3d_->v_dofs_to_set) {
// auto [dof, value] = dof_value;
// dT_drho.col(dof).setZero();
// }
// dc_dx
Eigen::VectorXd dc_dx = sp_mech_top3d_->drho_dx_ * dc_drho;
// dT_dx
Eigen::MatrixXd dT_dx = sp_mech_top3d_->drho_dx_ * dT_drho;
// mma solver
#define SENSITIVITY_SCALE_COEF 100
#define SENSITIVITY_SCALE_COEF 200
size_t num_constraints =
1 + dT_dx.cols();// volume and temperature constraints
@ -320,8 +299,8 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::VectorXd variables_tmp = flg_chosen ? xPhys_col(chosen_ele_id) : xPhys_col;
double f0val = c;
Eigen::VectorXd df0dx = flg_chosen
? dc_dx(chosen_ele_id).eval() / dc_dx(chosen_ele_id).cwiseAbs().maxCoeff()
: dc_dx / dc_dx.cwiseAbs().maxCoeff() ;
? dc_dx(chosen_ele_id).eval() / dc_dx(chosen_ele_id).cwiseAbs().maxCoeff()*SENSITIVITY_SCALE_COEF
: dc_dx / dc_dx.cwiseAbs().maxCoeff()*SENSITIVITY_SCALE_COEF;
// double fval = v - num_variables * sp_para_->volfrac;
Eigen::VectorXd fval = (Eigen::VectorXd(num_constraints) << (v / num_variables - sp_para_->volfrac),

5
src/Top3d.cpp
View File

@ -187,8 +187,7 @@ namespace da::sha {
void Top3d::Precompute() {
Eigen::MatrixXi mat_ele2dofs = sp_mesh_->GetEleId2DofsMap();
int dofs_each_ele = sp_mesh_->Get_NUM_NODES_EACH_ELE() *
sp_mesh_->Get_DOFS_EACH_NODE(); // 24 for mathe; 8 for heat
int dofs_each_ele = sp_mesh_->Get_DOFS_EACH_ELE();// 24 for mathe; 8 for heat
iK_ = Eigen::KroneckerProduct(mat_ele2dofs, Eigen::VectorXi::Ones(dofs_each_ele))
.transpose()
.reshaped();
@ -249,7 +248,7 @@ namespace da::sha {
Eigen::SparseMatrix<double> sp_inv_Hs(i_Hs.size(), i_Hs.size());
auto v_inv_Hs_tri = Vec2Triplet(i_Hs, i_Hs, Eigen::VectorXd(1.0 / Hs_.array()));
sp_inv_Hs.setFromTriplets(v_inv_Hs_tri.begin(), v_inv_Hs_tri.end());
drho_dx_ = sp_inv_Hs * H_;
drho_dx_ = sp_inv_Hs * H_.transpose();
}
} // namespace top

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