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Thermo-elasticTopologyOptimization
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todo: fix dT_drho

multiple_top
cflin 2 years ago
parent
61a071c61c
commit
d2787f90df
4 changed files with 61 additions and 43 deletions
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  1. 51
      examples/top-thermoelastic-regular-model/config.json
  2. 2
      examples/top-thermoelastic-regular-model/main.cpp
  3. 49
      src/ThermoelasticTop3d.cpp
  4. 2
      src/ThermoelasticTop3d.h

51
examples/top-thermoelastic-regular-model/config.json
View File

@ -1,34 +1,34 @@
{ {
"material": { "material": {
"E": 1.0, "E": 2e11,
"poisson_ratio": 0.3, "poisson_ratio": 0.3,
"thermal_conductivity":0.004, "unit": "W/K", "thermal_conductivity":43, "unit": "W/(m*K)",
"thermal_expansion_coefficient": 1e-6, "unit": "1/K" "thermal_expansion_coefficient": 1.21e-5, "unit": "1/K"
}, },
"topology": { "topology": {
"max_loop": 100, "max_loop": 100,
"volfrac": 0.5, "volfrac": 0.5,
"r_min": 1.5, "r_min": 1.5,
"T_ref": 295, "T_ref": 295,
"T_limit": 325, "T_limit": 345,
"R_E": 0, "R_E": 12,
"R_lambda": 0, "R_lambda": 8,
"R_beta": 0 "R_beta": 0
}, },
"model": { "model": {
"regular_model": { "regular_model": {
"lx": 2, "lx": 1,
"ly": 20, "ly": 50,
"lz": 30 "lz": 35
}, },
"visual_model":"2-box-refined.obj" "visual_model":"2-box-refined.obj"
}, },
"mechanical_boundary_condition":{ "mechanical_boundary_condition":{
"NBC": [ "NBC": [
{ {
"min": [0, 1, 0], "min": [0, 0.5, 0.5],
"max": [1, 1, 0], "max": [1, 0.5, 0.5],
"val": [0.0, 0.0, -1.0] "val": [0.0, 0.0, -1e1]
} }
], ],
@ -37,29 +37,38 @@
"min": [0, 0, 0], "min": [0, 0, 0],
"max": [1, 0, 1], "max": [1, 0, 1],
"dir": [1, 1, 1] "dir": [1, 1, 1]
},
{
"min": [0, 1, 0],
"max": [1, 1, 1],
"dir": [1, 1, 1]
} }
] ]
}, },
"thermal_boundary_condition": { "thermal_boundary_condition": {
"NBC": [ "NBC": [
{ {
"min": [0, 0.25, 0.5], "min": [0, 0.2, 0.5],
"max": [1, 0.25, 0.5], "max": [1, 0.2, 0.5],
"heat_flux": 1e-15, "unit": "W" "heat_flux": 0.335, "unit": "W"
}, },
{ {
"min": [0, 0.75, 0.5], "min": [0, 0.8, 0.5],
"max": [1, 0.75, 0.5], "max": [1, 0.8, 0.5],
"heat_flux": 1e-15, "unit": "W" "heat_flux": 0.335, "unit": "W"
} }
], ],
"DBC": [ "DBC": [
{ {
"min": [0, 0, 0], "min": [0, 0, 0],
"max": [1, 0, 1], "max": [1, 1, 0],
"temperature": 312, "unit": "K" "temperature": 325, "unit": "K"
},
{
"min": [0, 0, 1],
"max": [1, 1, 1],
"temperature": 325, "unit": "K"
} }
] ]
} }

2
examples/top-thermoelastic-regular-model/main.cpp
View File

@ -133,6 +133,6 @@ int main() {
write_tensor3d(output_dir / "txt" / "top_mach_regular_field_matrix.txt", ten_rho, sp_mech_mesh->GetOrigin(), write_tensor3d(output_dir / "txt" / "top_mach_regular_field_matrix.txt", ten_rho, sp_mech_mesh->GetOrigin(),
sp_mech_mesh->GetOrigin() + sp_mech_mesh->GetLenBox()); sp_mech_mesh->GetOrigin() + sp_mech_mesh->GetLenBox());
WriteTensorToVtk(output_dir / "vtk" / "top_mach_regular_field_matrix.vtk", ten_rho, sp_mech_mesh); WriteTensorToVtk(output_dir / "vtk" / "top_mach_regular_field_matrix.vtk", ten_rho, sp_mech_mesh);
// WriteUToVtk(output_dir / "vtk" / "top_thermoelastic_regular_U.vtk",ther_top3d.GetU(),sp_mech_mesh); WriteUToVtk(output_dir / "vtk" / "top_thermoelastic_regular_U.vtk",ther_top3d.GetU(),sp_mech_mesh);
} }

49
src/ThermoelasticTop3d.cpp
View File

@ -25,9 +25,11 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
int loop = 0; int loop = 0;
double change = 1.0; double change = 1.0;
double E0_m = sp_mech_top3d_->sp_fea_->sp_material_->E; double E0_m = sp_mech_top3d_->sp_fea_->sp_material_->E;
double E_min = E0_m * sp_mech_top3d_->sp_para_->E_factor;
double lambda0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_conductivity; double lambda0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_conductivity;
double lambda_min = lambda0 * sp_mech_top3d_->sp_para_->E_factor; double lambda_min = lambda0 * sp_mech_top3d_->sp_para_->E_factor;
double alpha0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_expansion_coefficient; double alpha0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_expansion_coefficient;
double alpha_min=alpha0 * sp_mech_top3d_->sp_para_->E_factor;
// Precompute // Precompute
Eigen::VectorXd dv(sp_mesh_->GetNumEles()); Eigen::VectorXd dv(sp_mesh_->GetNumEles());
@ -75,7 +77,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
spdlog::warn("using Eigen built-in direct solver!"); spdlog::warn("using Eigen built-in direct solver!");
#endif #endif
// start iteration // start iteration
while (change > sp_para_->tol_x && loop < sp_para_->max_loop) { while (change > sp_para_->tol_x*1e-6 && loop < sp_para_->max_loop) {
++loop; ++loop;
// filter // 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()).matrix().eval();
@ -94,10 +96,10 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
return (1 + R) / down.pow(2); return (1 + R) / down.pow(2);
}; };
auto CalE_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { auto CalE_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd {
return CalR_Vec(vec_rho, sp_para_->R_E) * E0_m; return E_min + CalR_Vec(vec_rho, sp_para_->R_E).array() * (E0_m - E_min);
}; };
auto CalDEDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { auto CalDEDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd {
return CalDRDrho_Vec(vec_rho, sp_para_->R_E) * E0_m; return CalDRDrho_Vec(vec_rho, sp_para_->R_E) * (E0_m - E_min);
}; };
auto CalLambda_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { auto CalLambda_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd {
return lambda_min + CalR_Vec(vec_rho, sp_para_->R_lambda).array() * (lambda0 - lambda_min); return lambda_min + CalR_Vec(vec_rho, sp_para_->R_lambda).array() * (lambda0 - lambda_min);
@ -106,14 +108,14 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
return CalDRDrho(rho, sp_para_->R_lambda) * (lambda0 - lambda_min); return CalDRDrho(rho, sp_para_->R_lambda) * (lambda0 - lambda_min);
}; };
auto CalDlambdaDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { auto CalDlambdaDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd {
return CalDRDrho_Vec(vec_rho, sp_para_->R_lambda) * (lambda0 - lambda_min); return CalDRDrho_Vec(vec_rho, sp_para_->R_lambda) * (lambda0 - lambda_min);
}; };
auto CalBeta = [&](double rho) { auto CalBeta = [&](double rho) {
return CalR(rho, sp_para_->R_beta) * E0_m * alpha0; return E_min*alpha_min+ CalR(rho, sp_para_->R_beta) * (E0_m * alpha0-E_min*alpha_min);
}; };
auto CalDBetaDrho = [&](double rho) { auto CalDBetaDrho = [&](double rho) {
return CalDRDrho(rho, sp_para_->R_beta) * E0_m * alpha0; return CalDRDrho(rho, sp_para_->R_beta) * (E0_m * alpha0-E_min*alpha_min);
}; };
// solve T // solve T
@ -150,6 +152,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
double beta_rho = CalBeta(xPhys_col(i)); double beta_rho = CalBeta(xPhys_col(i));
F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_; F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
} }
spdlog::info("||Fth|| / ||Fm||: {}",F_th.norm()/sp_mech_top3d_->F_.norm());
Eigen::VectorXd F = Eigen::VectorXd(sp_mech_top3d_->F_) + F_th; Eigen::VectorXd F = Eigen::VectorXd(sp_mech_top3d_->F_) + F_th;
sp_mech_top3d_->IntroduceFixedDofs(sp_mech_top3d_->K_, F); sp_mech_top3d_->IntroduceFixedDofs(sp_mech_top3d_->K_, F);
@ -191,7 +194,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::VectorXd ele_dFth_drho = 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); assert(ele_dFth_drho.size() == 24);
v_dFth_drho(Eigen::seqN(i * ele_dFth_drho.rows(), ele_dFth_drho.size())) = ele_dFth_drho; v_dFth_drho(Eigen::seqN(i * ele_dFth_drho.size(), ele_dFth_drho.size())) = ele_dFth_drho;
} }
auto v_dFth_drho_tri = Vec2Triplet(i_dFth_drho_, j_dFth_drho_, v_dFth_drho); auto v_dFth_drho_tri = Vec2Triplet(i_dFth_drho_, j_dFth_drho_, v_dFth_drho);
dFth_drho.setFromTriplets(v_dFth_drho_tri.begin(), v_dFth_drho_tri.end()); dFth_drho.setFromTriplets(v_dFth_drho_tri.begin(), v_dFth_drho_tri.end());
@ -209,7 +212,7 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::MatrixXd ele_dFth_dT = Eigen::MatrixXd ele_dFth_dT =
Eigen::VectorXd::Ones(dofs_th.size()) * 1.0 / 8.0 * beta_rho * Inted_.transpose(); Eigen::VectorXd::Ones(dofs_th.size()) * 1.0 / 8.0 * beta_rho * Inted_.transpose();
assert(ele_dFth_dT.rows() == 8 && ele_dFth_dT.cols() == 24); assert(ele_dFth_dT.rows() == 8 && ele_dFth_dT.cols() == 24);
v_dFth_dT(Eigen::seqN(i * ele_dFth_dT.rows(), ele_dFth_dT.size())) = ele_dFth_dT.reshaped(); 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); 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()); dFth_dT.setFromTriplets(v_dFth_dT_tri.begin(), v_dFth_dT_tri.end());
@ -236,12 +239,16 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
} }
Eigen::VectorXd lambda_t_Mul_dKt_drho_Mul_T = CalDlambdaDrho_Vec(xPhys_col).array() * ce_th.array(); Eigen::VectorXd lambda_t_Mul_dKt_drho_Mul_T = CalDlambdaDrho_Vec(xPhys_col).array() * ce_th.array();
// dc_drho // dc_drho
Eigen::VectorXd dc_drho = lambda_t_Mul_dKt_drho_Mul_T + // Eigen::VectorXd dc_drho = lambda_t_Mul_dKt_drho_Mul_T +
lambda_m_Mul_dKm_drho_Mul_U + // lambda_m_Mul_dKm_drho_Mul_U +
2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_); // 2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_);
// Eigen::VectorXd dc_drho = Eigen::VectorXd dc_drho =
// lambda_m_Mul_dKm_drho_Mul_U + lambda_t_Mul_dKt_drho_Mul_T
// 2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_); +
lambda_m_Mul_dKm_drho_Mul_U
+
2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_)
;
// dT_drho // dT_drho
Eigen::MatrixXd dT_drho = Eigen::MatrixXd::Zero(sp_thermal_top3d_->sp_mesh_->GetNumEles(), Eigen::MatrixXd dT_drho = Eigen::MatrixXd::Zero(sp_thermal_top3d_->sp_mesh_->GetNumEles(),
sp_thermal_top3d_->set_dofs_to_load.size()); sp_thermal_top3d_->set_dofs_to_load.size());
@ -285,10 +292,11 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
// dc_dx // dc_dx
Eigen::VectorXd dc_dx = sp_mech_top3d_->drho_dx_ * dc_drho; Eigen::VectorXd dc_dx = sp_mech_top3d_->drho_dx_ * dc_drho;
// dT_dx // dT_dx
Eigen::MatrixXd dT_dx = sp_mech_top3d_->drho_dx_ * dT_drho; Eigen::MatrixXd dT_dx = sp_mech_top3d_->drho_dx_ * dT_drho;
// mma solver // mma solver
#define SENSITIVITY_SCALE_COEF 100
size_t num_constraints = size_t num_constraints =
1 + dT_dx.cols();// volume and temperature constraints 1 + dT_dx.cols();// volume and temperature constraints
@ -298,14 +306,15 @@ da::sha::top::Tensor3d da::sha::top::ThermoelasticTop3d::TopOptMainLoop() {
Eigen::VectorXd variables_tmp = flg_chosen ? xPhys_col(chosen_ele_id) : xPhys_col; Eigen::VectorXd variables_tmp = flg_chosen ? xPhys_col(chosen_ele_id) : xPhys_col;
double f0val = c; double f0val = c;
Eigen::VectorXd df0dx = flg_chosen Eigen::VectorXd df0dx = flg_chosen
? dc_dx(chosen_ele_id).eval() / dc_dx(chosen_ele_id).cwiseAbs().maxCoeff() ? dc_dx(chosen_ele_id).eval() / dc_dx(chosen_ele_id).cwiseAbs().maxCoeff() *SENSITIVITY_SCALE_COEF
: dc_dx / dc_dx.cwiseAbs().maxCoeff(); : dc_dx / dc_dx.cwiseAbs().maxCoeff() *SENSITIVITY_SCALE_COEF;
// double fval = v - num_variables * sp_para_->volfrac; // double fval = v - num_variables * sp_para_->volfrac;
Eigen::VectorXd fval = (Eigen::VectorXd(num_constraints) << (v / num_variables - sp_para_->volfrac), Eigen::VectorXd fval = (Eigen::VectorXd(num_constraints) << (v / num_variables - sp_para_->volfrac),
T(v_dof).array() / sp_para_->T_limit - 1).finished(); T(v_dof).array() / sp_para_->T_limit - 1).finished() * SENSITIVITY_SCALE_COEF;
// Eigen::VectorXd dfdx = flg_chosen ? dv(chosen_ele_id) : dv; // Eigen::VectorXd dfdx = flg_chosen ? dv(chosen_ele_id) : dv;
Eigen::MatrixXd dfdx = (Eigen::MatrixXd(num_variables, num_constraints) Eigen::MatrixXd dfdx = (Eigen::MatrixXd(num_variables, num_constraints)
<< 1.0 / num_variables * dv, 1.0 / sp_para_->T_limit * dT_dx).finished().transpose(); << 1.0 / num_variables * dv , 1.0 / sp_para_->T_limit * dT_dx).finished().transpose() *SENSITIVITY_SCALE_COEF;
static Eigen::VectorXd low_bounds = Eigen::VectorXd::Zero(num_variables); static Eigen::VectorXd low_bounds = Eigen::VectorXd::Zero(num_variables);

2
src/ThermoelasticTop3d.h
View File

@ -37,7 +37,7 @@ namespace da::sha::top {
i_dFth_drho_ = (Eigen::VectorXi::LinSpaced(sp_mech_top3d_->sp_mesh_->GetNumEles(), 0, i_dFth_drho_ = (Eigen::VectorXi::LinSpaced(sp_mech_top3d_->sp_mesh_->GetNumEles(), 0,
sp_mech_top3d_->sp_mesh_->GetNumEles()) * sp_mech_top3d_->sp_mesh_->GetNumEles()) *
Eigen::RowVectorXi::Ones(sp_mech_top3d_->sp_mesh_->Get_DOFS_EACH_ELE())).reshaped(); Eigen::RowVectorXi::Ones(sp_mech_top3d_->sp_mesh_->Get_DOFS_EACH_ELE())).transpose().reshaped();
j_dFth_drho_ = sp_mech_top3d_->sp_mesh_->GetEleId2DofsMap().transpose().reshaped(); j_dFth_drho_ = sp_mech_top3d_->sp_mesh_->GetEleId2DofsMap().transpose().reshaped();
D0_ = sp_mech_top3d_->sp_fea_->computeD(1.0); D0_ = sp_mech_top3d_->sp_fea_->computeD(1.0);

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