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@ -15,364 +15,7 @@ namespace da::sha::top { |
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Precompute(); |
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} |
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Tensor3d TopOptMainLoop() { |
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auto &sp_mesh_ = sp_mech_top3d_->sp_mesh_; |
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auto &sp_para_ = sp_mech_top3d_->sp_para_; |
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Eigen::VectorXd xPhys_col(sp_mesh_->GetNumEles()); |
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xPhys_col.setConstant(sp_para_->volfrac); |
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bool flg_chosen = false; |
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Eigen::VectorXi chosen_ele_id; |
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// Eigen::VectorXi chosen_ele_id(sp_mesh_->GetChosenEleIdx());
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// bool flg_chosen = chosen_ele_id.size() != 0;
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// if (!flg_chosen) {
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// // no part chosen
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// xPhys_col.setConstant(sp_para_->volfrac);
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// } else {
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// // pick chosen part to sim
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// xPhys_col = sp_mesh_->GetInitEleRho();
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// xPhys_col(chosen_ele_id).setConstant(sp_para_->volfrac);
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// }
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int loop = 0; |
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double change = 1.0; |
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double E0_m = sp_mech_top3d_->sp_fea_->sp_material_->E; |
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double lambda0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_conductivity; |
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double lambda_min = lambda0 * sp_mech_top3d_->sp_para_->E_factor; |
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double alpha0 = sp_mech_top3d_->sp_fea_->sp_material_->thermal_expansion_coefficient; |
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// Precompute
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Eigen::VectorXd dv(sp_mesh_->GetNumEles()); |
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dv.setOnes(); |
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dv = sp_mech_top3d_->H_ * (dv.array() / sp_mech_top3d_->Hs_.array()).matrix().eval(); |
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Eigen::VectorXd ele_to_write = |
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Eigen::VectorXd::Zero(sp_mesh_->GetLx() * sp_mesh_->GetLy() * sp_mesh_->GetLz()); |
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Eigen::VectorXi pixel_idx = sp_mesh_->GetPixelIdx(); |
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// dofs of limited T
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struct LimitedDof { |
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int dof; |
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int idx_of_load_dof; |
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int idx_in_ele; |
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LimitedDof(int dof, int idx_of_load_dof, int idx_in_ele) : dof(dof), idx_of_load_dof(idx_of_load_dof), |
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idx_in_ele(idx_in_ele) {} |
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}; |
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std::map<int, std::vector<LimitedDof>> map_ele2Limit; |
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std::vector<int> v_dof(sp_thermal_top3d_->set_dofs_to_load.begin(), |
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sp_thermal_top3d_->set_dofs_to_load.end()); |
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{ |
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Eigen::MatrixXi ele2dof_map = sp_thermal_top3d_->sp_mesh_->GetEleId2DofsMap(); |
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// loop ele2dof_map
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for (int i = 0; i < ele2dof_map.rows(); ++i) { |
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for (int j = 0; j < ele2dof_map.cols(); ++j) { |
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for (int k = 0; k < v_dof.size(); ++k) { |
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if (ele2dof_map(i, j) == v_dof[k]) { |
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if (map_ele2Limit.find(i) == map_ele2Limit.end()) { |
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map_ele2Limit[i] = {LimitedDof(v_dof[k], k, j)}; |
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} else { |
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map_ele2Limit[i].push_back(LimitedDof(v_dof[k], k, j)); |
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} |
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} |
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} |
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} |
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} |
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} |
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spdlog::info("end Precompute"); |
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#ifdef USE_SUITESPARSE |
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spdlog::info("using suitesparse solver"); |
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#else |
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spdlog::warn("using Eigen built-in direct solver!"); |
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#endif |
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// start iteration
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while (change > sp_para_->tol_x * 1 && loop < sp_para_->max_loop) { |
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++loop; |
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// filter
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xPhys_col = sp_mech_top3d_->H_ * (xPhys_col.array() / sp_mech_top3d_->Hs_.array()).matrix().eval(); |
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auto CalR = [](double rho, double R) { |
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return rho / (1.0 + R * (1.0 - rho)); |
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}; |
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auto CalR_Vec = [](const Eigen::VectorXd &vec_rho, double R) -> Eigen::VectorXd { |
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return vec_rho.array() / (1.0 + R * (1.0 - vec_rho.array())); |
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}; |
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auto CalDRDrho = [](double rho, double R) { |
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double down = 1 + R * (1 - rho); |
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return (1 + R) / down * down; |
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}; |
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auto CalDRDrho_Vec = [](const Eigen::VectorXd &vec_rho, double R) -> Eigen::VectorXd { |
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auto down = 1 + R * (1 - vec_rho.array()); |
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return (1 + R) / down.pow(2); |
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}; |
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auto CalE_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { |
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return CalR_Vec(vec_rho, sp_para_->R_E) * E0_m; |
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}; |
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auto CalDEDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { |
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return CalDRDrho_Vec(vec_rho, sp_para_->R_E) * E0_m; |
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}; |
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auto CalLambda_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { |
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return lambda_min + CalR_Vec(vec_rho, sp_para_->R_lambda).array() * (lambda0 - lambda_min); |
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}; |
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auto CalDlambdaDrho = [&](double rho) { |
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return CalDRDrho(rho, sp_para_->R_lambda) * (lambda0 - lambda_min); |
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}; |
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auto CalDlambdaDrho_Vec = [&](const Eigen::VectorXd &vec_rho) -> Eigen::VectorXd { |
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return CalDRDrho_Vec(vec_rho, sp_para_->R_lambda) * (lambda0 - lambda_min); |
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}; |
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auto CalBeta = [&](double rho) { |
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return CalR(rho, sp_para_->R_beta) * E0_m * alpha0; |
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}; |
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auto CalDBetaDrho = [&](double rho) { |
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return CalDRDrho(rho, sp_para_->R_beta) * E0_m * alpha0; |
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}; |
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// solve T
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Eigen::VectorXd sK_th = |
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(sp_thermal_top3d_->sKe_ * CalLambda_Vec(xPhys_col).transpose()) |
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.reshaped(); |
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auto v_tri_th = Vec2Triplet(sp_thermal_top3d_->iK_, sp_thermal_top3d_->jK_, sK_th); |
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sp_thermal_top3d_->K_.setFromTriplets(v_tri_th.begin(), v_tri_th.end()); |
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sp_thermal_top3d_->IntroduceFixedDofs(sp_thermal_top3d_->K_, sp_thermal_top3d_->F_); |
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#ifdef USE_SUITESPARSE |
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Eigen::CholmodSupernodalLLT<Eigen::SparseMatrix<double>> solver_th; |
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#else |
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Eigen::SimplicialLLT<Eigen::SparseMatrix<double>> solver_th; |
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#endif |
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solver_th.compute(sp_thermal_top3d_->K_); |
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sp_thermal_top3d_->U_ = solver_th.solve(sp_thermal_top3d_->F_); |
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// solve U
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Eigen::VectorXd sK_m = |
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(sp_mech_top3d_->sKe_ * CalE_Vec(xPhys_col).transpose()) |
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.reshaped(); |
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auto v_tri_m = Vec2Triplet(sp_mech_top3d_->iK_, sp_mech_top3d_->jK_, sK_m); |
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sp_mech_top3d_->K_.setFromTriplets(v_tri_m.begin(), v_tri_m.end()); |
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// for each element
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Eigen::VectorXd &T = sp_thermal_top3d_->U_; |
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Eigen::VectorXd F_th = Eigen::VectorXd::Zero(sp_mech_top3d_->sp_mesh_->GetNumDofs()); |
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for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) { |
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Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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double Te = T(dofs_th).mean(); |
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double beta_rho = CalBeta(xPhys_col(i)); |
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F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_; |
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} |
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Eigen::VectorXd F = Eigen::VectorXd(sp_mech_top3d_->F_) + F_th; |
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sp_mech_top3d_->IntroduceFixedDofs(sp_mech_top3d_->K_, F); |
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#ifdef USE_SUITESPARSE |
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Eigen::CholmodSupernodalLLT<Eigen::SparseMatrix<double>> solver; |
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#else |
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Eigen::SimplicialLLT<Eigen::SparseMatrix<double>> solver; |
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#endif |
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solver.compute(sp_mech_top3d_->K_); |
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sp_mech_top3d_->U_ = solver.solve(F); |
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// compliance
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Eigen::VectorXd ce(sp_mesh_->GetNumEles()); |
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for (int i = 0; i < sp_mesh_->GetNumEles(); ++i) { |
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Eigen::VectorXi dofs_in_ele_i = sp_mesh_->MapEleId2Dofs(i); |
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Eigen::VectorXd Ue = sp_mech_top3d_->U_(dofs_in_ele_i); |
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ce(i) = Ue.transpose() * sp_mech_top3d_->Ke_ * Ue; |
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} |
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double c = |
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ce.transpose() * CalE_Vec(xPhys_col); |
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double v = flg_chosen ? xPhys_col(chosen_ele_id).sum() : xPhys_col.sum(); |
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// sensitivity
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// lambda_m
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Eigen::VectorXd lambda_m = -sp_mech_top3d_->U_; |
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// dFth_drho
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Eigen::SparseMatrix<double> dFth_drho(sp_mech_top3d_->sp_mesh_->GetNumEles(), |
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sp_mech_top3d_->sp_mesh_->GetNumDofs()); |
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Eigen::VectorXd v_dFth_drho(i_dFth_drho_.size()); |
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for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) { |
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Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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double Te = T(dofs_th).mean(); |
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// double beta_rho = CalBeta(xPhys_col(i));
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// F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
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Eigen::VectorXd ele_dFth_drho = |
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CalDBetaDrho(xPhys_col(i)) * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;// 24x1
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assert(ele_dFth_drho.size() == 24); |
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v_dFth_drho(Eigen::seqN(i * ele_dFth_drho.rows(), ele_dFth_drho.size())) = ele_dFth_drho; |
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} |
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auto v_dFth_drho_tri = Vec2Triplet(i_dFth_drho_, j_dFth_drho_, v_dFth_drho); |
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dFth_drho.setFromTriplets(v_dFth_drho_tri.begin(), v_dFth_drho_tri.end()); |
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// dFth_dT
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Eigen::SparseMatrix<double> dFth_dT(sp_thermal_top3d_->sp_mesh_->GetNumDofs(), |
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sp_mech_top3d_->sp_mesh_->GetNumDofs()); |
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Eigen::VectorXd v_dFth_dT(i_dFth_dT_.size()); |
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for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) { |
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Eigen::VectorXi dofs_th = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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Eigen::VectorXi dofs_m = sp_mech_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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double beta_rho = CalBeta(xPhys_col(i)); |
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// F_th(dofs_m) += beta_rho * (Te - sp_mech_top3d_->sp_para_->T_ref) * Inted_;
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Eigen::MatrixXd ele_dFth_dT = |
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Eigen::VectorXd::Ones(dofs_th.size()) * 1.0 / 8.0 * beta_rho * Inted_.transpose(); |
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assert(ele_dFth_dT.rows() == 8 && ele_dFth_dT.cols() == 24); |
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v_dFth_dT(Eigen::seqN(i * ele_dFth_dT.rows(), ele_dFth_dT.size())) = ele_dFth_dT.reshaped(); |
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} |
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auto v_dFth_dT_tri = Vec2Triplet(i_dFth_dT_, j_dFth_dT_, v_dFth_dT); |
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dFth_dT.setFromTriplets(v_dFth_dT_tri.begin(), v_dFth_dT_tri.end()); |
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Eigen::VectorXd rhs = dFth_dT * lambda_m; |
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for (auto dof_value: sp_thermal_top3d_->v_dofs_to_set) { |
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auto [dof, value] = dof_value; |
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rhs(dof) = sp_thermal_top3d_->K_.coeffRef(dof, dof) * value; |
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} |
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// lambda_t
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Eigen::VectorXd lambda_t = solver_th.solve(rhs); |
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// dF_drho
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Eigen::SparseMatrix<double> &dF_drho = dFth_drho; |
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// lambda_m_Mul_dKm_drho_Mul_U
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Eigen::VectorXd lambda_m_Mul_dKm_drho_Mul_U = |
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-CalDEDrho_Vec(xPhys_col).array() * ce.array(); |
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// lambda_t_Mul_dKt_drho_Mul_T
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Eigen::VectorXd ce_th(sp_thermal_top3d_->sp_mesh_->GetNumEles()); |
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for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) { |
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Eigen::VectorXi dofs_in_ele_i = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i); |
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Eigen::VectorXd Te = sp_thermal_top3d_->U_(dofs_in_ele_i); |
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Eigen::VectorXd lambda_t_e = lambda_t(dofs_in_ele_i); |
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ce_th(i) = lambda_t_e.transpose() * sp_thermal_top3d_->Ke_ * Te; |
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} |
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Eigen::VectorXd lambda_t_Mul_dKt_drho_Mul_T = CalDlambdaDrho_Vec(xPhys_col).array() * ce_th.array(); |
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// dc_drho
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Eigen::VectorXd dc_drho = lambda_t_Mul_dKt_drho_Mul_T + |
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lambda_m_Mul_dKm_drho_Mul_U + |
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2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_); |
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// Eigen::VectorXd dc_drho =
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// lambda_m_Mul_dKm_drho_Mul_U +
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// 2 * Eigen::VectorXd(dF_drho * sp_mech_top3d_->U_);
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// dT_drho
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Eigen::MatrixXd dT_drho = Eigen::MatrixXd::Zero(sp_thermal_top3d_->sp_mesh_->GetNumEles(), |
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sp_thermal_top3d_->set_dofs_to_load.size()); |
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for (auto it = map_ele2Limit.begin(); it != map_ele2Limit.end(); ++it) { |
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auto [ele_id, v_limited] = *it; |
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Eigen::VectorXi dofs_in_ele_i = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(ele_id); |
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Eigen::VectorXd dKe_th_Mul_T = |
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CalDlambdaDrho(xPhys_col(ele_id)) * sp_thermal_top3d_->Ke_ * T(dofs_in_ele_i); |
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Eigen::MatrixXd Ke_th(sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE(), |
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sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE()); |
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for (int j1 = 0; j1 < Ke_th.cols(); ++j1) { |
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for (int i1 = 0; i1 < Ke_th.rows(); ++i1) { |
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Ke_th(i1, j1) = sp_thermal_top3d_->K_.coeffRef(i1, j1); |
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} |
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} |
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Eigen::VectorXd ele_dT_drho = Ke_th.llt().solve(-dKe_th_Mul_T); |
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for (auto &limited: v_limited) { |
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dT_drho(ele_id, limited.idx_of_load_dof) = ele_dT_drho(limited.idx_in_ele); |
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} |
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} |
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// for (int i = 0; i < sp_thermal_top3d_->sp_mesh_->GetNumEles(); ++i) {
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// Eigen::VectorXi dofs_in_ele_i = sp_thermal_top3d_->sp_mesh_->MapEleId2Dofs(i);
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// Eigen::VectorXd dKe_th_Mul_T =
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// CalDlambdaDrho(xPhys_col(i)) * sp_thermal_top3d_->Ke_ * T(dofs_in_ele_i);
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// Eigen::MatrixXd Ke_th(sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE(),
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// sp_thermal_top3d_->sp_mesh_->Get_DOFS_EACH_ELE());
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// for (int j1 = 0; j1 < Ke_th.cols(); ++j1) {
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// for (int i1 = 0; i1 < Ke_th.rows(); ++i1) {
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// Ke_th(i1, j1) = sp_thermal_top3d_->K_.coeffRef(i1, j1);
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// }
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// }
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// Eigen::VectorXd ele_dT_drho = Ke_th.llt().solve(-dKe_th_Mul_T);
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// dT_drho(i, dofs_in_ele_i) = ele_dT_drho.transpose();
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// }
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// for (auto dof_value: sp_thermal_top3d_->v_dofs_to_set) {
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// auto [dof, value] = dof_value;
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// dT_drho.col(dof).setZero();
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// }
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// dc_dx
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Eigen::VectorXd dc_dx = drho_dx_ * dc_drho; |
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// dT_dx
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Eigen::MatrixXd dT_dx = drho_dx_ * dT_drho; |
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// mma solver
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size_t num_constraints = |
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1 + dT_dx.cols();// volume and temperature constraints
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size_t num_variables = flg_chosen ? chosen_ele_id.size() : sp_mesh_->GetNumEles(); |
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auto mma = std::make_shared<MMASolver>(num_variables, num_constraints); |
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Eigen::VectorXd variables_tmp = flg_chosen ? xPhys_col(chosen_ele_id) : xPhys_col; |
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double f0val = c; |
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Eigen::VectorXd df0dx = flg_chosen |
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? dc_dx(chosen_ele_id).eval() / dc_dx(chosen_ele_id).cwiseAbs().maxCoeff() |
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: dc_dx / dc_dx.cwiseAbs().maxCoeff(); |
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// double fval = v - num_variables * sp_para_->volfrac;
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Eigen::VectorXd fval = (Eigen::VectorXd(num_constraints) << (v / num_variables - sp_para_->volfrac), |
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T(v_dof).array() / sp_para_->T_limit - 1).finished(); |
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// Eigen::VectorXd dfdx = flg_chosen ? dv(chosen_ele_id) : dv;
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Eigen::MatrixXd dfdx = (Eigen::MatrixXd(num_variables, num_constraints) |
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<< 1.0 / num_variables * dv, 1.0 / sp_para_->T_limit * dT_dx).finished().transpose(); |
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static Eigen::VectorXd low_bounds = Eigen::VectorXd::Zero(num_variables); |
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static Eigen::VectorXd up_bounds = Eigen::VectorXd::Ones(num_variables); |
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// spdlog::info("mma update");
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mma->Update(variables_tmp.data(), df0dx.data(), fval.data(), dfdx.data(), low_bounds.data(), |
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up_bounds.data()); |
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if (flg_chosen) { |
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change = (variables_tmp - xPhys_col(chosen_ele_id)).cwiseAbs().maxCoeff(); |
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xPhys_col(chosen_ele_id) = variables_tmp; |
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} else { |
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change = (variables_tmp - xPhys_col).cwiseAbs().maxCoeff(); |
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xPhys_col = variables_tmp; |
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} |
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spdlog::critical("Iter: {:3d}, Comp: {:.3e}, Vol: {:.2f}, Change: {:f}", loop, c, v, change); |
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std::cout << fval.transpose() << std::endl; |
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#ifdef WRITE_TENSOR_IN_LOOP |
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// extract vtk
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ele_to_write(pixel_idx) = xPhys_col; |
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Tensor3d ten_xPhys_to_write(sp_mesh_->GetLx() * sp_mesh_->GetLy() * sp_mesh_->GetLz(), 1, 1); |
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for (int i = 0; i < ele_to_write.size(); ++i) { |
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ten_xPhys_to_write(i, 0, 0) = ele_to_write(i); |
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} |
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ten_xPhys_to_write = ten_xPhys_to_write.reshape(Eigen::array<Eigen::DenseIndex, 3>{ |
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sp_mesh_->GetLx(), sp_mesh_->GetLy(), sp_mesh_->GetLz()}); |
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top::WriteTensorToVtk( |
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da::WorkingResultDirectoryPath() / ("field_matrix" + std::to_string(loop) + ".vtk"), |
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ten_xPhys_to_write, sp_mesh_); |
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#endif |
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} |
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// result
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sp_mech_top3d_->rho_ = xPhys_col; |
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// set 0 to rho of unchosen part
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assert(xPhys_col.size()); |
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Eigen::VectorXi continue_idx = |
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Eigen::VectorXi::LinSpaced(xPhys_col.size(), 0, xPhys_col.size() - 1); |
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Eigen::VectorXi unchosen_idx = flg_chosen ? SetDifference(continue_idx, chosen_ele_id) : Eigen::VectorXi(); |
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{ |
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xPhys_col(unchosen_idx).setZero(); |
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ele_to_write(pixel_idx) = xPhys_col; |
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Tensor3d ten_xPhys_to_write(sp_mesh_->GetLx() * sp_mesh_->GetLy() * sp_mesh_->GetLz(), 1, 1); |
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for (int i = 0; i < ele_to_write.size(); ++i) { |
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ten_xPhys_to_write(i, 0, 0) = ele_to_write(i); |
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} |
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ten_xPhys_to_write = ten_xPhys_to_write.reshape(Eigen::array<Eigen::DenseIndex, 3>{ |
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sp_mesh_->GetLx(), sp_mesh_->GetLy(), sp_mesh_->GetLz()}); |
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sp_mech_top3d_->rho_field_zero_filled_ = ten_xPhys_to_write; |
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} |
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{ |
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xPhys_col(unchosen_idx).setOnes(); |
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ele_to_write(pixel_idx) = xPhys_col; |
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Tensor3d ten_xPhys_to_write(sp_mesh_->GetLx() * sp_mesh_->GetLy() * sp_mesh_->GetLz(), 1, 1); |
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for (int i = 0; i < ele_to_write.size(); ++i) { |
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ten_xPhys_to_write(i, 0, 0) = ele_to_write(i); |
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} |
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ten_xPhys_to_write = ten_xPhys_to_write.reshape(Eigen::array<Eigen::DenseIndex, 3>{ |
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sp_mesh_->GetLx(), sp_mesh_->GetLy(), sp_mesh_->GetLz()}); |
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sp_mech_top3d_->rho_field_one_filled_ = ten_xPhys_to_write; |
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} |
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return sp_mech_top3d_->rho_field_zero_filled_; |
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} |
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Tensor3d TopOptMainLoop(); |
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Eigen::VectorXd GetU() const { |
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return sp_thermal_top3d_->GetU(); |
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cflin
2 years ago