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188 lines
6.8 KiB
188 lines
6.8 KiB
3 years ago
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% @Author: Jingqiao Hu
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% @Date: 2021-08-25 17:26:51
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% @LastEditTime: 2021-09-09 14:25:42
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%--------------------------
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function [f0val, df0dx, fval, dfdx] = obj_cons_sens_micro(nelx, nely, microx, H_global, Hs_global, fext, U, nele_global, v0_micro, ...
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dk_micro, edofMat_ma, rho_cell, cell2global_id, e0, e1, penal, ke1, iK_mi, jK_mi, edofMat_mi, bdofs_num, dD, dofid, newdofs, ...
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bdofs_plus, ib_dofs, ii_dofs, regulated_matrix, bezier_B, dFdx, De)
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pnorm = 16;
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nele_macro = nelx * nely;
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nele_micro = microx^2;
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%% compliance & volume_macro
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comp = fext' * U;
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% compliance_sensitivities(nelx, nely, microx, dk_micro, U, edofMat_ma, 1, 1);
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% pnorm-volume constraint of micro
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volume_micro = reshape(mean(rho_cell, 1), [], 1); % [m,M] -> [1,M]
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cons_v_micro = (mean(volume_micro.^pnorm))^(1/pnorm) / v0_micro - 1;
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dpnorm = 1/nele_macro * (mean(volume_micro.^pnorm))^(1/pnorm-1) * (volume_micro.^(pnorm-1)) / v0_micro;
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dpn_expand = kron(ones(nele_micro, 1), dpnorm); % expand to [nele_global, 1]
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dv_micro = ones(nele_global, 1) / nele_global .* dpn_expand;
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% cons_v_micro = mean(rho_cell(:)) / v0_micro - 1;
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% dv_micro = ones(nele_global, 1) / nele_global / v0_micro;
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[dc_micro] = obj_sens_micro(nelx, nely, microx, dk_micro, U, edofMat_ma, cell2global_id);
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dc_micro1 = compliance_sensitivities(nelx, nely, microx, regulated_matrix, U, edofMat_ma, edofMat_mi, dofid, newdofs, ...
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e0, e1, penal, ke1, iK_mi, jK_mi, bdofs_num, dD, rho_cell, bdofs_plus, ib_dofs, ii_dofs, cell2global_id, bezier_B, dFdx, De);
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max(dc_micro(:) - dc_micro1(:))
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dc_micro(:) = H_global * (dc_micro(:) ./ Hs_global);
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dv_micro(:) = H_global * (dv_micro(:) ./ Hs_global );
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% CHECK: maybe need to be scaled to 1000 times
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%% sensitivities
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f0val = comp;
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df0dx = - dc_micro(:); % note the negetive sign
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fval = cons_v_micro;
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dfdx = dv_micro(:)';
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end
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% newdofs = [boundarys, inner];
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function dc_micro = compliance_sensitivities(nelx, nely, microx, regulated_matrix, U, edofMat_ma, edofMat_mi, dofid, newdofs, ...
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e0, e1, penal, ke1, iK_mi, jK_mi, bdofs_num, dD, rho, bdofs_plus, ib_dofs, ii_dofs, cell2global_id, bezier_B, dFdx, De)
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nele_macro = nelx * nely;
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nele_micro = microx^2;
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UM = U(edofMat_ma); % [M,v]
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order1 = dofid(edofMat_mi'); % order as [border,idofs]
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order2 = node2ele_id(dofid(edofMat_mi));
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% O2 = zeros(2*(microx+1)^2 - bdofs_num, 1);
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O = zeros(bdofs_num, 1);
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idofs_plus = 1 - bdofs_plus; % [8,m]
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dc = zeros(nele_micro, nele_macro);
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dc1 = zeros(nele_micro, nele_macro);
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for ele = 1: nele_macro
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rho_e = rho(:, ele);
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rho_penal = e0 + rho_e.^penal * (e1-e0); % m,1 micro-rho need to be penal
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drho = penal * rho_e.^(penal-1) * (e1 - e0);
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ue = UM(ele, :); % [1,v]
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Re = regulated_matrix{ele}; % [2n,v]
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former1 = Re * ue'; % [2n,1]
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former3 = former1(order1); % expand to [8,m]
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former4 = former3' * dD .* rho_penal; % [m,8]
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former5 = reshape(former4', [], 1);
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former6 = former5(order2); % assemble to [2n,1]
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former_sub = former6(bdofs_num + 1 : end); % choose dofs corresponding to k_22 of [2i,1]
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K = assemble_micro_k(dofid, rho_e, microx, e0, e1, penal, ke1, iK_mi, jK_mi);
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k22 = K(bdofs_num + 1 : end, bdofs_num + 1 : end); % [2i,2i]
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former_sub1 = k22 \ former_sub; % [2i,1]
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former7 = [O; former_sub1]'; % [1,2n]
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former = former7(order1); % [8,m]
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latter_b(:,1,:) = former3 .* bdofs_plus; % [8,1,m]
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latter_i(:,1,:) = - former3 .* idofs_plus; % [8,1,m]
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dke = ke1(:) * drho(:)'; % [8*8, m]
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dke1 = reshape(dke, 8, 8, nele_micro); % [8, 8, m]
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dk21 = dke1 .* ib_dofs; % [8, 8, m]
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dk22 = dke1 .* ii_dofs; % [8, 8, m]
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dM = mtimesx(dk22, latter_i) - mtimesx(dk21, latter_b); % [8,1,m]
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dM1 = squeeze(dM); % [8,m]
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% dM1 = reshape(dM1, [], 1);
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% dM2 = dM1(order2); % assemble to [2n,1]
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% dM2_sub = dM2(bdofs_num + 1 : end); % [2i,1]
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% latter_sub = k22 \ dM2_sub; % [2i,1]
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%
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% latter = [O; latter_sub];
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% latter = latter(order1); % [8,m]
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dc(:,ele) = 2 * sum(former .* dM1, 1); % [1,m]
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% dc(:,ele) = 2 * sum(former4' .* latter, 1); % [1,m]
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%%
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ndofs = 2 * (microx + 1)^2;
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dk = zeros(ndofs, ndofs);
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O = zeros(bdofs_num, 1);
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for ele_mi = 12:nele_micro
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edof = dofid(edofMat_mi(ele_mi, :));
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dke = ke1 * drho(ele_mi);
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dk(edof, edof) = dke; % assemble by the order of [dofid]
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dk21 = dk(bdofs_num+1 : end, 1 : bdofs_num) * former1(1:bdofs_num);
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dk22 = dk(bdofs_num+1 : end, bdofs_num+1 : end) * (-former1(bdofs_num+1:end));
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dk2_pre = k22 * (dk22 - dk21); % NOTE: not including \bO
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dphi = [O; dk2_pre];
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% a = dphi(edof);
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%
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% test = ke1 \ dM1(:,ele_mi);
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% a = former1(edof)' * dD * rho_penal(ele_mi);
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% max(dM1(:,ele_mi) - a)
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dc1(ele_mi,ele) = 2 * former1(edof)' * dD * rho_penal(ele_mi) * dphi(edof); % + former1(edof)' * dD * drho(ele_mi) * former1(edof);
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% dc2(ele_mi,ele) = 2 * former6(edof)' * dphi(edof);
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dk(:) = 0;
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end
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end
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dc_micro = dc(cell2global_id);
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dc_micro1 = dc1(cell2global_id);
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end
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function order_id = node2ele_id(edofMat_mi)
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order1 = reshape(edofMat_mi', [], 1);
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order1(:,2) = 1:size(order1,1);
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order2 = sortrows(order1, 1);
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[~,ia,ic] = unique(order2(:,1)); % C = A(ia)
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idx = order2(:,2);
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order_id = idx(ia);
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end
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% compliance_micro sensitivities
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function [dc_micro] = obj_sens_micro(nelx, nely, microx, dk_micro, U, edofMat_ma, cell2global_id)
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nele_micro = microx^2;
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nele_macro = nelx * nely;
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vdofs_num = size(edofMat_ma, 2);
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% tic
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UM = U(edofMat_ma); % [M,v]
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UM1 = kron(ones(nele_micro,1), UM)'; % [v,m*M]
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UM2 = reshape(UM1, vdofs_num, 1, nele_macro, nele_micro); % [v,1,M,m]
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UM3 = permute(UM2, [1,2,4,3]); % [v,1,m,M]
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UM4 = permute(UM3, [2,1,3,4]); % [1,v,m,M]
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dc5 = squeeze(mtimesx(mtimesx(UM4, dk_micro), UM3)); % [m,M]
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dc_micro = dc5(cell2global_id);
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% toc
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% tic
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% dc = zeros(nele_micro, nele_macro);
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% parfor ele = 1: nelx * nely
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% ue = UM(ele, :);
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%
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% dke = dk_micro(:,:,:,ele); % [v,v,m]
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% dk1 = reshape(dke, vdofs_num, []); % [v,v*m]
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%
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% dc_former = ue * dk1; % % [1,v*m]
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% dc1 = reshape(dc_former, vdofs_num, nele_micro);
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%
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% dc(:,ele) = dc1' * ue';
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% end
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% dc_micro1 = dc(cell2global_id);
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% toc
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%
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% max(dc_micro(:) - dc_micro1(:))
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end
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