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94 lines
3.3 KiB
94 lines
3.3 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-08-25 17:26:51
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% @LastEditTime: 2021-09-02 19:42:17
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%--------------------------
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function [f0val, df0dx, fval, dfdx] = obj_cons_sens(H_macro, Hs_macro, H_global, Hs_global, fext, U, nele_global, v0_macro, v0_micro, dK, cons_num, ...
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dk_micro, edofMat_ma, rho_cell, rho_macro, rho_global, e0,e1,penal)
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pnorm = 16;
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nele_macro = length(rho_macro(:));
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nele_micro = nele_global / nele_macro;
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vdofs_num = size(edofMat_ma, 2);
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%% compliance & volume_macro
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comp = fext' * U;
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cons_v_macro = mean(rho_macro(:)) / v0_macro - 1;
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% sensitivities - macro
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dc_macro = zeros(nele_macro, 1);
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dv_macro = ones(nele_macro, 1) / nele_macro / v0_macro;
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% micro
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volume_micro = zeros(nele_macro,1);
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for ele_ma = 1:nele_macro
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rho_micro = rho_cell{ele_ma};
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volume_micro(ele_ma) = mean(rho_micro(:));
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edof = edofMat_ma(ele_ma, :);
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ue = U(edof);
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dKe = reshape(dK(:, ele_ma), vdofs_num, vdofs_num);
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dc_macro(ele_ma) = ue' * dKe * ue;
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end
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% cons_v_micro = (mean(volume_micro.^pnorm))^(1/pnorm) / v0_micro - 1;
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%
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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_global(:)) / 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(rho_macro, dk_micro, U, edofMat_ma, e0,e1,penal);
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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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dc_macro(:) = H_macro * (dc_macro(:) ./ Hs_macro);
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dv_macro(:) = H_macro * (dv_macro(:) ./ Hs_macro);
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%% sensitivities
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df0dx = zeros(nele_macro + nele_global, 1);
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dfdx = zeros(cons_num, nele_macro + nele_global);
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f0val = comp;
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df0dx(1 : nele_macro) = - dc_macro(:); % note the negetive sign
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df0dx(nele_macro+1 : end) = - dc_micro(:); % note the negetive sign
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fval(1) = cons_v_macro;
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dfdx(1, 1 : nele_macro) = dv_macro;
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fval(2) = cons_v_micro;
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dfdx(2, nele_macro+1 : end) = dv_micro(:);
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% fval = cons_v_micro;
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% dfdx(1, :) = dv_micro(:);
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end
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% compliance_micro sensitivities
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function [dc_micro] = obj_sens_micro(macro_rho, dk_micro, U, edofMat_ma, e0,e1,penal)
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nele_macro = size(macro_rho(:), 1);
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nele_micro = size(dk_micro{1}, 2);
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vdofs_num = size(edofMat_ma, 2);
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% jac = dx^2/4;
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dc_micro = zeros(nele_micro * nele_macro, 1);
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for ele_ma = 1:nele_macro
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% rho_e = rho_cell{ele_ma}(:);
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% tmp = speye(length(rho_e)) .* (e0 + rho_e.^penal * (e1-e0)); % m,m micro-rho need to be penal
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% D = kron(tmp, D1); % 3m,3m
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dk = dk_micro{ele_ma}; % [6r^2, nele_micro]
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edof = edofMat_ma(ele_ma, :);
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ue = U(edof);
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for ele_mi = 1:nele_micro
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global_ele = (ele_ma-1) * nele_micro + ele_mi;
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dk_mi = reshape(dk(:, ele_mi), vdofs_num, []);
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dc_micro(global_ele) = ue' * dk_mi * ue * (e0 + macro_rho(ele_ma)^penal * (e1-e0));
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end
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end
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end
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