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124 lines
3.8 KiB
124 lines
3.8 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-09-27 15:20:17
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% @LastEditTime: 2021-09-29 15:23:19
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%--------------------------
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function [H, H2, dH] = mmc_project2H(lx, nelx, nely, microx, mmc_descriptor, MMCs, nodes_in_ele, coorx, coory, e1)
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dx = lx / microx;
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globalx = microx * nelx;
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globaly = microx * nely;
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epsilon = 4*dx;
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phi_max = repmat(-1e5, globaly+1, 1+globalx);
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phi_cell = cell(nely*nelx*20, 1); idx = 1;
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for i = 1 : nelx
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for j = 1 : nely
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mmc = mmc_descriptor{j,i};
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for ci = 1:20
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cx = mmc(ci, 1);
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cy = mmc(ci, 2);
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l = mmc(ci, 3);
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sint = mmc(ci, 4);
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t = MMCs(ci,j,i);
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phi = phi_func(coorx, coory, sint, cx, cy, t, l);
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phi_max = max(phi_max, phi);
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phi_cell{idx} = phi;
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idx = idx + 1;
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end
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% phi_cell{j,i} = phi_max((j-1)*(microx+1)+1:j*(microx+1), (i-1)*(microx+1)+1:i*(microx+1));
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end
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end
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heav = Heaviside(phi_max, epsilon);
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H = reshape(sum(heav(nodes_in_ele), 2) /4, globaly, globalx);
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H2 = reshape(sum(heav(nodes_in_ele).^2, 2)/4, globaly, globalx) * e1;
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dH = sensitivies_dt(phi_cell, heav, lx, nelx, nely, microx, mmc_descriptor, MMCs, nodes_in_ele, coorx, coory);
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end
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function dH = sensitivies_dt(phi_cell, heav, lx, nelx, nely, microx, mmc_descriptor, MMCs, nodes_in_ele, coorx, coory)
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% compute dH2/dt = dH2 * dHdt
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dx = lx / microx;
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globalx = microx * nelx;
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globaly = microx * nely;
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epsilon = 4*dx;
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step = max(2*dx, 5e-3);
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dH = cell(nely, nelx, 20);
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for i = 1:nelx
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for j = 1:nely
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mmc = mmc_descriptor{j,i};
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for ci = 1:20
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global_ci = ((i-1)*nely + j - 1)*20 + ci;
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cx = mmc(ci, 1);
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cy = mmc(ci, 2);
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l = mmc(ci, 3);
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sint = mmc(ci, 4);
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t_plus = MMCs(ci,j,i) + step;
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phi_plus = phi_func(coorx, coory, sint, cx, cy, t_plus, l);
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for ck1 = 1 : global_ci-1
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phi_max_plus = max(phi_cell{ck1}, phi_plus);
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end
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for ck2 = global_ci+1 : nelx*nely*20
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phi_max_plus = max(phi_cell{ck2}, phi_plus);
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end
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t_minus = max(MMCs(ci,j,i) - step, 1e-3);
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phi_minus = phi_func(coorx, coory, sint, cx, cy, t_minus, l);
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for ck1 = 1 : global_ci-1
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phi_max_minus = max(phi_cell{ck1}, phi_minus);
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end
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for ck2 = global_ci+1 : nelx*nely*20
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phi_max_minus = max(phi_cell{ck2}, phi_minus);
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end
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heav_plus = Heaviside(phi_max_plus, epsilon);
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heav_minus = Heaviside(phi_max_minus, epsilon);
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dHdt = (heav_plus - heav_minus) / 2*step;
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dH_i = 2*heav .* dHdt;
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dH{j, i, ci} = reshape(sum(dH_i(nodes_in_ele), 2)/4, globaly, globalx);
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end
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end
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end
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end
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function H = Heaviside(phi, epsilon)
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alpha = 1e-3;
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[y,x] = size(phi);
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H = zeros(x*y, 1);
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num_all=[1 : x*y]';
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num1=find(phi>epsilon);
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H(num1)=1;
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num2=find(phi<-epsilon);
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H(num2)=alpha;
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num3=setdiff(num_all,[num1;num2]);
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H(num3)=3*(1-alpha)/4*(phi(num3)/epsilon-phi(num3).^3/(3*(epsilon)^3))+ (1+alpha)/2;
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H = reshape(H, y, x);
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end
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function phi = phi_func(coorx, coory, sint, cx, cy, t, l)
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cost = sqrt(abs(1-sint^2));
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% center coordinate of ellipse is (cx, cy)
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x1 = cost*(coorx-cx) + sint*(coory-cy);
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y1 = -sint*(coorx-cx) + cost*(coory-cy);
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% NOTE: negative sign!!!
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phi = -((x1/l).^6 + (y1/t).^6 - 1);
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end
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