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89 lines
3.5 KiB
89 lines
3.5 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2022-01-12 20:53:52
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% @LastEditTime: 2022-01-12 23:27:18
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% triangulation mesh
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%--------------------------
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function xPhys = top88_nonregular(volfrac, e1, nu, F, fixeddofs, nodes, faces)
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penal=2;
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Emin = 1e-9;
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[sK0, area] = intKE_triangle(nodes, faces, e1, nu); % sK: [36,m]
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area0 = sum(area);
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[iK, jK, edofMat, ~, ~] = forAssemble_trimesh(faces);
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alldofs = 2*size(nodes, 1);
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U = zeros(alldofs, 1);
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freedofs = setdiff(1:alldofs,fixeddofs);
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%% INITIALIZE ITERATION
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nele = size(faces, 1);
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x = repmat(volfrac, nele, 1);
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xPhys = x;
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loop = 0;
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change = 1;
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x1 = nodes(:, 1); % [n, 1]
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x1 = x1(faces); % [m, 3]
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y1 = nodes(:, 2); % [n, 1]
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y1 = y1(faces); % [m, 3]
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m = 1; % The number of general constraints. 绾︽潫鏉′欢涓暟
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n = nele; % The number of design variables x_j. 璁捐鍙橀噺x涓暟nelx * nely
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xmin = zeros(n,1); % Column vector with the lower bounds for the variables x_j. x鐨勪笅鐣岀殑鍒楀悜閲?
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xmax = ones(n,1); % Column vector with the upper bounds for the variables x_j. x鐨勪笂鐣岀殑鍒楀悜閲?
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xold1 = x(:); % xval, one iteration ago (provided that iter>1). 涓?釜杩唬涔嬪墠鐨剎val
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xold2 = x(:); % xval, two iterations ago (provided that iter>2). 涓や釜杩唬涔嬪墠鐨剎val
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low = ones(n,1); % Column vector with the lower asymptotes from the previous iteration (provided that iter>1). 涓婁竴涓凯浠ｇ殑涓嬫笎杩戠嚎鐨勫垪鍚戦噺
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upp = ones(n,1); % Column vector with the upper asymptotes from the previous iteration (provided that iter>1). 涓婁竴涓凯浠ｇ殑涓婃笎杩戠嚎鐨勫垪鍚戦噺
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a0 = 1; % The constants a_0 in the term a_0*z.
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a = zeros(m,1); % Column vector with the constants a_i in the terms a_i*z.
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c_MMA = 1000*ones(m,1); % Column vector with the constants c_i in the terms c_i*y_i.
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d = zeros(m,1); % Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2.
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%% START ITERATION
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while change > 0.01 && loop < 100
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loop = loop + 1;
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%% FE-ANALYSIS
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sK = sK0 .* (Emin+xPhys(:)'.^penal*(e1-Emin)); % [36,m]
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K = sparse(iK,jK,sK(:)); K = (K+K')/2;
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U(freedofs) = K(freedofs,freedofs)\F(freedofs);
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%% OBJECTIVE FUNCTION AND SENSITIVITY ANALYSIS
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U1(1, :, :) = U(edofMat)'; % [1,6,n]
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U2(:, 1, :) = U(edofMat)'; % [6,1,n]
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sK1 = sK0 .* (penal*(e1-Emin)*xPhys'.^(penal-1)); % [36,m]
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sK2 = reshape(sK1, 6, 6, []);
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dc = mtimesx(mtimesx(U1, sK2), U2);
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dc = squeeze(dc);
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c = F' * U;
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v = sum(area .* xPhys(:));
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dv = area;
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%% MMA
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xval = x(:);
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f0val = c;
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df0dx = - dc(:);
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fval = v/(volfrac*area0) - 1;
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dfdx = dv(:)';
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[xnew, ~, ~, ~, ~, ~, ~, ~, ~, low,upp] = mmasub(m, n, loop, xval, ...
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xmin, xmax, xold1, xold2, f0val,df0dx,fval,dfdx,low,upp,a0,a,c_MMA,d);
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% Update MMA Variables
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xPhys = xnew(:);
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xold2 = xold1(:); xold1 = x(:);
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change = max(abs(xnew(:)-x(:)));
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x = xnew;
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fprintf(' It.:%5i Obj.:%11.4f Vol.:%7.3f ch.:%7.3f\n',loop,c, v/area0, change);
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figure(1); colormap(gray); patch(x1', y1', 1-x); caxis([0,1]); axis equal;
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end
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end
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