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106 lines
3.2 KiB
106 lines
3.2 KiB
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-12-25 11:36:43
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% @LastEditTime: 2022-01-05 12:25:18
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% pre-compute the principle stress field
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%--------------------------
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function [stress, pmax] = stress_field_init(nelx, nely, scalar, optDesign, vF, e, nu)
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nelx = nelx * scalar;
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nely = nely * scalar;
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dx = 1 / scalar;
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[freedofs, fixeddofs, F, loadnid] = designDomain(optDesign, nelx, nely, vF);
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A11 = [12 3 -6 -3; 3 12 3 0; -6 3 12 -3; -3 0 -3 12];
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A12 = [-6 -3 0 3; -3 -6 -3 -6; 0 -3 -6 3; 3 -6 3 -6];
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B11 = [-4 3 -2 9; 3 -4 -9 4; -2 -9 -4 -3; 9 4 -3 -4];
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B12 = [ 2 -3 4 -9; -3 2 9 -2; 4 9 2 3; -9 -2 3 2];
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KE = 1/(1-nu^2)/24*([A11 A12;A12' A11]+nu*[B11 B12;B12' B11]);
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nodenrs = reshape(1:(1+nelx)*(1+nely),1+nely,1+nelx);
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edofVec = reshape(2*nodenrs(1:end-1,1:end-1)+1,nelx*nely,1);
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edofMat = repmat(edofVec,1,8)+repmat([0 1 2*nely+[2 3 0 1] -2 -1],nelx*nely,1);
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iK = reshape(kron(edofMat,ones(8,1))',64*nelx*nely,1);
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jK = reshape(kron(edofMat,ones(1,8))',64*nelx*nely,1);
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xPhys = ones(nelx * nely, 1);
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U = zeros(2*(nely+1)*(nelx+1),1);
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sK = reshape(KE(:)*(xPhys(:)'*e),64*nelx*nely,1);
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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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U1 = U(edofMat)'; % [8,N]
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[~, ~, D] = material_paras(e, nu);
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optKE = 2;
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S = intS(dx/2, dx/2, D, optKE);
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gp = 1;
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s0 = S{gp} * U1; % [3,n]
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s11 = s0(1, :);
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s22 = s0(2, :);
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s12 = s0(3, :);
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% plot
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% figure;
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% [gx, gy] = meshgrid(1:nelx, 1:nely);
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% gy = flipud(gy);
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stress = zeros(size(s0,2), 2);
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pmax = zeros(size(s0,2), 1);
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for i = 1:size(s0,2)
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se = [s11(i), s12(i);
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s12(i), s22(i)];
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[v, dv] = eig(se);
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dv = abs(diag(dv) * 100);
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[a, j] = max(dv);
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vi = v(:, j);
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stress(i, :) = vi;
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pmax(i) = a;
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% ellipse(gx(i), gy(i), a, dv(3-j), atan2(vi(2), vi(1))); hold on;
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end
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stress = stress ./ vecnorm(stress, 2, 2);
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pmax = pmax ./ max(pmax);
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% figure; quiver(gx(:), gy(:), s1(:,1), s1(:,2), 1, 'LineWidth',1); axis equal; hold on;
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end
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function S = intS(a, b, DH, optKE)
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GaussNodes = [-1/sqrt(3); 1/sqrt(3)]; GaussWeigh = [1 1];
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if optKE==1
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L = [1 0 0 0; 0 0 0 1; 0 1/2 1/2 0];
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else
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L = [1 0 0 0; 0 0 0 1; 0 1 1 0];
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end
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S = cell(4, 1);
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% (-1,-1), (-1,1), (1,-1), (1,1)
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for i = 1:length(GaussNodes)
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for j = 1:length(GaussNodes)
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GN_x = GaussNodes(i);
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GN_y = GaussNodes(j);
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dN_y = 1/4*[-(1-GN_x) -(1+GN_x) (1+GN_x) (1-GN_x)];
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dN_x = 1/4*[-(1-GN_y) (1-GN_y) (1+GN_y) -(1+GN_y)];
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J = [dN_x; dN_y]*[ -a a a -a;
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-b -b b b]';
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G = [inv(J) zeros(size(J));
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zeros(size(J)) inv(J)];
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dN(1,1:2:8) = dN_x; dN(2,1:2:8) = dN_y;
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dN(3,2:2:8) = dN_x; dN(4,2:2:8) = dN_y;
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Be = L*G*dN;
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S{j + (i-1)*2, 1} = GaussWeigh(i)*GaussWeigh(j)*det(J)*DH*Be;
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end
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end
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end
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