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71 lines
2.4 KiB
71 lines
2.4 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2020-11-17 17:04:34
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% @LastEditTime: 2021-03-14 22:06:51
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% NOTE: The overall domain must be in [-a, a] & [-b, b]
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% The integration is:
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% \int_{min_y}^{max_y} \int_{min_x}^{max_x} B(N(x, y)) dxdy
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% N(x, y) = 1/4(1 - x/a)(1 - y/b)
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% a = lx/2; b = ly/2
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%--------------------------
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% function B = shape_derivative_local2(coor, a, b)
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% GaussNodes = [-1/sqrt(3); 1/sqrt(3)]; GaussWeigh = [1 1];
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% L = [1 0 0 0; 0 0 0 1; 0 1 1 0];
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%
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% minx = coor(1,1); maxx = coor(1,2);
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% miny = coor(2,1); maxy = coor(2,2);
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%
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% B = cell(4,1);
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%
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% for i = 1:2
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% for j = 1:2
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% % projection to [-1, 1]
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% GN_x = (maxx+minx + abs(maxx-minx)*GaussNodes(i))/2;
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% GN_y = (maxy+miny + abs(maxy-miny)*GaussNodes(j))/2;
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%
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% dN_x = 1/4*[-(1-GN_y/b) (1-GN_y/b) (1+GN_y/b) -(1+GN_y/b)]/a;
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% dN_y = 1/4*[-(1-GN_x/a) -(1+GN_x/a) (1+GN_x/a) (1-GN_x/a)]/b;
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%
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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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%
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% Be = L*dN;
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% B{2*(i-1)+j} = GaussWeigh(i)*GaussWeigh(j)*Be;
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% end
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% end
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% end
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function gradN = shape_derivative_local(coor, a, b)
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GaussNodes = [-1/sqrt(3); 1/sqrt(3)];
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gradN = cell(4,1);
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L = [1 0 0 0; 0 0 0 1; 0 1 1 0];
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minx = coor(1,1); maxx = coor(1,2);
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miny = coor(2,1); maxy = coor(2,2);
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for i = 1:2
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for j = 1:2
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gp = 2*(i-1)+j;
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% GN_x = GaussNodes(i);
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% GN_y = GaussNodes(j);
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GN_x = (maxx+minx + abs(maxx-minx)*GaussNodes(i))/2;
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GN_y = (maxy+miny + abs(maxy-miny)*GaussNodes(j))/2;
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dN_x = 1/4*[-(1-GN_x) (1-GN_x) (1+GN_x) -(1+GN_x)];
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dN_y = 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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% dNdx = 3*8
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dN1(1,1:2:8) = dN_x; dN1(2,1:2:8) = dN_y;
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dN1(3,2:2:8) = dN_x; dN1(4,2:2:8) = dN_y;
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B2 = L*G*dN1;
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gradN{gp} = B2;
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end
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end
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end
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