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52 lines
2.0 KiB
52 lines
2.0 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-02-19 21:19:39
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% @LastEditTime: 2021-02-19 21:52:22
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% gradient of shape function on one ele, 8 nodes, N1 ~ N8
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% dN: [9*24]
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% [dN1dx, 0, 0, ...
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% 0, dN1dx, 0, ...
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% 0, 0, dN1dx, ...
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% dN1dy, 0, 0, ...
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% 0, dN1dy, 0, ...
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% 0, 0, dN1dy, ...
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% dN1dz, 0, 0, ...
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% 0, dN1dz, 0, ...
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% 0, 0, dN1dz, ...
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% This sequence is setted for computaion
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%--------------------------
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function B = shape_grad(a, b, c)
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GN_x=[-1/sqrt(3),1/sqrt(3)]; GN_y=GN_x; GN_z=GN_x;
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B = cell(2,2,2);
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% L = zeros(6,9);
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% L(1,1) = 1; L(2,5) = 1; L(3,9) = 1;
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% L(4,2) = 1; L(4,4) = 1; L(5,6) = 1;
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% L(5,8) = 1; L(6,3) = 1; L(6,7) = 1;
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for i=1:length(GN_x)
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for j=1:length(GN_y)
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for k=1:length(GN_z)
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x = GN_x(i);
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y = GN_y(j);
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z = GN_z(k);
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dNx = 1/8*[-(1-y)*(1-z) (1-y)*(1-z) (1+y)*(1-z) -(1+y)*(1-z) -(1-y)*(1+z) (1-y)*(1+z) (1+y)*(1+z) -(1+y)*(1+z)];
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dNy = 1/8*[-(1-x)*(1-z) -(1+x)*(1-z) (1+x)*(1-z) (1-x)*(1-z) -(1-x)*(1+z) -(1+x)*(1+z) (1+x)*(1+z) (1-x)*(1+z)];
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dNz = 1/8*[-(1-x)*(1-y) -(1+x)*(1-y) -(1+x)*(1+y) -(1-x)*(1+y) (1-x)*(1-y) (1+x)*(1-y) (1+x)*(1+y) (1-x)*(1+y)];
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J = [dNx;dNy;dNz]*[ -a a a -a -a a a -a ;
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-b -b b b -b -b b b;
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-c -c -c -c c c c c]';
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G = [inv(J) zeros(3) zeros(3);
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zeros(3) inv(J) zeros(3);
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zeros(3) zeros(3) inv(J)];
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dN(1,1:3:24) = dNx; dN(2,1:3:24) = dNy; dN(3,1:3:24) = dNz;
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dN(4,2:3:24) = dNx; dN(5,2:3:24) = dNy; dN(6,2:3:24) = dNz;
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dN(7,3:3:24) = dNx; dN(8,3:3:24) = dNy; dN(9,3:3:24) = dNz;
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Be = G*dN;
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B{i,j,k} = Be([1,4,7,2,5,8,3,6,9], :);
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end
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end
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end
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end
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