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49 lines
3.8 KiB
49 lines
3.8 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-02-28 14:59:56
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% @LastEditTime: 2021-02-28 15:00:18
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%--------------------------
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function Ke = intKE(a, b, c, DH)
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GN_x=[-1/sqrt(3),1/sqrt(3)]; GN_y=GN_x; GN_z=GN_x; GaussWeigh=[1,1];
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Ke = zeros(24,24); 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);y = GN_y(j);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 ; -b -b b b -b -b b b; -c -c -c -c c c c c]';
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G = [inv(J) zeros(3) zeros(3);zeros(3) inv(J) zeros(3);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 = L*G*dN;
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Ke = Ke + GaussWeigh(i)*GaussWeigh(j)*GaussWeigh(k)*det(J)*(Be'*DH*Be);
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end
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end
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end
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end
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%======================================================================================================================%
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% Subfunction elementMatVec3D: %
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% A compact and efficient MATLAB code to evaluate the 3D isoparametric element stiffness matrix %
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% %
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% Developed by: Jie Gao, Zhen Luo, Liang Xia and Liang Gao* %
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% Email: gaoliang@mail.hust.edu.cn (GabrielJie_Tian@163.com) %
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% %
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% Main references: %
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% %
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% (1) Jie Gao, Zhen Luo, Liang Xia, Liang Gao. Concurrent topology optimization of multiscale composite structures %
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% in Matlab. Accepted in Structural and multidisciplinary optimization. %
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% %
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% (2) Xia L, Breitkopf P. Design of materials using topology optimization and energy-based homogenization approach in %
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% Matlab. % Structural and multidisciplinary optimization, 2015, 52(6): 1229-1241. %
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% %
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% ********************************************* Disclaimer ******************************************************* %
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% The authors reserve all rights for the programs. The programs may be distributed and used for academic and %
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% educational purposes. The authors do not guarantee that the code is free from errors,and they shall not be liable %
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% in any event caused by the use of the program. %
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%======================================================================================================================%
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