27 lines
1.2 KiB
Matlab
27 lines
1.2 KiB
Matlab
function ke=ele_stiff_matrix(E_ID,Nodes,Elements,E,u,Width)
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ENodes(:,1) = Elements(E_ID,:);
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iN = size(ENodes,1);
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ke = zeros(2*iN,2*iN);
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D=[E/(1-u^2),u*E/(1-u^2),0;
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u*E/(1-u^2),E/(1-u^2),0;
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0,0,E/(2*(1+u))];
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% 计算高斯积分点坐标
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r = [-sqrt(1/3) sqrt(1/3)]; % 2*2 高斯积分点
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s = [r(1) r(1) r(2) r(2)];
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t = [r(2) r(1) r(1) r(2)]; % 高斯积分点坐标
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% 高斯积分计算单元刚度矩阵
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for i=1:4
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J = Jacobi(E_ID,s(i),t(i),Elements,Nodes); % 雅可比矩阵
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Nst = DiffShapeFun(s(i),t(i)); % 形函数关于自然坐标s,t求导
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Nxy = zeros(8,2);
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for j=1:8
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Nxy(j,:) = (J\Nst(j,:)')'; % 形函数关于 x,y 求导=inv(J)*Nst
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end
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Bm = [Nxy(1,1) 0 Nxy(2,1) 0 Nxy(3,1) 0 Nxy(4,1) 0 Nxy(5,1) 0 Nxy(6,1) 0 Nxy(7,1) 0 Nxy(8,1) 0;
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0 Nxy(1,2) 0 Nxy(2,2) 0 Nxy(3,2) 0 Nxy(4,2) 0 Nxy(5,2) 0 Nxy(6,2) 0 Nxy(7,2) 0 Nxy(8,2);
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Nxy(1,2) Nxy(1,1) Nxy(2,2) Nxy(2,1) Nxy(3,2) Nxy(3,1) Nxy(4,2) Nxy(4,1) Nxy(5,2) Nxy(5,1) Nxy(6,2) Nxy(6,1) Nxy(7,2) Nxy(7,1) Nxy(8,2) Nxy(8,1)];
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ke = ke+det(J)*Bm'*D*Bm*Width;
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end
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end |