How can I evaluate the double integration of the stiffness matrix using Gaussian quadrature in Matlab?
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Hi there everybody. In finite elements analysis, the stiffness matrix using Galerkin method is found to be expressed as this: K(i,j)=int(int(-D*((d2Ndx2(j)*d2Ndx2(i))+ v*(d2Ndy2(j)*d2Ndx2(i))+(d2Ndy2(j)*d2Ndy2(i))+ v*(d2Ndx2(j)*d2Ndy2(i))+(2*(1-v)*(d2Ndxdy(j)*d2Ndxdy(i))))dx)dy). N is a vector containing the shape function D and v are material properties. I'm using 4 node rectangular element with 3 degrees of freedom at each node which means ( N ) is a vector of 12 shape functions. Can anyone help me writing a Matlab code to evaluate the stiffness matrix using Gaussian quadrature rule or at least show me how to transform the second derivatives from (x-y)domain to (xi-eta)domain . thanks a lot.
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