Shape functions for different elements used in finite element analysis

Shape functions or interpolation functions are functions used to represent behaviour of a field variable within an element. In finite element analysis we deal with different elements. The elements can be linear, quadratic, 8- noded, 9-noded etc. The shape function for these elements is required to be determined to draw a relationship between the nodal displacements and displacement function chosen for the entire element. Starting from a two noded linear element we can calculate the shape function for 4 noded square element. Quadratic or 3 noded element can be used for determining the shape functions for 9- noded square element. 8- noded element is quiet tricky and we can use the solutions for 2 noded square element to get its shape function. I have presented in the attached literature, a simple way of arrive at shape function for 4, 8 and 9 noded square finite elements.

 

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