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.
[google-drive-embed url=”https://drive.google.com/a/civildigital.com/file/d/0B-zZkuNv8Pmwb0JZcVgzd0dDUlU/preview?usp=drivesdk” title=”SHAPE-FUNCTIONS.pdf” icon=”https://ssl.gstatic.com/docs/doclist/images/icon_12_pdf_list.png” width=”100%” height=”400″ style=”embed”]