Shape Functions or Interpolation Functions

In FEA we discretize the solution region into finite elements. To conduct the analysis we assume a displacement model to approximately indicate the variations of the displacement within the element. The polynomial chosen to interpolate the field variables over the element are called shape functions. Denoted by[N], they establish the relationship between the displacement at any point in the element with the modal displacement of the element.

u = N1u1 + N2u2+ ….

Simple Element Shapes

Simple Element Shapes

The note on shape function or interpolation function will give an insight about its application in finite element analysis. Solved problem show how we can derive shape functions using lagrange’ interpolation formula.