What are Shape Functions?

Shape functions are polynomial functions that interpolate the discrete displacements into continuous functions. They are therefore also known as interpolation functions. The order of polynomial represents the maximal capability of the shape functions to model a displacement field within each element.

Practical decisions in choosing the order of shape functions require the best balance between accuracy and computational cost. Similar to stiffness and force matrices, shape functions are first defined locally and subsequently assembled into global shape functions.

Steps to Derive k and Assemble into K

Figure 1 is a flowchart illustrating the sequence for computing the stiffness matrix of a simple problem (the concept is similar to more complex problems). Computing the stiffness matrix involves two main steps:

1. Derive local stiffness matrices (k)
2. Assemble k into K, the global stiffness matrix