# Nonlinear finite elements/Homework 3

## Problem: The Patch TestEdit

The patch test is one of the first checks used to determine the accuracy of a finite element.

Your first task is to read the following paper on the patch test.

Taylor, R.L., Simo, J.C., Zienkiewicz, O.C., and Chan, A.C.H, 1986, **The patch test - a condition for assessing FEM convergence**, * International Journal for Numerical Methods in Engineering*, 22, pp. 39-62.

After reading the paper, please answer the following questions:

- What is the patch test and why is it used?
- What are the consistency requirement and the stability condition?
- What do the authors mean by convergence?
- List the 2-D structural elements available in ANSYS and describe what shape functions and degrees of freedom each uses.
- Check whether each of these elements passes the patch test. Show details of your calculations.
- Which parts of the paper did you not understand?