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:

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