Nonlinear finite elements/Homework 3

Problem: The Patch Test
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?