Nonlinear finite elements/Homework 3
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Problem: The Patch Test
[edit | edit source]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?