6. One-element in-plane stress analysis test

This test is based on Example 6.6 of the in the textbook by K.J. Bathe[37]. A rectangular plate with edges of length 2 is stretched in-plane at the upper right corner with a displacement of (1., 0.5), as shown in the figure below:

Stress test: Undeformed and deformed shape

Figure 118. Stress test: Undeformed and deformed shape

The test checks the linear and non-linear in-plane behaviour of quadrilateral shell and 2D elements (plane-stress conditions). The strains and the stresses are compared to the analytical solution for the linear case. For the nonlinear case, the Green-Lagrange strains and the Cauchy stresses are separately computed by the test and compared to the strains and stresses obtained from the FE analysis.

For elements having internal degrees-of-freedom, those degrees-of-freedom are locked in this test. Otherwise, the interpolated FE strains and stresses will not correspond to those computed by the test.

[37] Klaus-Juergen Bathe. "Finite element procedures." Prentice-Hall, 1996.