v3.04.111 SSLV111 - Error estimator on a perforated plate in linear elasticity#
Summary:
This test validates and compares the 2 versions of the Zhu-Zienkiewicz error estimator (version 1 from 1987, noted \(\mathrm{ZZ1}\), and version 2 from 1992, noted \(\mathrm{ZZ2}\)) applied to the linear elasticity system, statically.
It includes 5 plane stress models, each corresponding to a type of finite element (TRIA3, QUAD4, TRIA6, QUAD8, QUAD9).
The analytical solution is known and allows the estimated errors to be compared with the exact error.
This test also validates version 1 of the Zhu-Zienkiewicz error estimator applied to 2 3D models. The first modeling includes the finite elements HEXA8, PYRAM5 and TETRA4 and the second, the finite elements PENTA6. The solution does not depend on the value along the z-axis. The results are therefore compared with the analytical values used in 2D.
The advantage of the test lies in:
in the comparison between the constraints smoothed with \(\mathrm{ZZ1}\) (continuous global smoothing) and \(\mathrm{ZZ2}\) (smoothing local to element patches),
in comparing the estimators with each other,
in the qualitative and quantitative analysis of the results (global and local relative errors)
in the validation of the Zhu-Zienkiewicz smoothing estimator version 1 in 3D.
The test highlights the good behavior of \(\mathrm{ZZ2}\) on all types of elements and the poor results of \(\mathrm{ZZ1}\) on quadratic elements when the solution does not have a strong singularity, which is the case.