The patch test conditions and some multivariable finite element formulations

From a uniÞed viewpoint, this article establishes the practical and general constant stress patch test conditions (PTC) for analysing and ensuring convergence or robustness of some multivariable Þnite element (MFE) formulations, such as hybrid-mixed and incompatible element formulations. The proposed PTC are applied to develop new general MFE formulations which pass PTC and a family of corresponding MFE for stress analysis. Several numerical examples are also given.