Relations between enhanced strain methods and the HR method

Abstract

The three-field Hu–Washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems. In particular we will analyse the limitation phenomena concerning two mixed methods, respectively denoted the strain gap method and the mixed enhanced strain method, and the two-field Hellinger–Reissner (HR) finite element formulation. Accordingly two original limitation principles are contributed. We provide the theoretical motivation of the numerical observations, provided in computational literature, on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the HR method if different choices of shape functions are made. It is further shown that the HR method provides the exact stress solution and the exact nodal displacements with one element. The related analytical motivation are thus given. The theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks.