Relations between enhanced strain methods and the HR method. (English) Zbl 1054.74055

Summary: The three-field Hu-Washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems. In particular, we 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 numerical observations, provided in computational literature, on the coincidence of 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 exact stress solution and exact nodal displacements with one element. The related analytical motivation is given. The theoretical analyses presented in the paper are supported by numerical examples on typical benchmarks.


74S05 Finite element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
74K20 Plates
Full Text: DOI


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