Conditions for equivalence between the Hu-Washizu and related formulations, and computational behavior in the incompressible limit. (English) Zbl 1123.74020

Djoko, J. K.; Lamichhane, B. P.; Reddy, B. D.; Wohlmuth, B. I.

Comput. Methods Appl. Mech. Eng. 195, No. 33-36, 4161-4178 (2006).

Summary: The relationship among Hu-Washizu mixed formulation and other mixed and enhanced formulations is examined in detail, in the context of linear elasticity, with a view to present a unified framework for such formulations. The Hu-Washizu formulation is considered in both its classical form and in a modified form that is suited to establish the well-posedness in incompressible limit. Recently established theoretical results on uniform well-posedness are studied computationally by considering a range of numerical examples, which illustrate where appropriate the good behavior predicted by the theory, as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied.

MSC:

74G65	Energy minimization in equilibrium problems in solid mechanics
74B05	Classical linear elasticity
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

mixed finite elements; enhanced strains; low-order approximations; well-posedness

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