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On some mixed finite element methods for plane membrane problems. (English) Zbl 0926.74111

Summary: An analysis of some quadrilateral dual mixed finite element methods for plane membrane problems is presented. The methods are based on a variational formulation which a priori does not involve symmetric stresses. After having presented the governing equations of the problem under discussion in the linear framework, a detailed analysis of a method already proposed by A. Cazzani and S. N. Atluri [Comput. Mech. 11, No. 4, 229-251 (1993; Zbl 0773.73085)] is performed. In particular, a result setting the equivalence of the method and another one involving symmetric stresses is established. Two other methods, this time not equivalent to any symmetric stress method, are presented and for them an analysis is outlined. Finally, some numerical tests showing the method performance are provided.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates

Citations:

Zbl 0773.73085
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