On some mixed finite element methods for plane membrane problems

Abstract

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 in Cazzani and Atluri (1993) 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 performances are provided.