In this paper we present a new mixed variational formulation for the problem of linear elastostatics. Our formulation is very similar to the classical HellingerReissner formulation, but appears superior for finite element discretization. To make plain the relation between the Hellinger-Reissner formulation and the present one, we consider first an elastic body occupying a region g? in Euclidean...

The critical points of the generalized complementary energy variational principles are clarified. An open problem left by Hellinger and Reissner is solved completely. A pure complementary energy (involving the Kirchhoff type stress only) is constructed. We prove that the well-known generalized Hellinger-Reissner’s energy L(u, s) is a saddle point functional if and only is the Gao-Strang gap fun...

The critical points of the generalized complementary energy variational principles are clariied. An open problem left by Hellinger and Reissner is solved completely. A pure complementary energy (involving the Kirchhoo type stress only) is constructed. We prove that the well-known generalized Hellinger-Reissner's energy L(u; s) is a saddle point functional if and only is the Gao-Strang gap funct...

Abstract This note aims at illustrating the application of Virtual Element Method to elasticity problems in mixed form, following Hellinger-Reissner variational principle. In order highlight potential and flexibility our approach, we focus on a three-dimensional low-order scheme, but similar considerations apply two-dimensional higher-order methods.

How, in a discretized model, to utilize the duality and complementarity of two saddle point variational principles is considered in the paper. A homology family of optimality conditions, different from the conventional saddle point conditions of the domain-decomposed Hellinger–Reissner principle, is derived to enhance stability of hybrid finite element schemes. Based on this, a stabilized hybri...

We extend the applicability of the augmented dual-mixed method introduced recently in [4, 5] to the problem of linear elasticity with mixed boundary conditions. The method is based on the Hellinger–Reissner principle and the symmetry of the stress tensor is imposed in a weak sense. The Neuman boundary condition is prescribed in the finite element space. Then, suitable Galerkin least-squares typ...

We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

We construct first order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger– Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

It is well-known that the complementary energy principle for large deformation elasticity was first proposed by Hellinger in 1914. Since Reissner clarified the boundary conditions in 1953, the complementary energy principles and methods in finite deformation mechanics have been studied extensively during the last forty years (cf. e.g. Koiter, 1976; Nemat-Nasser, 1977; Atluri, 1980; Lee & Shield...