We present a stabilized finite element method for the Hu-Washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node-based uniform strain elements. We show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case.

The classical Hu-Washizu mixed formulation for plane problems in elasticity is examined afresh, with the emphasis on behavior in the incompressible limit. The classical continuous problem is embedded in a family of Hu-Washizu problems parametrized by a scalar α for which α = λ/μ corresponds to the classical formulation, with λ and μ being the Lamé parameters. Uniform well-posedness in the incom...

Abstract An original, variational formulation of the Virtual Element Method (VEM) is proposed, based on a Hu–Washizu mixed statement for 2D linear elastostatics. The proposed framework appears to be ideal VEs, whereby compatibility enforced in weak sense and strain model can prescribed priori, independently unknown displacement model. It shown how ensuing freedom definition conveniently exploit...