An Anisotropic Locking-Free Nonconforming Triangular Finite Element Method for Planar Linear Elasticity Problem

Abstract

The main aim of this paper is to study the nonconforming linear triangular Crouzeix-Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and $L^2$-norm are obtained, which are independent of lamé parameter $λ$. Numerical results are given to demonstrate the validity of our theoretical analysis.