A locking-free nonconforming finite element method for planar linear elasticity

Abstract

We propose a locking-free nonconforming finite element method based on quadrilaterals to solve for the displacement variable in the pure displacement boundary value problem of planar linear elasticity. The method proposed in this paper is optimal and robust in the sense that the convergence estimates in the energy and L-2-norms are independent of the Lame parameter lambda.