New second order nonconforming triangular element for planar elasticity problems

In the use of finite element methods to the planar elasticity problems, one difficulty is to overcome locking when elasticity constant λ → ∞. In the case of traction boundary condition, another difficulty is to make the discrete Korn's second inequality valid. In this paper, a triangular element is presented. We prove that this element is locking-free, the discrete Korn's second inequality holds and the convergence order is two.