A New Locking-Free Virtual Element Method for Linear Elasticity Problems

This paper devises a new lowest-order conforming virtual element method(VEM)for planar linear elasticity with the pure displacement/traction boundary condition.The main trick is to view a generic polygon K as a new one K with additional vertices consisting of interior points on edges of K,so that the discrete admissible space is taken as the V1 type virtual element space related to the partition{K}instead of{K}.The method is proved to converge with optimal convergence order both in H^(1)and L^(2)norms and uniformly with respect to the Lam´e constantλ.Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.