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 \ instead of \. The method is proved to converge with optimal convergence order both in H¹ and L² norms and uniformly with respect to the Lamé constant λ. Numerical tests are presented to illustrate the good performance of the proposed VEM and confirm the theoretical results.