On Locking-Free Finite Element Schemes for Three-Dimensional Elasticity

Abstract

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lamé constant $\lambda \rightarrow\infty$. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to $\lambda\in (0,+\infty)$ are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.