Locking Effects in the Finite Element Approximation of Elasticity Problems

摘要

In this paper, we analyze the phenomenon of Poisson Locking. This is said tooccur when the approximations obtained using the finite element method for elasticity problems deteriorate as a result of the Poisson ratio being close to 0.5. Using the general theory developed in an earlier paper on locking, we give precise mathematical definitions of locking and robustness and apply some abstract theorems to analyze the locking of various h, p and h-p finite element schemes. In particular, we analyze two types of rectangular elements for the h-version. Extensions to the three-dimensional case are also discussed.