On locking-free finite element schemes for three-dimensional elasticity

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lame constant lambda -> infinity. 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 is an element of (0, +infinity) 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.