ON THE SELECTION OF A LOCKING-FREE hp ELEMENT FOR ELASTICITY PROBLEMS

We consider the design of robust elements that can be used in hp codes for elasticity problems. Our goal is to identify an element that is free of locking for the case of a nearly incompressible material, both in terms of the h version and the p version. By this we mean that the displacements as well as the stresses should converge optimally. For the standard Þnite element method, locking is observed in the stresses for the p version and in both the stresses and displacements for the h version. Hence, we recommend a mixed formulation. Several mixed methods are tested, and a method that is optimal both in terms of h and p is identiÞed.