LOCKING EFFECTS IN THE FINITE-ELEMENT APPROXIMATION OF ELASTICITY PROBLEMS

We consider the finite element approximation of the 2D elasticity problem when the Poisson ratio v is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates as v --> 0, a phenomenon called locking. We analyze this phenomenon and characterize the strength of the locking and robustness of various h-version schemes using triangular and rectangular elements. We prove that the p- and h-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3 D problem is also discussed.