A locking-free finite difference method on staggered grids for linear elasticity problems

A finite difference method on staggered grids is constructed on general nonuniform rectangular partition for linear elasticity problems. Stability, optimal-order error estimates in discrete H1-norms on general nonuniform grids and second-order superconvergence on almost uniform grids have been obtained. These theoretical results are uniform about the Lamé constant λ∈(0,∞) so the finite difference method is locking-free. The method and theoretical results can be extended to three dimensional problems. Numerical experiments using the method show agreement of the numerical results with theoretical analysis.