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

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Abstract

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.

Keywords

Linear elasticity
Locking-free
Staggered grids
Finite difference
Convergence and superconvergence

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The work is supported by the National Natural Science Foundation of China Grant No. 11671233, 91330106.