A locking-free finite difference method on staggered grids for linear elasticity problems. (15th September 2018)

• Record Type: Journal Article
• Authors: Rui, Hongxing; Sun, Ming
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 6(2018)
• Page Start: 1301
• Page End: 1320
• Publication Date: 2018-09-15
• Subjects: Linear elasticity -- Locking-free -- Staggered grids -- Finite difference -- Convergence and superconvergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.06.023
• Languages: English
• ISSNs: 0898-1221

Abstract

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 H 1 -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.