A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements. (15th September 2020)

• Record Type: Journal Article
• Authors: Harper, Graham; Wang, Ruishu; Liu, Jiangguo; Tavener, Simon; Zhang, Ran
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 6(2020)
• Page Start: 1578
• Page End: 1595
• Publication Date: 2020-09-15
• Subjects: Enrichment of Lagrangian elements -- Hexahedral meshes -- Linear elasticity -- Locking-free -- Quadrilateral meshes -- Deal.II implementation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.07.014
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear Lagrangian elements. It solves the primal variable displacement in the strain–div formulation and can handle both displacement and traction boundary conditions. It is a locking-free solver based on conforming finite elements. The solver has second order accuracy in displacement and first order accuracy in stress and dilation (divergence of displacement), as validated by theoretical analysis and illustrated by numerical experiments on benchmarks. deal.II implementation is also discussed.