A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements

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.