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.

中文翻译：

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基于拉格朗日元素富集的四边形和六面体网格上的线性弹性的无锁定解算器

本文基于经典双线性或三线性拉格朗日元素的富集，提出了一种新的四边形和六面体网格上线性弹性的有限元求解器。它解决了应变-div公式中的原始变量位移，并且可以处理位移和牵引边界条件。它是基于一致有限元的无锁定求解器。该求解器具有位移的二阶精度以及应力和膨胀（位移的发散）的一阶精度，这已通过理论分析验证并通过基准上的数值实验进行了说明。还讨论了Deal.II的实现。