Mixed displacement-rotation-pressure formulations for linear elasticity
Mixed displacement-rotation-pressure formulations for linear elasticity
复制标题
DOI：
10.1016/j.cma.2018.09.029
复制
发表时间：
2019-02-01
影响因子：
7.2
通讯作者：
Ruiz-Baier, Ricardo
中科院分区：
文献类型：
--
作者：
Anaya, Veronica;de Wijn, Zoa;Ruiz-Baier, Ricardo
我们提出了一个新的锁定自由家庭的混合有限元和有限体积元方法的近似线性弹性静力学，制定的位移，旋转矢量和压力。基于BabuSka-Brezzi理论，建立了三场连续方程的唯一可解性，以及Galerkin和Petrov-Galerkin方法的良好确定性和稳定性.最佳的先验误差估计使用鲁棒的Lame常数，把这些数值方法特别吸引人的几乎不可压缩的材料。我们通过在2D和3D中进行一些计算测试来验证准确性（在适当加权的范数中），以及新配方和混合方案的适用性，还包括我们的理论分析未涵盖的情况。(C)2018作者（S）由爱思唯尔公司出版
We propose a new locking-free family of mixed finite element and finite volume element methods for the approximation of linear elastostatics, formulated in terms of displacement, rotation vector, and pressure. The unique solvability of the three-field continuous formulation, as well as the well-definiteness and stability of the proposed Galerkin and Petrov-Galerkin methods, is established thanks to the BabuSka-Brezzi theory. Optimal a priori error estimates are derived using norms robust with respect to the Lame constants, turning these numerical methods particularly appealing for nearly incompressible materials. We exemplify the accuracy (in a suitably weighted norm), as well the applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2D and 3D, also including cases not covered by our theoretical analysis. (C) 2018 The Author(s). Published by Elsevier B.V.