A virtual element method for transversely isotropic elasticity
A virtual element method for transversely isotropic elasticity
复制标题
横观各向同性弹性的虚拟元法
DOI：
10.1007/s00466-019-01690-7
复制
发表时间：
2018
影响因子：
4.1
通讯作者：
D. van Huyssteen
中科院分区：
文献类型：
--
作者：
B. Reddy;D. van Huyssteen
本文采用低阶虚元法（VEM）研究了横观各向同性弹性力学平面问题的近似解，重点研究了近似不可压缩性和近似不可扩展性。此外，均匀的问题，其中各向同性的平面是固定的;和非均匀的问题，其中定义各向同性平面的纤维方向随位置而变化，进行了探讨。在后一种情况下，各种选项被认为是近似的非均匀的纤维方向在元素水平。通过一系列的数值例子的VEM近似被证明是强大的和锁定的几个元素的几何形状和纤维方向，对应于温和和强烈的非均匀性。此外，VEM的收敛速度被证明是可比经典的低阶标准有限元方法。
This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order virtual element method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored. In the latter case various options are considered for approximating the non-homogeneous fibre directions at an element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to both mild and strong non-homogeneity. Further, the convergence rate of the VEM is shown to be comparable to classical low-order standard finite element approaches.