We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to the proposed technique as the node-based uniform strain virtual element method (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in compressible and nearly incompressible elasticity as well as in elastodynamics, we demonstrate that the NVEM is accurate, optimally convergent and devoid of volumetric locking.
翻译:我们建议采用综合节点集成和虚拟要素方法,以压缩和几乎无法压缩的弹性,使压力在与周围虚拟元素紧张的节点上平均,在平均程序方面,在平均程序方面,将节点平均操作器建成一个节点平均操作器,对有限元素采用基于节点的统一弹性方法的虚拟要素;我们把拟议的技术称为基于节点的统一弹性虚拟要素方法(NVEM);在这种方法中不再引入更多的自由度,从而导致一种基于流离失所的配方;NVEM的一个突出特点是,压力和压力成为与异变一样的节点变量,可以在非线性模拟中加以利用。通过在可压缩和几乎不可压缩的弹性性以及岩浆动力学方面的若干基准问题,我们证明NVEM是准确的,最优化的趋同,并且没有体积锁定。