We propose a combined nodal integration and virtual element method for compressible and nearly incompressible plane 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 these new elements as node-based uniform strain virtual elements (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 plane elasticity, we demonstrate that the NVEM is accurate and optimally convergent, and devoid of volumetric locking in the nearly incompressible limit.

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平面弹性,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,利用节点平均操作程序,将节点平均操作器建成为对有限元素采用基于节点的统一收缩方法的虚拟要素,将这些新要素称为基于节点的统一收缩虚拟要素(NVEM),在这一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,压力和紧张变成与异变一样的节点变量,可以在非线性模拟中加以利用。我们通过在平面弹性方面的几个基准问题,证明NVEM是准确和最佳集中的,并且没有将体积锁定在几乎不可压缩的极限中。