We propose a displacement-based approach to solve problems in compressible and nearly incompressible plane elasticity that combines a nodal integration technique and the virtual element method (VEM), wherein the strain is averaged around 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). 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 thereby providing room for further development of this novel approach. 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:我们建议采用基于迁移的办法来解决压缩和几乎无法压缩的平面弹性问题,这种办法结合节点集成技术和虚拟元素方法(VEM),使压力平均围绕与周围虚拟元素菌株的节点。对于平均压力程序,将节点平均操作器建成一个节点平均操作器,将基于节点的统一压力方法的虚拟元素概括为有限的元素。我们将这些新元素称为基于节点的统一线菌株虚拟元素。NVEM的一个突出特点是,压力和压力成为节点变量,就像流离失所一样,可以在非线性模拟中加以利用,从而为进一步发展这一新方法提供空间。我们通过在平面弹性方面的几个基准问题,证明NVEM是准确和最佳趋同的,并且没有在几乎不可压缩的极限中进行体积锁定。