The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric virtual element method is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.

翻译：虚拟元方法（VEM）允许使用二维多边形和三维多面体对弹塑性问题进行离散化。这些多边形（及多面体）可具有任意数量的边且可为凹或凸形。这些特性使得该技术在复杂几何体网格划分中具有吸引力。然而，据作者所知，文献中尚未出现轴对称虚拟元方法。因此，本文首次将一阶一致轴对称虚拟元方法应用于弹塑性问题。文中给出了求解轴对称模拟所需的VEM具体实现细节及改进措施，展示了包含压力容器和圆形板的代表性基准算例。算例结果还表明该方法能成功求解近不可压缩性问题。本研究证明，轴对称VEM公式能有效解决特定类别的固体力学问题。文章最后讨论了当前公式的计算结果及未来研究方向。