Application of Virtual Element Method for Plane Stress–Plane Strain Problems

Virtual element method (VEM) is an extension of the standard finite element method (FEM), providing a more generalized approach to overcome the drawbacks of the FEM. A comprehensive literature review is carried out to observe the current applications of VEM for two-dimensional structural problems. However, it is observed that the current applications do not focus specifically on the importance of the stability parameter of the VEM. Therefore, this research is focused to study the effects of the stability parameter on the robustness and the stability of the VEM developing a general-purpose VEM code for analysis of the plane stress/plane strain problems. For this purpose, simple shaped polygons are proposed as the discretized element since they fully utilize the importance of VEM. Four case studies are carried out to compare the results obtained from the VEM and the FEM with the exact solution. Analytical results show that the stability parameter of the VEM can be categorized into three regions, and it is very much sensitive to the aspect ratio. This study proposes an equation to estimate the stability parameter as a function of aspect ratio to obtain more accurate results than the standard FEM results. Furthermore, this study concludes that VEM can be effectively used to model the structure using the non-convex element.