A Comparative Study of Polygonal Element Formulations for Linear Elasticity

ABSTRACT With the rising complexity of architectural design, a growing interest in topology optimization, and the increasing need to model crack propagation, there is a higher demand for highly flexible geometry descriptions that go hand in hand with robust element formulations. Methods relying on polygonal meshes, such as the virtual element method (VEM), element formulations based on Wachspress shape functions, and the scaled boundary finite element method (SBFEM) have proven to be versatile in solving physical problems. Arbitrarily shaped elements are beneficial when it comes to highly localized meshes, treatment of hanging nodes, and flexibility of the meshing of complex domains. This paper provides a comparative study of polygonal element formulations, focusing specifically on the VEM, the semi‐analytical SBFEM, and the fully discretized SBFEM. The study evaluates these methods in terms of stability, convergence behavior, and flexibility in the context of linear elasticity. The potential of the formulations is evaluated by applying them to several benchmark problems and by comparing the results. In doing so, the flexibility of the considered formulations is also proven. To this end, several indicators are considered, such as error norms, convergence rates, and displacements.