Speaker
Description
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 of highly flexible geometry descriptions that go 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 complicated 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. Hence, it is crucial to have a comparison of polygonal element formulations to gain a better understanding of advantages and drawbacks.
This presentation 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 measurements are considered such as error norms, convergence rates and deformation measures.
References:
Beirão da Veiga, L., Franco Brezzi, Andrea Cangiani, Gianmarco Manzini, L. Donatella Marini, and Alessandro Russo. "Basic principles of virtual element methods." Mathematical Models and Methods in Applied Sciences 23, no. 01 (2013): 199-214.
Klinkel, S., and R. Reichel. "A finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics." Computer Methods in Applied Mechanics and Engineering 347 (2019): 295-315.
Song, Chongmin. The scaled boundary finite element method: introduction to theory and implementation. John Wiley \& Sons, 2018.
