A Comparative Study of Polygonal Element Formulations for Linear Elasticity

PAMM, vol. 25

Abstract

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.

Authors 8

1. Ajay Kumar Pasupuleti corresponding

   University of Duisburg-Essen

   Affiliation as printed

   Institute of Structural Analysis University of Duisburg‐Essen Essen Germany

2. Mathias Reichle Aachen chair Institute of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair and Institute of Structural Analysis and Dynamics RWTH Aachen University Aachen Germany

3. Anna Hellers Aachen chair Institute of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair and Institute of Structural Analysis and Dynamics RWTH Aachen University Aachen Germany

4. Njomza Pacolli Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

5. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   University of Siegen Siegen Germany

6. Hagen Holthusen

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Institute of Applied Mechanics University of Erlangen‐Nuremberg Erlangen Germany

7. Sven Klinkel Aachen chair Institute of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair and Institute of Structural Analysis and Dynamics RWTH Aachen University Aachen Germany

8. Carolin Birk

   University of Duisburg-Essen

   Affiliation as printed

   Institute of Structural Analysis University of Duisburg‐Essen Essen Germany