A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method
Abstract
In this work, a polygonal Reissner-Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced for the parametrization of the scaling and the radial direction. This yields a fully discretized formulation, which enables the use of non-star-convex-polygonal elements with an arbitrary number of edges, simplifying the meshing process. To address the common effect of transverse shear locking for low-order Reissner-Mindlin elements in the thin-plate limit, an assumed natural strain approach for application on the polygonal scaled boundary finite elements is derived. Further, a two-field variational formulation is introduced to incorporate three-dimensional material laws. Here the plane stress assumptions are enforced on the weak formulation, facilitating the use of material models defined in three-dimensional continuum while considering the effect of Poisson's thickness locking. The effectiveness of the proposed formulation is demonstrated in various numerical examples.
Cite
@article{arxiv.2510.20044,
title = {A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method},
author = {Anna Hellers and Mathias Reichle and Sven Klinkel},
journal= {arXiv preprint arXiv:2510.20044},
year = {2025}
}