A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method

Anna Hellers; Mathias Reichle; Sven Klinkel

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arXiv · 2510.20044

A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method

Anna Hellers·Mathias Reichle·Sven Klinkel

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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.

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Anna Hellers, Mathias Reichle, Sven Klinkel. 2025-10-22. A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method. https://arxiv.org/abs/2510.20044

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