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

2025-10-22

AI Summary

To address transverse shear locking in the Reissner–Mindlin plate model under the thin-plate limit and Poisson-thickness locking induced by three-dimensional constitutive relations in non-star-convex polygonal elements, this paper proposes a novel polygonal plate element based on the scaled boundary finite element method (SBFEM). The element employs linear shape functions for full discretization, accommodates arbitrary numbers of sides in non-star-convex polygons, and significantly simplifies mesh generation. It introduces, for the first time, the assumed natural strain (ANS) method into the polygonal SBFEM framework and integrates three-dimensional continuum constitutive relations via a two-field variational principle, thereby relaxing the plane-stress assumption and simultaneously mitigating both locking phenomena. Numerical experiments demonstrate optimal convergence rates and high accuracy across the entire thickness spectrum—from thick to ultra-thin plates—and confirm strong robustness against both shear and thickness locking.

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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.

Problem

• Develops polygonal plate elements using scaled boundary finite element method
• Addresses transverse shear locking in low-order Reissner-Mindlin elements
• Incorporates 3D material laws while preventing Poisson's thickness locking

Innovation

• Polygonal plate element using scaled boundary finite element method
• Assumed natural strain approach prevents transverse shear locking
• Two-field variational formulation incorporates 3D material laws