A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912665717178368 |
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| author | Hellers, Anna Reichle, Mathias Klinkel, Sven |
| author_facet | Hellers, Anna Reichle, Mathias Klinkel, Sven |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method Hellers, Anna Reichle, Mathias Klinkel, Sven Computational Engineering, Finance, and Science 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. |
| title | A polygonal Reissner-Mindlin plate element based on the scaled boundary finite element method |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2510.20044 |