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arXiv · 1906.04869

An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation

Thomas Führer·Norbert Heuer·Francisco-Javier Sayas
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Abstract

We develop and analyze an ultraweak variational formulation of the Reissner-Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness $t$. We also prove weak convergence of the Reissner-Mindlin solution to the solution of the corresponding Kirchhoff-Love model when $t\to 0$. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.

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Thomas Führer, Norbert Heuer, Francisco-Javier Sayas. 2019-06-12. An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation. https://arxiv.org/abs/1906.04869

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