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

06/12/2019

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by   Thomas Führer, et al.

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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→ 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.