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 \(t\rightarrow 0\). 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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Dedicated to our dear friend Francisco “Pancho” Javier Sayas who passed away in April 2019.
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Supported by CONICYT through FONDECYT Projects 1190009, 11170050, and by NSF through Grant DMS-1818867.
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Führer, T., Heuer, N. & Sayas, FJ. An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation. Numer. Math. 145, 313–344 (2020). https://doi.org/10.1007/s00211-020-01116-0
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DOI: https://doi.org/10.1007/s00211-020-01116-0