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 $$t\rightarrow 0$$ 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.

中文翻译：

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Reissner-Mindlin 板弯曲模型和 DPG 近似的超弱公式

我们开发并分析了 Reissner-Mindlin 板弯曲模型的超弱变分公式，适用于夹紧和软简支情况。我们证明了公式的适定性，关于板厚 t 是均匀的。我们还证明了当 $$t\rightarrow 0$$ t → 0 时，Reissner-Mindlin 解对相应 Kirchhoff-Love 模型的解的弱收敛性。基于超弱公式，我们引入了具有最优测试函数 (DPG) 的不连续 Petrov-Galerkin 类型的离散化，并证明了其一致的准最优收敛性。我们的理论涵盖了非凸多边形板的情况。一些具有固定载荷的光滑模型解的数值实验证实了我们的方案是无锁定的。