Reissner-Mindlin板弯曲模型的超弱形式和DPG近似
An ultraweak formulation of the Reissner-Mindlin plate bending model and DPG approximation
摘要：
我们开发和分析的Reissner-Mindlin板弯曲模型的固支和软简支的情况下的超弱变分制剂。我们证明了适定性的配方，均匀相对于板的厚度$t$。证明了当$t\to 0$ .基于超弱形式，我们引入了一个具有最优检验函数（DPG）的间断Petrov-Galerkin型离散化，并证明了它的一致拟优收敛性。我们的理论涵盖了非凸多边形板的情况。对固定载荷下的光滑模型解的数值实验证实了该格式是无锁定的。
英文摘要：
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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