We present a discontinuous Petrov-Galerkin (DPG) method with optimal test functions for the Reissner-Mindlin plate bending model. Our method is based on a variational formulation that utilizes a Helmholtz decomposition of the shear force. It produces approximations of the primitive variables and the bending moments. For any canonical selection of boundary conditions the method converges quasi-optimally. In the case of hard-clamped convex plates, we prove that the lowest-order scheme is locking free. Several numerical experiments confirm our results.

翻译：我们提出了一个不连续的Petrov-Galerkin(DPG)方法,该方法对Reissner-Mindlin板块弯曲模型具有最佳测试功能。我们的方法基于一种变式配方,它使用剪切力的赫尔姆霍茨分解法,产生原始变量和弯曲时间的近似值。对于任何对边界条件的卡通选择,该方法都接近于极极致。对于硬压的convex板块,我们证明最低顺序方案是免费锁定的。一些数字实验证实了我们的结果。