We present and analyze a new hybridizable discontinuous Galerkin method (HDG) for the Reissner-Mindlin plate bending system. Our method is based on the formulation utilizing Helmholtz Decomposition. Then the system is decomposed into three problems: two trivial Poisson problems and a perturbed saddle-point problem. We apply HDG scheme for these three problems fully. This scheme yields the optimal convergence rate ($(k+1)$th order in the $\mathrm{L}^2$ norm) which is uniform with respect to plate thickness (locking-free) on general meshes. We further analyze the matrix properties and precondition the new finite element system. Numerical experiments are presented to confirm our theoretical analysis.

翻译：我们提出并分析了一种用于Reissner-Mindlin板弯曲系统的新型可混合化不连续伽辽金方法（HDG）。该方法基于Helmholtz分解的变分形式，将系统分解为三个子问题：两个平凡的Poisson问题和一个扰动鞍点问题。我们对这三个问题完全应用HDG格式。该格式在一般网格上实现了最优收敛速度（$\mathrm{L}^2$范数下$(k+1)$阶精度），且对于板厚具有一致性（无锁现象）。我们进一步分析了矩阵性质并预处理了该新型有限元系统。数值实验验证了我们的理论分析。