A new weak Galerkin finite element method is introduced and analyzed for the Reissner–Mindlin plate model in the primary form (without introducing shear strain as an extra unknown), which results in a linear system with symmetric positive definite stiffness matrix. The proposed method achieves uniform convergence with respect to plate thickness (the so-called locking-free) without introducing any projection, reduced integration, etc. In addition, the new method can be applied to general polygonal meshes; in particular, we implement pentagonal and hexagonal meshes in our numerical tests. The numerical study confirms our theory.

中文翻译：

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多边形网格上Reissner-Mindlin板的无锁定弱Galerkin有限元方法

引入了一种新的弱Galerkin有限元方法，并对其进行了初步形式的Reissner-Mindlin板模型分析（没有引入剪切应变作为额外的未知数），从而得到了具有对称正定刚度矩阵的线性系统。所提出的方法实现了关于板厚度的均匀收敛（所谓的无锁定），而没有引入任何凸出，减少了积分等。特别是，我们在数值测试中实现了五边形和六边形网格。数值研究证实了我们的理论。