A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes

摘要

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. (C) 2020 Elsevier Ltd. All rights reserved.