A locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation

The problem of shear-locking in the thin-plate limit is a well known issue that must be overcome when discretising the Reissner–Mindlin plate equations. In this paper we present a shear-locking-free method utilising meshfree maximum-entropy basis functions and rotated Raviart–Thomas-Nédélec elements within a mixed variational formulation. The formulation draws upon well known techniques in the finite element literature. Due to the inherent properties of the maximum-entropy basis functions our method allows for the direct imposition of Dirichlet (essential) boundary conditions, in contrast to methods based on moving least squares basis functions. We present benchmark problems that demonstrate the accuracy and performance of the proposed method.

► We propose a novel meshfree method for Reissner–Mindlin plate equation. ► First meshfree formulation to address shear-locking using a mixed variational form. ► We use Maximum Entropy basis functions which allow easy imposition of Dirichlet boundary conditions. ► We show the good performance of the method in the thin-plate limit.