A Virtual Element Method for the Static Bending Analysis of Reissner-Mindlin Plates

Abstract

Introduction: The virtual element method (VEM), introduced in [3] is designed for solving numerical problems de ned on arbitrarily shaped polygonal/polyhedral discretizations. Therefore, it will greatly alleviate the heavy burden placed on meshing complex CAD geometries when compared with the traditional nite element method. Furthermore, VEM could handle the non-conforming discretizations by allowing the existence of hanging nodes, which are treated as normal nodes in the element. The local h-re nement and p-version re nement could be easily implemented under the VEM framework. So far VEM has been successfully applied to solve various problems including topology optimization, contact, fracture, plate bending and vibration, inelasticity. In this work, we develop an arbitrary order virtual element method for the static bending analysis of Reissner-Mindlin plates. The transverse displacement and rotations are independently interpolated with the functions de ned in VEM spaces. The interpolation functions for transverse displacement are one degree higher than the functions for rotations. A benchmark problem is studied to verify the developed method. The optimal convergence rates for transverse displacement and rotations could be obtained from the numerical example.