Locking-free polygonal plate element based on the discrete shear projection method

Abstract

A novel shear locking free arbitrary polygonal element is proposed for thin/thick plates modelled by Reissner-Mindlin plate theory. The shear locking problem is alleviated by adopting a shear projection method. To do this, on each edge of the element, temporary variables are introduced, which facilitates approximating the rotations with a quadratic function. These are then written in terms of the nodal unknowns by employing the orthogonality condition. With a few standard patch tests and benchmark examples, it is demonstrated that the proposed element yields accurate results for thin/thick plates and an optimal convergence rate that is in the appropriate norm.