A polygonal finite element method for plate analysis

A Reissner-Mindlin plate formulation on arbitrary polygonal meshes is proposed for plate analysis. We consider four barycentric shape function types named Wachspress, mean-value, Laplace and piecewise-linear and show its properties in numerical computation for Reissner-Mindlin plate problems. We then generalize an assumed strain field along sides of polygons under the enforcement of the Timoshenko's beam assumption. The present approach is numerically verified by the bending patch test. It offers a general yet simple form for Reissner-Mindlin plate elements that is not only implementable for arbitrary polygonal meshes but also avoids transverse shear locking phenomenon at thin plate limit. The performance of the proposed elements is found through numerical examples. Our key contribution to this work is that the present formulation is established in a compact (or unified) form which is valid for triangular, quadrilateral and arbitrary polygonal meshes.