Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

Abstract

A non-standard formulation is applied to find analytical solutions for elastic plates considering shear deformation using a computer-aided approach. Classical formulations of mechanics of elastic body solve each particular problem by obtaining standard differential equations. In contrast, the unified formulation used in this paper, which is described in Tassinari et al. [9], is based on a matrix framework inspired by the finite element method. For this reason, an implementation using mathematical software can be efficiently applied. The aim of this study is to use the proposed computer-aided method to solve analytically the problem and to compare the results with the finite element model predictions. In order to illustrate this approach, the case of the Reissner-Mindlin plate problem with simply support on two opposite edges is investigated (Reissner [6], Mindlin [7]). In addition, the general validity of the method and its applicability to several problems of structural mechanics is discussed. The analytical solution for a particular load case is presented showing the differences between the Reissner-Mindlin solution and the predictions given by the Love-Kirchhoff model (Kirchhoff [4], Love [5]). Finally, the vertical displacement field obtained analytically for different thickness-to-side ratios is compared with finite element method predictions. The results obtained from the proposed analytical method and numerical models presented in this study are comparable.