Bending Solution for Thick Plates with Quadrangular Boundary

Abstract

A numerical solution technique, which is based on the differential quadrature method, is presented for investigation of the static characteristics of thick Reissner/Mindlin plates on quandrangular planforms. The basic idea of the solution technique is: (1) to map an arbitrary straight-sided quadrilateral physical domain onto a unit-square computational domain by using the subparametric mapping concept; (2) to transform, with this geometric mapping, the governing differential equations and boundary conditions of the plate from the physical domain into the computational domain; and (3) to discretize, by using the differential quadrature procedure, the transformed system equations into a set of linear algebraic equations. Detailed mathematical formulations of this solution technique for the bending analysis of arbitrary quadrilateral Reissner/Mindlin plates with straight sides are described. The bending solutions are calculated for uniformly loaded plates with trapezoidal and irregular quadrilateral boundaries. These example problems simply demonstrate the convergence, accuracy, versatility, and simplicity of the analysis method.