Analysis of orthotropic plates based on three theories by segmentation method

Abstract

The scope of the segmentation method is extended to the solution of orthotropic rectangular plates, simply supported on two opposite edges and with any other boundary conditions on the remaining two edges. Governing first-order ordinary differential equations are derived for each of three theories, Kirchhoff, Reissner-Mindlin, and a higher-order theory. A wide range of problems of plates are solved, and the solutions obtained are compared with three-dimensional (3-D) elasticity solutions wherever available. New results of orthotropic plates with different boundary conditions are presented. It is shown that for geometrically thin plates, solutions from all three plate theories converge to the classical Kirchhoff solution, while for thick plates, solutions from only the higher-order theory are found to be close to the 3-D elasticity solution.