Applying Differential Transform Method on the Effect of the Elastic Foundation on the out - Plane Displacement of the Functionally Graded Circular Plates

Abstract

In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursive relations and boundary conditions are changed into algebraic equations. Since the problem of plates on elastic foundation have a great practical importance in modern engineering structures and Winkler foundation model is widely used, plate is assumed on Winkler elastic foundation. In this article functionally graded plate is considered in which material properties vary through the thickness direction by power-law distribution. Analysis results of out of plane displacement of plate on elastic foundation under uniform transverse loads are obtained in different terms of foundation stiffness, material properties and boundary conditions. In order to validate the solution technique, results obtained are compared with the results of the finite element method (FEM).