Axisymmetric Bending Analysis of Two Directional Functionally Graded Circular Plates Using Third Order Shear Deformation Theory

Abstract

Bending analysis of a functionally graded circular plate with clamped and simply supported boundary conditions is carried out. Material properties of the plate are assumed to be functionally graded in two directions, namely in the radial direction and through the thickness of the plate, obeying exponential distribution laws. Poisson’s ratio is assumed to be constant throughout the plate. Governing equations of a circular plate with material properties varying only through the thickness of the plate, based on the third order shear deformation theory are employed. In order to carry out the bending analysis of a two directional functionally graded circular plate, the plate is divided into number of annular plates with material properties graded only through the thickness. Material properties of each annular plate are defined by the corresponding exponential grading rule and the radial position of its center, hence these properties are assumed to be constant for each annular plate but different from its adjacent plates. Imposing the overall boundary conditions and compatibility conditions of adjacent annular plates, the governing equations of all annular plates are obtained and solved simultaneously. The analytical results are compared with the results obtained by the first order shear deformation theory and finite element method which are found to be in good agreement.