Static and Vibration Analysis of Functionally Graded Plates Using The Simple Higher Order Shear Deformation Theory (S-HSDT)

Abstract

     This paper used the simple higher order shear deformation theory (S-HSDT) to analyse the static and free vibration of simply supported (diaphragm), elastic functionally graded (FG), rectangular, plates. Functionally graded materials (FGMs), although heterogeneous are idealized as continua with their mechanical properties changing smoothly with respect to the spatial coordinates. Poisson’s ratio is assumed to be constant, but their Young’s moduli and densities vary continuously in the thickness direction according to the volume fraction of constituents, which is mathematically modelled as power law function. The equations of motion are obtained using Hamilton’s principle employing S-HSDT. Navier’s solution is used to solve the equations of motion. The effect of variation of material properties in terms of gradation index, the effects of aspect ratios, thickness-to-side ratio on the bending, the stresses and the natural frequencies of FG plates are studied in this article. The numerical results are also compared with results available in the literature to validate theoretical model of the paper.