On accurate analyses of rectangular plates made of functionally graded materials

Abstract

Functionally graded materials (FGMs) are recently developed advanced composite materials and are being widely used in various innovative engineering appliances. In recent years FGMs are gaining considerable importance and finding wide applications in high temperature environments, such as, fusion-based nuclear reactors, chemical plants, aerospace structural applications, etc. A mixture of ceramic and metal or, a combination of different materials is used to make FGMs. New methodologies need to be developed for engineering characterization of FGMs with their increase in applications in various fields, and also to analyse and design structural components, viz., beams, plates and shells made of these advanced materials with reasonably high accuracy and computational efforts. In view of above, an accurate higher order shear and normal deformation plate theory is employed for stress and free vibration analyses of functionally graded (FG) elastic, rectangular, and simply supported (diaphragm) plates in the present study. The theoretical model is based on Taylor’s series expansion of in-plane and transverse displacements in thickness coordinate defining the plate deformations. FGMs are idealized as continua with mechanical properties changing smoothly with respect to spatial coordinates. The material properties of FG plates are assumed to be varying through thickness of plate in a continuous manner. Poisson’s ratios of FG plates are assumed constant, but their Young’s moduli and densities vary continuously in thickness direction according to the volume fraction of constituents which is modelled here as exponential and power law functions. The effect of variation of material properties in terms of its gradation index on deformations, stresses and natural frequency of FG plates are studied.