A REFINED SHEAR DEFORMATION PLATE THEORY FOR STATIC AND FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES

Abstract

In thisresearch, an efficient shear deformation plate theory  for a functionally graded  plate  has been investigated by the use of the newfour variable refined plate theory. Unlike any other theory, the number ofunknown functions involved is only four, as against five in case of other sheardeformation theories. The theory account for higher-order variation oftransverse shear strain through the depth of the plate and satisfies the zerotraction boundary conditions on the surfaces of the plate without using shearcorrection factors. Based on the present  higher-order  shear deformation  plate  theory, the  equations  of the  motion  are derived from  Hamilton’s  principal. The plate faces are assumed tohave isotropic, two-constituent material distribution through the thickness,and the modulus of elasticity, Poisson’s ratio of the faces, and thermalexpansion coefficients are assumed to vary according to a power lawdistribution in terms of the volume fractions of the constituents. The validityof the present theory is investigated by comparing some of the present resultswith those of the classical, the first-order and the other higher-ordertheories. The influences played by the transverse shear deformation, aspectratio, side-to-thickness ratio, and volume fraction distribution are studied.Numerical results for deflections and stresses of functionally graded plate areinvestigated.