Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method

The collocation multiquadric radial basis functions are used to analyze static deformations of a simply supported functionally graded plate modeled by a third-order shear deformation theory. The plate material is made of two isotropic constituents with their volume fractions varying only in the thickness direction. The macroscopic response of the plate is taken to be isotropic and the effective properties of the composite are derived either by the rule of mixtures or by the Mori-Tanaka scheme. Effects of aspect ratio of the plate and the volume fractions of the constituents on the centroidal deflection are scrutinized. When Poisson's ratios of the two constituents are nearly equal, then the two homogenization techniques give results that are close to each other. However, for widely varying Poisson's ratios of the two constituents, the two homogenization schemes give quite different results. The computed results are found to agree well with the solution of the problem by an alternative meshless method.