Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions

Infinitesimal deformations of a thick functionally graded elastic plate have been analyzed by using the meshless local Petrov-Galerkin (MLPG) method and the higher-order shear and normal deformable plate theory (HOSNDPT). Radial basis functions (RBF) are employed for constructing trial functions, while a spline function is used as the weighting function over a local subdomain. The present method employs a number of randomly located nodes in the domain. It does not require a mesh for either interpolation of the field variables or integration of the weak form and hence is truly meshless. Two types of RBFs, i.e. Multiquadrics (MQ) and Thin Plate Splines (TPS), are used. Effective material moduli of the plate, made of two isotropic constituents with volume contents varying only in the thickness direction, are computed using the Mori-Tanaka homogenization technique. Computed results for a simply supported plate are found to agree well with their analytical solutions. The through-the-thickness distributions of the deflection and stresses in the plate are also presented for three types of boundary conditions: simply supported, clamped and free.