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In this paper, a thick functionally graded plate based on three-dimensional equations of elasticity and subjected to nonuniform transverse loading is considered. The Young’s modulus of the plate is assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents and the Poisson’s ratio is assumed to be constant. Three-dimensional graded finite element method based on Rayleigh–Ritz energy formulation has been applied to study the static response of the plate. The plate deflection and in-plane stress for different values of the power law exponent, thickness-to-length ratio, and various boundary conditions have been investigated. To verify the presented method and data, the results are compared to published data.

In this paper three dimensional free vibration and transient response of a cylindrical panel made of two directional functionally graded materials (2D-FGMs) based on three dimensional equations of elasticity and subjected to internal impact loading is considered. Material properties vary through both radial and axial directions continuously. The 3D graded finite element method (GFEM) based on Rayleigh-Ritz energy formulation and Newmark direct integration method has been applied to solve the equations in space and time domains. The fundamental normalized natural frequency, time history of displacements and stresses in three directions and velocity of radial stress wave propagation for various values of span angel of cylindrical panel and different power law exponents have been investigated. The present results show that using 2D-FGMs leads to a more flexible design than conventional 1D-FGMs. The GFEM solution have been compared with the results of an FG thick hollow cylinder and an FG curved panel, where a good agreement between them is observed.