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This paper presents a static analysis of functionally graded (FG) single and sandwich plates using Carrera Unified Formulation with five new displacement fields of the non-polynomial form. In particular, trigonometric, exponential and hyperbolic displacement fields are employed. The simply supported FG single and sandwich plates are subjected to a bi-sinusoidal load. The governing equations for the static bending analysis are obtained employing the Principal of Virtual Displacement (PVD) under CUF and solved using Navier type solutions. The results show that non-polynomial thickness functions are accurate although, in a few cases, the influence of some non-polynomial terms may be detrimental.

In this study, two dimensional (2D) and quasi three-dimensional (quasi-3D) shear deformation theories are presented for static and free vibration analysis of single-layer functionally graded (FG) plates using a new hyperbolic shape function. The material of the plate is inhomogeneous and the material properties assumed to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The fundamental governing equations which take into account the effects of both transverse shear and normal stresses are derived through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. In-plane stress components have been obtained by the constitutive equations of composite plates. The transverse stress components have been obtained by integrating the three-dimensional stress equilibrium equations in the thickness direction of the plate. The accuracy of the present method is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature. © 2015 Elsevier Ltd. All rights reserved.