A refined simple first-order shear deformation theory is developed to investigate the static bending and free vibration of advanced composite plates such as functionally graded plates. By introducing the new distribution shape function, the transverse shear strain and shear stress have a parabolic distribution across the thickness of the plates, and they equal zero at the surfaces of the plates. Hence, the new refined theory needs no shear correction factor. The Navier solution is applied to investigate the static bending and free vibration of simply supported advanced composite plates. The proposed theory shows an improvement in calculating the deflections and frequencies of advanced composite plates. The formulation and transformation of the present theory are as simple as the simple first-order shear deformation. The comparisons of deflection, axial stresses, transverse shear stresses, and frequencies of the plates obtained by the proposed theory with published results of different theories are carried out to show the efficiency and accuracy of the new theory. In addition, some discussions on the influence of various parameters such as the power-law index, the slenderness ratio, and the aspect ratio are carried out, which are useful for the design and testing of advanced composite structures.

This paper introduces a comprehensive investigation of bi-directional functionally graded sandwich plates using higher-order shear deformation theory and finite element method for the first time. A special procedure incorporating with a bi-linear four-node quadrilateral element is used to treat the free condition of shear stresses on two surfaces of the sandwich plates. Four types of the bi-directional functionally graded sandwich plates with several thickness ratios of layers are considered, in which the material properties of the layers are assumed to vary in both the thickness and the in-plane directions. The present results are compared with published data in some special cases to demonstrate the convergence and accuracy of the present algorithm. The investigations show that the variation of the material ingredients and properties, the boundary conditions, the thickness ratio of layers play significant roles on the bending, free vibration and buckling behaviors of bi-directional functionally graded sandwich plates.