An efficient and simple refined theory for bending and vibration of functionally graded plates

A two-dimensional theory of functionally graded plates is presented using a mixed variational approach. The theory accounts for a displacements field in which the in-plane displacements vary linearly through the plate thickness, while the out-of-plane displacement is a second-degree function of thickness coordinate. The advantages of the present theory are that it contains both the transverse normal strain and stress in complete consistence with the boundary conditions at the top and bottom surfaces of the plates without loss of its simplicity. Therefore, the rationale for the shear correction factor used in such theories is obviated. The bending and free vibration problems of isotropic plates with material properties varying in the thickness direction are solved. Numerical results for frequencies are presented for two-phase graded material with a power-law through the plate thickness variation of the volume fractions of the constituents based on Mori–Tanaka scheme. In addition, numerical results of transverse deflections are obtained for FG simply supported isotropic plates with Young’s modulus varying exponentially through the thickness and constant Poisson’s ratio. The validity of the present theory is investigated by comparing some of the present results with their counterparts obtained due to three-dimensional approaches by Qian et al. and by Kashtalyan. The influence of the transverse normal strain on the bending and vibration of the FG plates is illustrated.