Carry-over Factors of Levy-type rectangular FGM plates subjected to edge moment or deflection

Abstract

The purpose of this study is to carry out the rotational stiffness, shear stiffness, and carry-over-factors (COFs) of Levy-type rectangular FGM plates on the basis of the classical elastic theory. Three fundamental problems of Levy-type rectangular FGM plates subjected to edge moment or vertical deflection are under consideration. The Poisson's ratios of these FGM plates are assumed to be constant, while their Young's moduli vary continuously throughout the thickness direction with the volume fractions of the constituents obeying sigmoid functions. By using the technique of one-direction Fourier series expanding, the general solutions of FGM rectangular plate with Levy boundary conditions are derived. Then the COFs of these Levy-type fundamental problems are obtained. In addition, by superposing the fundamental solutions, the series-solutions of the S-FGM and S-FGM-coated plates subjected to constant edge moment are also developed and investigated. Results reveal that the obtained COFs of three fundamental problems are independent of Young's modulus, but depend on the aspect ratio. And, although the COFs, rotational and shear stiffnesses of the fundamental problems remain constant as the aspect ratio is small than one, the COFs sharply decay to zero while the rotational and shear stiffnesses rapidly increase as the aspect ratio is approximately greater than one. This event is attributed to that the simply-supported edges significantly affect the COFs for big aspect ratio. Notably, the obtained COFs and stiffnesses reported for the first time are applicable to the technique of moment distribution in solving the continuous FGM plates, and the obtained stiffnesses can serve as entries of the stiffness matrix of FGM plates in numerical calculation.