Multiple gradations coupling effects in the bending of thin elastic FGM plates

Abstract

In this paper we present the derivation of the governing equations and boundary conditions for thin elastic plates with functionally graded Young's modulus and thickness of the plate. The derivation is based on the assumptions of the Kirchhoff-Love theory for bending of thin elastic plates. The combination of the transversal gradation of Young's modulus with in-plane gradations of Young's modulus and/or thickness of the plate yields the multiple gradations coupling effects. The main manifestation of these effects is a finite deflection of the plate even if it is subjected only to in-plane loading on the boundary edge. Of course the response of the plate is affected by coupling between the in-plane deformation and bending modes. In numerical simulations of the multiple gradations coupling effects, the meshless strong formulation with MLS (Moving Least Squares) approximation of field variables are employed for solution of formulated boundary value problems. Several numerical results are presented for illustration of the multiple gradations coupling effects in bending of thin elastic FGM (Functionally Graded Material) plates.

Vibration of thin elastic FGM plates with multi-gradation effects

“…It has been shown that the transversal gradation of the Young's modulus and/or mass density yields coupling between the bending and in-plane deformation modes in plates subjected to transversal loading. Moreover, it has been shown [6] that the combined gradation of material coefficients in the transversal and in-plane directions into multi-gradation coupling effects in plates subjected to stationary transversal and/or tension loadings. The main goal of this paper is to study the multi-gradation coupling effects in plates subjected to transient tension loads.…”