Author(s)

V. Sladek, L. Sator, J. Sladek

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.

Keywords

Kirchhoff-Love theory, functional gradations of Young’s modulus, variable thickness, transversal and in-plane gradations, strong formulation, MLS approximations