Analysis of functionally graded plates based on a variable separation method

Abstract

This work deals with the modeling of plate structures constituted of Functionally Graded Material through a variable separation approach. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x, y and the transverse coordinate z. This choice yields to a nonlinear problem that can be solved by an iterative process. Two 2D and 1D linear problems are solved successively. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used. The number of unknowns is reduced compared to classical LayerWise (LW) approach. Classical numerical tests encountered in the literature are provided to show the accuracy of the present LW method. The plate can be constituted of a FGM layer or combined FGM/orthotropic layers. Different slenderness ratios and anisotropy indexes are also considered. Accurate results with a low computational cost are obtained when compared with reference solutions and models available in literature.

Keywords:

• Functionally graded materials
• LayerWise approach
• separation of variables
• finite element