Stability of functionally graded hybrid composite plates

Abstract

This paper presents a formulation of the stability problem for a rectangular composite plate reinforced by two types of fibers, one of them being both stiffer and more expensive than the other. An obvious design solution based on cost containment is to concentrate stiffer and more expensive fibers in the area of the plate where they can provide a maximum benefit to its stability. In the present paper, the stiffer fibers replace a certain fraction of “ordinary” fibers in the layers of the plate oriented along the load direction. Moreover, a distribution of the volume fraction of these fibers across the width of the corresponding layers is nonuniform (piece-wise distribution).

The goal is to maximize the buckling load subject to the constraint on the total cross-sectional area of the stiffer fibers. The solution can be obtained exactly by integrating the equation of equilibrium for each plate region where the stiffnesses are constant and satisfying the continuity and boundary conditions. Another approach, which is employed in this paper, is based on the Galerkin procedure. Numerical examples illustrate a possibility of a significant enhancement of the buckling load using functionally graded hybrid composite plates.