Effects of in-plane restraints on the stability of laminated composite plates

Abstract

Stability predictions of uniaxially compressed laminates have consisted mainly of solutions based on assumptions of free in-plane edges avoiding consideration of Poisson's effect in the prebuckling stage. The paper considers a practical problem of uniaxial buckling of rectangular, anisotropic laminates with in-plane restrained unloaded edges where a transverse in-plane force due to Poisson's effect is predominant to an extent that induces premature instability and causes significant departure from classical behavior. Two general classes of laminates, namely, (± θ) sym and ( φ 1, φ 2) sym, are studied under various combinations of out-of-plane simple and clamped boundary conditions. A wide variation in Poisson's ratio with respect to the fiber orientation is observed that, in turn, results in dramatic changes in the buckling as well as postbuckling behavior. It is clearly shown that the classical optimal fiber angles become practically meaningless when the effect of in-plane edge restraints is incorporated in the analysis. For the analysis a computerized Ritz method, in conjunction with Gram-Schmidt orthogonal polynomials as coordinate functions, is developed, which is capable of modeling a variety of boundary conditions, viz. simple, clamped, free and their combinations. The paper investigates a little known but practical mode of instability, high-lights the effect of fiber orientation and aspect ratio, explores the possibility of controlling buckling by tailoring laminates to exhibit negative Poisson's ratio and cautions against improper selection of boundary conditions in the design and optimization of composite plates.