Stress Analysis and Optimization of a Laminated Composite Plate Weakened by Discontinuity

Abstract

The enormous applications of composite materials in structural, mechanical, automobile and aerospace industries demand a deep understanding of the behavior of materials under various types of loading conditions. Generally, design or service requires holes and cutouts in plate like structural members that affect adversely to the stress field around them. The study of loading conditions, geometry of cut-outs, fiber angle, stacking sequence and ply groups is indispensable as the behavior of the plates strongly depend on them. The present analytic investigations emphasis on the effects of these parameters on the failure strength, stress and moment distribution in orthotropic and symmetric laminated plate weakened by various shaped holes considering in-plane and bending loadings. The generalized solution of both loadings for stress and moment distribution around cut-outs is presented by using the Muskhelishvili’s complex variable formulation. Anisotropy provides a good opportunity to tailor-made the properties of composites. In order to obtain desired properties, optimization of various parameters is needed. The optimization of composites is difficult as it requires complicated derivatives of objective functions, multitudinous design variables, multiple objectives, etc. Stress analysis using Muskhelishvili’s complex variable approach is successfully associated with the optimization through a hybridized genetic algorithm to optimize orthotropic and composite plate weakened by various shaped holes. The optimum design of 4, 8 and 16 layered symmetric laminated plate subjected to various in-plane loadings, is achieved by considering, Tsai-Hill quadratic interaction criterion as an objective function and ply orientations as design variables. The optimum design of carbon/epoxy, kevlar/epoxy, graphite/epoxy, and glass/epoxy orthotropic and symmetric laminated plate weakened by circular, elliptical and polygonal hole is investigated. The behavior of optimally designed composites is also studied.