Optimum design of perforated symmetric laminates using evolutionary algorithm

Abstract

Here, analytical studies have been carried out to determine the optimal values of effective parameters on the stress concentration factor around a cutout using genetic algorithm. Optimum designs of single lamina as well as symmetric laminates with 4, 8 and 12 layers of graphite/epoxy and glass/epoxy plates containing a circular cutout with various sizes are presented. The work focuses on extending the analytical solution given by Greszczuk to determine the stress distribution in multilayered composite plates subjected to arbitrary in-plane loadings. This is achieved by introducing an arbitrary oriented uniaxial, biaxial and shear loading conditions into Greszczuk solution. In order to mimic as much as possible the real structural behavior, the finite-width correction factor given by Tan is used. Effective parameters on stress distribution around the circular cutout in composite plates considered as design variables include: load angle, fiber orientation, cutout size and stacking sequence of the laminate. The objective function in this study is the minimization of maximum stress concentration around the cutout which is calculated by the present analytical solution. The first ply failure load predicted using Tsai–Wu criterion is maximized for both single lamina and symmetric laminates. Also, the weight of the plates is minimized by increasing the hole size to width ratio. The results obtained by the present analytical solution compare favorably with those obtained using complex variable method. For laminated plate subjected to shear loading, the stress concentration factor decreased drastically by 48.79% compared to a single lamina. The failure load is also increased in most of the loading cases. The results also showed that the genetic algorithm code converges rapidly in most of the cases. The accuracy, quickness, low computational cost and the simplicity of the present solution encourage the designers to use it in practical applications.