Optimum design of composite laminates for maximum buckling load capacity using simulated annealing Ozgur Erdal, Fazil O. Sonmez * Department of Mechanical Engineering, Bogazici University, Istanbul, Bebek 34342, Turkey Available online 11 November 2004 Abstract This paper presents a method to find globally optimum designs for two-dimensional composite structures subject to given in- plane static loads for which the critical failure mode is buckling. The aim is to maximize the buckling load capacity of laminated composites. For this purpose an improved version of simulated annealing algorithm, which is direct simulated annealing (DSA), was utilized. Fiber orientation in each layer was taken as a design variable. A computer code was developed, and results were obtained for several load cases. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Buckling strength optimization; Direct simulated annealing; Composite laminates; Optimal design 1. Introduction Composite materials are mostly used in applications where their superior stiffness-to-weight or strength-to- weightratiosarecritical.Asafurtheradvantage,configu- rationofalaminate,i.e.fiberorientation,plythickness, stacking sequence, reinforcement geometry (continuous fibers, particulates, etc.), volume fraction of reinforce- ment,canbetailoredtoreduceitsweightwithoutcom- promising its performance, or improve the performance without increasing its weight. This can be achieved throughaprocessofdesignoptimization. Optimization provides the engineers with a tool that is essential in finding the best design among countless number of designs. Design optimization of composite structures was observed to be a global optimization problem,withmultiplelocaloptimaandcomplexdesign space. A deterministic algorithm, in which a monotoni- cally decreasing value of an objective function is iteratively created, may stuck into any local optimum point rather than globally optimum one depending on the starting point. Therefore, its success depends on thechoiceofinitialdesign.Theusualapproachistoem- ploy the algorithm many times starting from different configurationswiththehopethatoneoftheinitialposi- tions be sufficiently close to the globally optimum con- figuration, and then to choose the lowest value as the globally optimum solution. Another disadvantage is that if the starting point is outside the feasible region, the algorithm may converge to a local optimum within the infeasible domain. Inordertofindtheabsoluteoptimumofanobjective functionwithoutbeingsensitivetothestartingposition, a global optimization method has to be employed in structural optimization problems. Stochastic optimiza- tiontechniquesarequitesuitableinthisrespect.Among theiradvantages,theyarenotsensitivetostartingpoint, they can search a large solution space, and they can es- cape local optimum points because they allow occa- sional uphill moves. The genetic algorithm (GA) and the simulated annealing algorithm (SA) are two of the most popular stochastic optimization techniques. 0263-8223/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.09.008 * Corresponding author. Tel.: +90 212 359 7196; fax: +90 212 287 2456. E-mail address: sonmezfa@boun.edu.tr (F.O. Sonmez). Composite Structures 71 (2005) 45–52 www.elsevier.com/locate/compstruct