Stacking Sequence Optimizations Using Fractal Branch and Bound Method for Laminated Composites

Abstract

The present study shows a mechanism of fractal branches of stacking sequences of laminated composites and proposes a novel approach for stacking sequence optimizations named the fractal branch and bound method. Applications of the method are limited to the stacking sequence optimizations that can be computed only by out-of-planes lamination parameters. First, values of the objective function are approximated by response surfaces as a function of the out-of-plane lamination parameters using design of experiments and the least-square-error method, and an optimal set of lamination parameters is obtained. Next, a set of candidates of optimal stacking sequences is collected using a branch-and-bound method near the optimal point of the set of lamination parameters. All of the candidates are examined thoroughly and the actual optimal stacking sequence is obtained. The fractal branch and bound method is applied to the stacking sequence optimization problems for a maximization of buckling load of a simply supported rectangular plate, and the method obtained the exact optimal stacking sequence with very low computational cost.