Stacking sequence optimizations using fractal branch and bound method for laminated composites

The present study shows a mechanism of fractal branches of stacking sequenc es of laminated composites and proposes a novel approach for stacking seque nce optimizations named the fractal branch and bound method. Applications o f 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 o btained. Next, a set of candidates of optimal stacking sequences is collect ed using a branch-and-bound method near the optimal point of the set of lam ination parameters. All of the candidates are examined thoroughly and the a ctual optimal stacking sequence is obtained. The fractal branch and bound m ethod is applied to the stacking sequence optimization problems for a maxim ization of buckling load of a simply supported rectangular plate, and the m ethod obtained the exact optimal stacking sequence with very low computatio nal cost.