Improved Fractal Branch and Bound Method for Stacking-Sequence Optimizations of Laminates

In the present study, a mechanism of fractal pattern of feasible laminates in lamination parameter coordinates is discussed in detail, and a new improved stacking-sequence optimization method is proposed for complicated structures that include both in-plane and out-of-plane lamination parameters. The new method employs a branch-and-bound method for the optimizations of stacking sequences. For the estimation of the fractal branch of stacking sequences, the new method requires approximation of the objective function of the optimizations with a quadratic polynomial using both in-plane and out-of-plane lamination parameters. The new method is applied to a stacking-sequence optimization problem of a maximization of buckling load of a hat-type stiffener structure. The method gives successfully optimal stacking sequences in an excellently short CPU time.