Stacking sequence optimizations for composite laminates using fractal branch and bound method: Application for supersonic panel flutter problem with buckling load condition

The fractal branch and bound method was developed by the authors for optimization of stacking sequences to maximize buckling load of composite structures. The method demands an approximation of a design space with a response surface comprising quadratic polynomials for pruning fractal branches of stacking sequences. Approximation of the objective function with quadratic polynomials was confirmed for buckling load maximizations and flutter speed limit maximizations using lamination parameters as predictors. In the present study, flutter speed maximization with a constraint of buckling load is employed as an example of stacking sequence optimization by means of the fractal branch and bound method with a strength constraint. The present paper describes the theoretical background of the fractal branch and bound method. Then approximations are performed using quadratic polynomials with lamination parameters as predictors. After that, effectiveness of this method for supersonic panel flutter of composite laminates was investigated using two cases. Results indicate that the method was applied successfully; a practical optimal stacking sequence was obtained using modified response surfaces.