Stacking-sequence optimization using fractal branch-and-bound method for unsymmetrical laminates

The fractal branch-and-bound method has been developed by the authors for stacking-sequence optimizations of symmetric and balanced composite laminates comprise of two in-plane and two out-of-plane lamination parameters. Cylindrical structures such as tanks or pipes, however, are usually made from balanced laminates. In the present study, therefore, we focus on the stacking-sequence optimizations of unsymmetrical composite laminates. In the unsymmetrical laminates, nine lamination parameters including three coupling-lamination parameters exist, and its feasible design region of fractal pattern is unrevealed. The paper clarifies the feasible region in which the in-plane, out-of-plane and coupling lamination parameters create fractal patterns of tetrahedrons or tetradecahedrons. Using the fractal patterns of lamination parameters, the improved fractal branch-and-bound method is proposed for unsymmetrical laminates including coupling lamination parameters. This new method is applied to stacking-sequence optimization problems of maximization of buckling load of cylindrical laminated shells. As a result, the method is successfully applied, and a practical optimal stacking sequence is obtained with low computational cost.