Stacking sequence optimization of doubly-curved laminated composite shallow shells for maximum fundamental frequency by sequential permutation search algorithm

A sequential permutation search (SPS) optimization algorithm is proposed for the stacking sequence design of doubly-curved laminated composite shallow shells. The SPS algorithm takes advantages of the inherent physical–mechanical features of composite laminates that the outer layers contribute more than the inner layers to bending rigidity and the convexity of lamination parameters. In SPS, the linear and nonlinear sensitive detection techniques are introduced, which detect the sensitive ply orientation at a proper stacking position. By assigning identical ply orientation at respective stacking position, and designing the stacking sequence from the inner to the outer positions sequentially and iteratively using the sensitive ply orientation, the solution will converge to the optimum when no sensitive ply orientation can be detected at any stacking position. In addition, the bending-twisting coupling effects of the laminates are regulated by means of a sign optimization algorithm (SOA) coupled in SPS. The stacking sequences of doubly-curved laminated composite shallow shells exhibit various boundaries and geometries are optimized to maximize the fundamental frequency, and the Rayleigh-Ritz method is developed for vibration analysis. The optimal results are compared with those of layerwise optimization approach and genetic algorithm, demonstrating the robustness and efficiency of the SPS algorithm.