Tailoring the optimal load-carrying efficiency of hierarchical stiffened shells by competitive sampling

The hierarchical stiffened shell is a promising aerospace structure configuration with high load-carrying capacity, however, it is challenging to fully explore its optimal load-carrying efficiency. Therefore, a bi-level optimization framework is proposed for hierarchical stiffened shells. In the first level of the optimization framework, a parallel computing numerical-based smeared stiffener method (NSSM) is first introduced for the fast prediction of critical buckling load and mode, by combining the numerical implementation of asymptotic homogenization (NIAH) method with the Rayleigh-Ritz method. Then, a large-scale Latin hypercube sampling (LHS) is performed in the entire design space based on NSSM, and a set of competitive sampling points is collected from the Pareto front of LHS results according to a screening criterion of load-carrying efficiency. In the second level, a surrogate-based optimization using radial basis function (RBF) technique is performed based on generated competitive sampling points with high load-carrying efficiency. Finally, detailed comparisons between optimal results of the proposed optimization method based on the competitive sampling method and the traditional surrogate-based optimization method based on the RBF technique and the LHS sampling method are made from the viewpoint of computational efficiency and global optimizing ability. Spending an approximate computational time, the optimal buckling result of the proposed method increases by 23.7% than that of the traditional method. In order to achieve an approximate global optimization result, the proposed method is able to reduce the computational time by 74.4% than the traditional method. By evaluating competitive sampling results, it can also be concluded that the partial global buckling mode and global buckling mode are most dominant buckling modes for hierarchical stiffened shells with the thick skin and closely-spaced stiffeners, which are prone to obtain a higher load-carrying efficiency.