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The surrogate-based optimization of hierarchical stiffened composite shells against buckling is a typical multimodal and multivariables optimization problem. To improve the computational efficiency and global optimizing ability of the surrogate-based optimization of hierarchical stiffened composite shells, an enhanced variance reduction method based on Latinized partially stratified sampling and multifidelity analysis methods is proposed in this paper and then integrated into the surrogate-based optimization framework. In the offline step of the optimization framework, candidate pairing strategies of design variables are generated by Latinized partially stratified sampling and compared by performing priori optimizations based on the low-fidelity analysis method, and the optimal pairing strategy is therefore determined. On the basis of the optimal pairing strategy, the surrogate-based optimization is carried out using the high-fidelity analysis method in the online step. With less computational cost in the offline step, the proposed enhanced variance reduction method overcomes the limitation of Latinized partially stratified sampling that the optimal pairing strategy is not obvious in complex problems. Then, extensive optimization examples are carried out to verify the efficiency and effectiveness of the proposed optimization framework. Given an approximate computational cost, the optimal buckling result of the proposed framework using enhanced variance reduction method increases by 18.2% than that of the traditional framework based on Latin hypercube sampling. In particular, the advantage of enhanced variance reduction method in the space-filling ability is highlighted in comparison to Latin hypercube sampling. When achieving an approximate global optimal solution, the proposed framework reduces the total computational cost by 76.3% than the traditional framework. Finally, the numerical implementation of asymptotic homogenization method is used herein for the accurate prediction of effective stiffness coefficients of the initial design and optimal results. Through comparison, it is concluded that the high axial stiffness and bending stiffness are the main mechanism for the high load-carrying capacity of optimal results. [ABSTRACT FROM AUTHOR]

Abstract 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. Highlights • The highlights should be revised as 'An efficient parallel computing numerical-based smeared stiffener method is proposed. • The proposed competitive sampling method can increase sampling efficiency. • The bi-level buckling optimization framework has excellent global optimizing ability. [ABSTRACT FROM AUTHOR]

Buckling is usually initiated from a local region near the cutout for cylindrical stiffened shells under axial compression, and then the evolution of buckling waves is governed by the combined effects of local and global stiffness, which limit the load-carrying capacity. Therefore, a simultaneous buckling pattern is crucial for improving the structural efficiency. In this study, a multi-step optimization strategy for the integrated design of near and far fields away from cutouts is proposed, and the convergence criterion of buckling optimization is improved as a deformation-based index. The numerical implementation of the asymptotic homogenization method is utilized to construct an efficient finite element model for post-buckling analysis. A 5 m diameter stiffened shell in a launch vehicle demonstrates that the proposed framework can provide a simultaneous buckling design with high structural efficiency in an efficient manner. Both the buckling deformations and stress of the optimum design are more uniform compared to other optimum designs. [ABSTRACT FROM AUTHOR]

Influenced by numerous local features, the post-buckling analysis and optimization for hierarchical stiffened shells suffer from heavy computational costs. By smearing the minor stiffeners based on a novel numerical implementation of asymptotic homogenization (NIAH) method, a novel hybrid model for hierarchical stiffened shells is presented. Then, the high prediction accuracy and efficiency of the hybrid model for post-buckling analysis and imperfection sensitivity analysis are validated. Furthermore, a grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity is established. The illustrative examples indicate that, the hierarchical stiffened shell with candidate sub-structures is more competitive in load-carrying capacity than that with the fixed grid-pattern, and the presence of imperfections would greatly affect the results of grid-pattern optimizations. [ABSTRACT FROM AUTHOR]

As a potential aerospace structural concept, hierarchical stiffened plates under axial compression are characterized by multiple local features, which lead to the buckling analysis and optimization suffering from heavy computational costs, by means of exact Finite Element Method (FEM). Thus, an efficient and simple hybrid framework for the buckling analysis and optimization of hierarchical stiffened plates is presented in this study. Firstly, the skin and minor stiffeners are equivalent to an unstiffened anisotropic plate based on a novel numerical implementation of asymptotic homogenization method (NIAH), which can be easily realized using commercial software as a black box, indicating a strong applicability for rather complicated minor stiffener configurations. Then, the equivalent plate together with major stiffeners can be treated as a hybrid model to be calculated by FEM. Further, a surrogate-based optimization based on this hybrid model is performed. Finally, three illustrative examples are established to demonstrate the effectiveness and simplicity of the proposed framework. [ABSTRACT FROM AUTHOR]

Stiffened shells are widely used in aerospace structures such as launch vehicles and aircraft wings. This paper presents a novel two-scale topology optimization method to design the innovative grid-stiffened pattern for maximizing the critical buckling load of thin-walled cylindrical shells. On the micro-scale, the asymptotic homogenization method is employed to calculate the general stiffness coefficients of the cell. On the macro-scale, the maximum critical buckling load is set as the objective to drive the topology optimization on the micro-scale. Besides, the repeated eigenvalues are considered both in the sensitivity analysis of buckling loads and the optimization solver with a sub-problem based on the Method of Moving Asymptotes (MMA). Through the optimization, we can obtain the optimal configuration of the grid-stiffened cell. In this paper, an illustrative example of the grid-stiffened cylindrical shell for maximizing the critical buckling load is carried out to validate the effectiveness of the proposed optimization method. In comparison to the optimal orthogrid shell, the critical buckling load with the optimal pattern obtained by the proposed optimization method have a dramatically increase of 21.7%. It can be concluded that the proposed method has huge potential to design the configuration of the grid-stiffened cell of cylindrical shells. • A novel two-scale buckling topology optimization framework is established to design the innovative grid-stiffened pattern. • The repeated eigenvalue problem has been taken into consideration with a sub-problem based the Method of Moving Asymptotes. • In comparison to the optimal orthogrid shell, the optimal result obtained achieves a significantly increase of 21.7%. [ABSTRACT FROM AUTHOR]