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To resist external pressure, stiffened spherical domes have been widely used in underwater vehicles. In traditional design of these thin-walled structures, uniform stiffeners are usually utilized and overly conservative safety factor method is employed to envelop the multi-source uncertainties mainly caused by manufacturing. In this study, a concept of non-uniformly stiffened spherical dome (NUSPD) is developed to improve the structural buckling capacity. Furthermore, an efficient reliability-based design optimization (RBDO) framework is established for NUSPD, which includes a deterministic optimization loop to fix the stiffener layout, and subsequently followed by a RBDO loop to determine the detailed stiffener dimensions and decrease the structural weight under geometric and material property uncertainties. Since the RBDO of stiffened spherical domes is very complex, an improved enhanced chaos control method together with surrogate model is proposed to improve the convergence rate. Finally, the efficiency of the proposed RBDO framework is demonstrated by the NUSPD example. [ABSTRACT FROM AUTHOR]

Abstract Reliability-based design optimization (RBDO) is a powerful tool to handle the influence of various uncertainties during optimization. However, unbearable computation cost is one of the largest barriers for its application, especially for the finite element method (FEM)-based RBDO. In this paper, an efficient and accurate RBDO framework is established based on isogeometric analysis (IGA) for complex engineering problems. Furthermore, an enhanced step length adjustment (ESLA) iterative algorithm and a second-order reliability method-based stepped-up sequential optimization and reliability assessment approach (SSORA-SORM) are proposed to boost the efficiency of RBDO. According to the situation of iteration process, the step length of search the most probable target point can be adaptively updated by the proposed criterion to improve the robustness in ESLA. In the proposed framework, the analytical first-order sensitivity is derived based on IGA in the optimization process to substitute the time-consuming finite difference method. The robustness, accuracy and efficiency of proposed methods are verified via several numerical benchmarks. Besides, three complex IGA-based examples demonstrate that the proposed method is able to save much computational cost without losing accuracy, which is inherently suitable for the RBDO of complex engineering problems. [ABSTRACT FROM AUTHOR]

• An augmented step size adjustment (ASSA) method is proposed to boost the iterative process of reliability analysis. • A fire-new strategy is established to identify the oscillation during iterative process and define the iterative step size. • The ASSA method is proven to achieve a well efficient and robust performance for RBDO problems. Heavy computational burden has been one of the largest barriers to the application of reliability-based design optimization (RBDO) in real-world structures. The key difficulty of RBDO lies in how to perform reliability analysis efficiently and robustly. In performance measure approach (PMA)-based RBDO, the reliability analysis process searches for the minimum performance target point (MPTP) with the target reliability index in standard normal space. Many methods have been proposed to improve the efficiency and robustness of the PMA. However, these methods may face the convergence problem for highly nonlinear constraint functions; or high computational cost for weakly nonlinear ones. More importantly, most existing methods are very sensitive to the selection of algorithm parameters. In this paper, an augmented step size adjustment (ASSA) method is proposed to boost the iterative process in terms of both efficiency and robustness. According to the relative positions of the direction vector and negative gradient direction and the angle between them at each iterative point, a fire-new strategy is established to identify the oscillation during the iterative process and define the iterative step size. Seven inverse reliability analysis problems and three RBDO benchmarks are used to validate the performance of the ASSA method. The results indicate that the ASSA method has wide applicability for nonlinear constraint functions and achieves efficient and robust performance. Furthermore, the results demonstrate that the ASSA method can be regarded as a reliable and effective method for addressing PMA-based RBDO problems. [ABSTRACT FROM AUTHOR]

• An efficient bi-stage RBDO framework of composite structures is established. • Lamination parameters are used to obtain an approximated optimal layer number. • IGA is utilized for buckling analysis and derivation of analytical sensitivity. Composite variable-stiffness (VS) panels with curvilinear fiber paths are very promising for aerospace structures. Due to the inherent complexity of VS laminates, buckling analysis and design optimization are extremely time-consuming and challenging, especially when uncertainties are considered, i.e. reliability-based design optimization (RBDO). In this study, an efficient bi-stage RBDO framework via isogeometric analysis (IGA) is established to release the tremendous computational burden. In Stage I, the layer thickness and lamination parameters are used as design variables to obtain an approximated layer number, which greatly reduces the design variable size. In Stage II, intermediate density variables are introduced, and IGA is employed for the buckling analysis and derivation of the analytical sensitivity. Furthermore, the augmented step size adjustment (ASSA) algorithm is used to enhance the efficiency and robustness of the RBDO process. Numerical results of VS panels are used to validate the performance of the proposed RBDO framework. The optimal results indicate that the proposed framework can find the optimal lightweight design that satisfies the manufacturing constraints in an efficient and accurate manner. [ABSTRACT FROM AUTHOR]