On Fast Design of Innovative Hierarchical Stiffened Shells Against Imperfections

Abstract

Inspired by the hierarchical features of some bionics structures like glass sponges, we propose the innovative hierarchical stiffened shell from the point-of-view of increasing the hierarchies of grid-patterns. Differing from the traditional hierarchical stiffened shells, the innovative ones are composed of major and minor stiffeners with diverse grid-patterns. However, its post-buckling analysis and imperfection sensitivity analysis are too time-consuming. Therefore, it is crucial to develop an efficient equivalent model and optimization framework. Since various buckling modes may occur in hierarchical stiffened shells, it is essential to establish a more flexible equivalent strategy than the traditional single equivalent strategy. Firstly, the Numerical-based Smeared Stiffener Method (NSSM) is derived. Based on the NSSM, a reasonable adaptive equivalent strategy is developed from the concept of hierarchy reduction. Its core idea is to self-adaptively decide which hierarchy of the structure should be equivalent according to the critical buckling mode rapidly predicted by NSSM. On basis of the proposed adaptive equivalent strategy, an effective grid-pattern optimization framework is proposed. Firstly, the RBF surrogate model is constructed based on the equivalent model. Then, the inner optimization is performed on the surrogate model using global optimization algorithm. Furthermore, the optimum result is validated with the corresponding exact detailed model simulation, and the relative percentage error is served as a convergence criterion, to decide whether the adding the exact detailed model result into original surrogate model to generate a new one. Until the relative percentage error converges, the entire optimization is finally completed. Finally, representative illustrative examples indicate that one hierarchical stiffened shell with closely-spaced major stiffeners and triangle gird sub-structure is competitive in resisting imperfections.