Multilevel Optimization Framework for Hierarchical Stiffened Shells Accelerated by Adaptive Equivalent Strategy

In order to improve the post-buckling optimization efficiency of hierarchical stiffened shells, a multilevel optimization framework accelerated by adaptive equivalent strategy is presented in this paper. Firstly, the Numerical-based Smeared Stiffener Method (NSSM) for hierarchical stiffened shells is derived by means of the numerical implementation of asymptotic homogenization (NIAH) method. Based on the NSSM, a reasonable adaptive equivalent strategy for hierarchical stiffened shells 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. Compared with the detailed model, the high prediction accuracy and efficiency of the proposed model is highlighted. On the basis of this adaptive equivalent model, a multilevel optimization framework is then established by decomposing the complex entire optimization process into major-stiffener-level and minor-stiffener-level sub-optimizations, during which Fixed Point Iteration (FPI) is employed to accelerate convergence. Finally, the illustrative examples of the multilevel framework is carried out to demonstrate its efficiency and effectiveness to search for the global optimum result by contrast with the single-level optimization method. Remarkably, the high efficiency and flexibility of the adaptive equivalent strategy is indicated by compared with the single equivalent strategy.