Improved adaptive growth method of stiffeners for three-dimensional box structures with respect to natural frequencies

Abstract

Adaptive growth method is a structural topology optimization approach based on the growth mechanism of natural biological branching systems, and it has been successfully applied for the static reinforcement of three-dimensional box structures. However, due to the effect of structural characteristics towards natural frequencies, it is difficult for adaptive growth method to effectively grow stiffeners inside three-dimensional box structures considering dynamic performance. And this paper proposes an improved version of adaptive growth method to solve this problem. Firstly, apart from the growth mechanism of natural branching systems in the initial adaptive growth method, the morphology of root tips is introduced into the growth process of internal stiffeners. The thickness of stiffeners during the optimization can be divided into four different zones: initial thickness zone, immediate thickness zone, allowable thickness zone and maturation zone. Then, a material interpolation scheme with different thickness zones is introduced to simultaneously penalize the elastic modulus and density of material of internal stiffeners according to their thicknesses. By applying this bio-inspired method, obstacles of the ground structure in dynamic design of stiffeners in three-dimensional box structures can be effectively eliminated. And notably, the internal stiffeners can successfully grow from “seed lines” and gradually bifurcate or degenerate along the optimal direction to improve the natural frequencies of structures with a clear layout pattern. Finally, the effectiveness and advantages of the proposed method are illustrated by several numerical examples.