薄壁结构多层级并发加筋拓扑优化研究

新一代航天装备的主承力薄壁舱段在追求极致轻量化的同时,还具有更高的刚度和抗屈曲等设计指标.传统结构形式和设计方法难以满足轻质高承载的设计要求.为此,本文提出了一种薄壁结构多层级并发加筋拓扑优化方法,通过构建主层级稀疏加筋和次层级密集点阵增强结构整体和局部力学性能,扩展结构设计空间,有效提升材料利用率.其中,主层级加筋布局通过变密度拓扑优化方法获得,次层级点阵构型通过基于改进的渐进均匀化方法提出的两种设计方法获得,并基于材料插值模型,建立了多层级并发加筋拓扑优化框架,实现在一次拓扑优化求解中同时获得主层级加筋布局和次层级单胞拓扑构型.基于上述方法,本文分别给出了考虑结构刚度和稳定性设计需求的优化算例,并与传统单层级加筋拓扑优化进行了对比.结果 表明,多层级并发加筋方法可以根据承载边界和设计目标寻找优化的结构形式,且在相同质量下,其优化构型相比传统单层级拓扑优化结果表现出更高的承载性能,证明了本方法在薄壁结构设计上的优势.

Concurrent topology optimization of hierarchical stiffened thin-walled structures

With the advanced targets of high stiffness and high stability of new generation aerospace equipment''s main bearing thin-walled structures pursuing extreme lightweight design, the traditional structure form and design methods are difficult to meet design requirements of lightweight and high bearing capacity. Therefore, this paper proposed a hierarchical topology optimization method of stiffened shells. The main-stage sparse stiffener and the secondary-stage dense lattice are employed to reinforce the global and local properties of the structures, expanding the design domain and effectively improving the utilization of materials. To realize this design, the main-stage stiffener is obtained by Simplified Isotropic Material with Penalization method and the secondary-stage lattice is obtained by two proposed methods based on an improved homogenization method, and a hierarchical concurrent topology optimization framework is established based on material interpolation model to obtain the main-stage stiffener layout and secondary-stage lattice configuration simultaneously in a single topology optimization procedure. Based on the proposed method, the paper shows two examples of stiffness and stability design. The results show that the hierarchical concurrent topology optimization method can search for an optimal overall structural form according to the bearing conditions and design targets, display a noteworthy bearing advantage over traditional single-level design under the same mass, and prove the advantage of the proposed method.