Abstract:The lattice structures, due to their characteristics of higher strength-to-weight and stiffness-to-weight ratios, good vibration damping, and strong thermal insulation and energy absorption abilities, have been widely applied in the design of load-bearing components in various fields, such as aerospace and transportation. However, the designs of existing lattice structures are mostly based on the assumption of uniform cross-sections, severely restricting the optimization space for material distribution and failing to meet the urgent demand for extreme lightweight designs. Present researches on variable cross-section lattice structure design mostly rely on the experimental "trial and error" methods, lacking a corresponding sound theoretical design approach. This paper proposes an efficient method for designing the variable cross-section lattice structures based on the grey wolf optimization algorithm. Firstly, an explicit geometric descriptive model of variable cross-section lattices is constructed based on level-set functions to achieve a flexible description of their geometric shapes. Secondly, an energy-based homogenization method is employed to predict the macroscopic equivalent elastic tensor of variable cross-section lattice unit cells, establishing an inherent connection between macroscopic lattice structures and variable cross-section cell configurations. Subsequently, with minimum compliance of lattice structures as the objective function, the allowable material usage amount as the constraint conditions and the geometric descriptive parameters of variable cross-section lattices as design variables, an optimization mathematical model for variable cross-section lattices is constructed. The grey wolf optimization algorithm is then used to efficiently solve the aforementioned model, obtaining an optimized variable cross-section lattice structure. Finally, the correctness and effectiveness of the proposed method are verified through 2D and 3D numerical examples and simulation analyses, comparing the load-bearing capacity with that of lattice structures under the same conditions. The results indicate that the compliance of the optimized variable cross-section lattice structure can be reduced by over 30% compared to lattice structures with uniform cross-sections under the same conditions, demonstrating a superior load-bearing capacity. This research enriches the theoretical design of variable cross-section lattice structures and holds significant application prospects in the field of extreme lightweight design for high-end equipment.