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张树佰, 丁喆, 黄垲轩, 张严. 基于灰狼优化算法的变截面点阵结构设计及性能优化. 力学学报, 2024, 56(4): 1-11. DOI: 10.6052/0459-1879-23-592
引用本文: 张树佰, 丁喆, 黄垲轩, 张严. 基于灰狼优化算法的变截面点阵结构设计及性能优化. 力学学报, 2024, 56(4): 1-11. DOI: 10.6052/0459-1879-23-592
Zhang Shubai, Ding Zhe, Huang Kaixuan, Zhang Yan. Design and optimization of variable cross-section lattice structure based on grey wolf optimization algorithm. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-11. DOI: 10.6052/0459-1879-23-592
Citation: Zhang Shubai, Ding Zhe, Huang Kaixuan, Zhang Yan. Design and optimization of variable cross-section lattice structure based on grey wolf optimization algorithm. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-11. DOI: 10.6052/0459-1879-23-592

基于灰狼优化算法的变截面点阵结构设计及性能优化

DESIGN AND OPTIMIZATION OF VARIABLE CROSS-SECTION LATTICE STRUCTURE BASED ON GREY WOLF OPTIMIZATION ALGORITHM

  • 摘要: 点阵结构因其比强度高、比刚度高, 减振降噪性好和隔热吸能能力强等特点, 已被广泛应用于航空航天和交通运输等领域主承力零部件设计. 但现有的点阵结构设计大都基于等截面假设开展, 严重制约了材料分布优化的寻优空间, 无法满足质量敏感领域极致轻量化设计的迫切需求. 而目前关于变截面点阵结构设计的研究大都基于实验的“试错式”经验调配模式, 其相应的理论设计方法尚不完善. 文章基于灰狼智能优化算法, 提出了一种高效的变截面点阵结构设计方法. 首先, 基于水平集函数构建变截面点阵的显式几何描述模型, 以实现变截面点阵几何形状的自由描述; 其次, 采用能量均匀化方法预测变截面点阵单胞的宏观等效力学属性, 建立宏观点阵结构与变截面单胞构型间的内在联系; 然后, 以变截面点阵的几何描述参数为设计变量, 材料用量为约束条件, 最小化柔度为目标函数, 构建变截面点阵优化数学模型, 并采用灰狼优化算法实现上述模型的高效求解, 得到性能优化的变截面点阵结构; 最后, 通过二维和三维数值算例和仿真分析共同验证了所提方法的正确性和有效性, 并与相同条件下等截面点阵结构的承载能力进行了比较. 结果表明: 优化后变截面点阵结构的柔度相较于相同条件下的等截面点阵结构可降低30%以上, 具有更优异的承载能力. 研究结果丰富了变截面点阵结构设计理论, 在高端装备极致轻量化设计领域具有重要应用前景.

     

    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.

     

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