中空各向同性点阵结构优化设计方法

doi:10.3901/JME.260255

摘要/Abstract

摘要： 针对中空点阵结构参数化建模困难、各向同性属性优化效率与精度低的问题，提出了一种中空各向同性点阵结构优化设计方法。引入水平集隐式建模方法，构造了基础实心微结构的符号距离函数，通过布尔求差操作建立了中空点阵参数化几何模型。利用均匀化方法计算了微结构的弹性性能，并进一步构建了中空点阵样本数据库和Kriging代理模型，完成了弹性性能的高精高效预测。建立了中空各向同性点阵结构优化数学模型，引入遗传算法进行求解，实现了特定体积分数下微结构各向同性性能的快速优化。优化得到了6种构型的中空各向同性点阵，并通过压缩试验验证了结构的各向同性性能。数值结果表明所提出方法能够有效实现中空点阵结构参数化设计，并且在兼顾计算精度的同时显著降低了各向同性属性优化成本。

关键词: 中空点阵, 各向同性, 优化设计, 隐式建模, 代理模型

Abstract: To achieve parameterized modeling of hollow lattice structures and to overcome the issues of low efficiency and accuracy in optimizing isotropic properties, an optimization design method for hollow isotropic lattice structures is proposed. By introducing the level set implicit modeling method, the signed distance function of the basic solid microstructure is constructed. Then a parameterized geometric model of the hollow lattice is established through Boolean subtraction operations. The elastic properties of the microstructure are calculated using homogenization methods. Whereafter a database of hollow lattice samples and a Kriging surrogate model are constructed to achieve high-precision and efficient prediction of elastic properties. An optimization mathematical model for hollow isotropic lattice structures is established, and a genetic algorithm is introduced to achieving rapid optimization of microstructural isotropic properties at a specific volume fraction. Six types of hollow isotropic lattice configurations are studied and compression tests are conducted, verifying structural isotropic properties. Numerical results demonstrate that the proposed method can effectively realize the parameterized design of hollow lattice structures, and significantly reduce the cost of isotropic property optimization while ensure computational accuracy.

Key words: hollow lattice, isotropic property, optimization design, implicit modeling, surrogate model

中图分类号:

TH11

舒正涛, 赵康, 高亮, 李好. 中空各向同性点阵结构优化设计方法[J]. 机械工程学报, 2026, 62(5): 408-418.

SHU Zhengtao, ZHAO Kang, GAO Liang, LI Hao. Optimization Design Method for Hollow Isotropic Lattice Structures[J]. Journal of Mechanical Engineering, 2026, 62(5): 408-418.

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链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260255

http://www.cjmenet.com.cn/CN/Y2026/V62/I5/408

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