航空学报2025，Vol.46Issue(21)：70-87,18.DOI:10.7527/S1000-6893.2025.32386
广义周期点阵结构的高阶渐近展开分析方法
A high-order asymptotic expansion analysis method for generalized periodic lattice structures
摘要
Abstract
This paper proposes a novel high-order asymptotic expansion analysis method for generalized periodic lat-tice structures,aimed at accurately predicting their physical and mechanical behaviors and equivalent performances.The proposed method converts the homogenization problem of generalized periodic lattice structures into the classical two-scale homogenization problem for a cubic unit cell,thereby elucidating the intrinsic mapping mechanisms of the generalized two-scale homogenization approach.This conversion clarifies the fundamental properties of the equivalent performance of generalized periodic two-scale homogenization,substantially reducing the computational and program-ming complexities involved.By employing typical numerical examples,this paper compares the outcomes from the proposed mapping method with those derived from classical periodic two-scale homogenization and fine-scale finite el-ement methods.The results affirm the universality and effectiveness of the proposed method,which exhibits high computational precision for addressing both static and dynamic issues,such as natural frequency calculations,thus providing strong theoretical support and practical pathways for designing high-performance,lightweight structures in generalized periodic lattice configurations.关键词
广义周期点阵结构/多尺度分析/均匀化/渐近展开分析/映射方法/高阶近似Key words
generalized periodic lattice structures/multi-scale analysis/homogenization/asymptotic expansion analysis/mapping method/high-order approximation分类
航空航天引用本文复制引用
徐仕杰,张卫红..广义周期点阵结构的高阶渐近展开分析方法[J].航空学报,2025,46(21):70-87,18.基金项目
国家自然科学基金(12032018,12220101002) National Natural Science Foundation of China(12032018,12220101002) （12032018,12220101002）
