摘要
针对广义周期多尺度点阵结构的高精度分析计算需求,提出了一种高阶渐近展开分析改进方法。该方法首先通过映射变换,将广义周期点阵单胞微结构均匀化问题转换为正方形单胞微结构的经典周期均匀化问题,再通过能量法计算单胞的等效性能,进一步采用有限元方法实现位移场、应变场及应力场的高阶渐近展开分析计算。通过典型数值算例,分析比较了高阶渐近展开分析方法的计算精度。计算结果表明,该方法对于静力学、动力学固有频率等问题均具有良好的计算精度,为广义周期点阵结构的高性能轻量化结构设计提供了有效支撑。
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.
作者
徐仕杰
张卫红
XU Shijie;ZHANG Weihong(School of Mechanical Engineering,Northwestern Polytechnical University,Xi'an 710072,China;TaiHang National Laboratory,Chengdu 610200,China)
出处
《航空学报》
北大核心
2025年第21期70-87,共18页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(12032018,12220101002)。
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
generalized periodic lattice structures
multi-scale analysis
homogenization
asymptotic expansion analysis
mapping method
high-order approximation
