力学超结构设计方法研究进展  

A Review of Design Methods for Mechanical Metastructures

作　　者：姚谦 杨钊[1,2] 王昕[2] 翟智[1] 李振[2] 耿新宇 李秉洋 王鹏飞 YAO Qian;YANG Zhao;WANG Xin;ZHAI Zhi;LI Zhen;GENG Xinyu;LI Bingyang;WANG Pengfei(Space Intelligent Manufacturing Research Center,Xi’an Jiaotong University,Xi’an 710049,P.R.China;Advanced Materials and Energy Center,China Academy of Aerospace Science and Innovation,Beijing 100088,P.R.China)

机构地区：[1]西安交通大学空间智能制造研究中心,西安710049 [2]中国航天科技创新研究院先进材料与能源研究中心,北京100088

出　　处：《应用数学和力学》2024年第8期974-1000,共27页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(U22B2013,12402407);北京市科技新星项目(20230484287)。

摘　　要：力学超结构是具有超常力学性能的人工设计结构,其独特属性主要来自特殊设计的代表性单元的拓扑结构,其数学基础、超常特性、工程制造、多功能集成与应用近年来受到广泛关注.为优化力学超结构设计流程、确定未来趋势与潜在跨学科创新,该文聚焦力学超结构基本设计理念与研究进展,探讨了优化方向.首先,按照正向设计与逆向设计概念针对力学超结构设计方法进行分类;其次,针对正向设计分类型探讨周期性超结构、表面缺陷超结构与数学模型启发超结构设计方法的设计原理、适用领域与优化方向,针对逆向设计分析了各类优化算法与学习算法近年在力学超结构领域取得的进展与存在的问题;最后,对开放性问题与未来挑战进行了总结.Mechanical metastructures have superior mechanical properties coming from the topology of special⁃ly designed representative elements,and have attracted wide attention due to their mathematical basis,super⁃normal features and broad applications.To optimize the design procedure,grasp the future trends and promote the interdisciplinary innovation,the fundamental design concepts and research advancements of mechanical metastructures were reviewed.First,the design methods for mechanical metastructures were classified based on the forward and inverse design concepts.Second,within the forward design category,the principles,appli⁃cable fields,and optimization directions of periodic superstructures,surface defect superstructures,and math⁃ematical modelbased superstructures were discussed.For the reverse design category,the progresses and existing problems in the application of optimization algorithms and learning algorithms in the field of mechanical metastructures were analyzed,with future challenges and open issues concluded.

关 键 词：力学超结构 点阵结构 折纸 极小曲面 逆向设计 机器学习 

分 类 号：O347[理学—固体力学]