力学学报 ›› 2018, Vol. 50 ›› Issue (3): 467-476.doi: 10.6052/0459-1879-18-031

• 研究综述 • 上一篇    下一篇

折纸及其折痕设计研究综述

李笑, 李明*   

  1. 大连理工大学工程力学系, 工业装备结构分析国家重点实验室,大连 116024
  • 收稿日期:2018-01-30 出版日期:2018-05-15 发布日期:2018-06-11
  • 通讯作者: 李明,副教授,主要研究方向:优化设计、纳米力学、柔性电子. E-mail:mingli@dlut.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11672056).

A REVIEW OF ORIGAMI AND ITS CREASE DESIGN

Li Xiao, Li Ming*   

  1. State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China
  • Received:2018-01-30 Online:2018-05-15 Published:2018-06-11

摘要: 折纸是指不经剪裁和粘接,将二维平面纸张折叠成三维立体的方法,具有设计简单、成形迅速、适用范围广等优点,在可展开式结构、结构组装与自成型等领域有着广阔的应用前景. 本文首先简述了多种典型的新式折纸应用,如屈曲诱导的微尺度三维结构、可折叠太阳能电池板、DNA螺旋组装结构等;根据折纸的曲线折痕数量、相对运动、刚性折叠面、使用纸张数量界定折纸的分类;然后 折痕设计是实现折纸结构的核心问题,着重阐述了折纸的折痕设计方面,包括梳理折痕设计的基本条件,给出若干典型折痕设计如三浦折痕设计、水弹折痕设计、吉村式折痕设计和对角线型折痕设计,介绍典型折痕设计的显著特点及几何条件,将目前折纸折痕设计的创新方法归纳为对经典折痕设计适当改进、形成折痕设计数据库、利用拓扑优化方法、借助成型的汇编算法等;最后,基于当前折纸的研究进展对未来的研究方向进行了展望,其中涉及到可重构折纸结构、四维折纸、多材料折纸和多尺度折纸等.

关键词: 折纸|折痕|几何条件|折叠公理|折痕设计方法|拓扑优化

Abstract: Origami is to fold a two dimensional paper into the three dimensional structure without cutting and adhesion. With the merits of simple design, rapid forming and wide range of applications, origami has the promising applications in the fields of deployable structures, structural assembly and self-forming. Firstly, this paper reviews several typical origami applications, such as buckling-induced microscale three dimensional structures, foldable solar panels and DNA spiral assembled structures; Then, we define the classifications of origami according to different criteria, such as the number of curved creases, relative motion, the assumption of rigid folding surface, the number of used papers. Since the crease design problem is the key issue of origami, we focus on the origami crease design, including summarizing the basic principles of the crease design, addressing several typical crease design samples such as Miura, waterbomb, Yoshimura and diagonal crease designs. Furthermore, we introduce the distinctive features and geometrical relations of the typical crease design. For the recent innovative crease design methods, the improvement of the classic crease design, establishment of the crease design database, use of topology optimization method and the recent crease design algorithms are briefly discussed. Finally, we prospect the future research orientations of origami based on current research progress of origami, including the transformable structures, four-dimension origami, multi-material origami and multi-scale origami.

Key words: origami|crease|geometric relations|folding axioms|crease design method|topology optimization

中图分类号: 

  • O342