基于图论方法与优化算法的六折痕折纸结构构型研究  

Research on origami patterns for six-fold origami structures using graph theory and optimization algorithms

作　　者：严嘉怡 李佳强 陈耀[1,2] 冯健[1,2] YAN Jiayi;LI Jiaqiang;CHEN Yao;FENG Jian(Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education,Southeast University,Nanjing 211189,China;National Prestress Engineering Research Center,Southeast University,Nanjing 211189,China)

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,江苏南京211189 [2]东南大学国家预应力工程技术研究中心,江苏南京211189

出　　处：《建筑结构学报》2022年第9期277-285,共9页Journal of Building Structures

基　　金：国家自然科学基金项目(51978150,52050410334)。

摘　　要：近年来,折纸结构快速发展并成功应用于诸多领域,但其仍存在折纸新构型难以构建、构型与折展运动难以协调等难题。为了研发多折痕折纸结构,考虑折纸构型的规整性及可折叠性,基于图论方法描述折纸折痕构型,建立折纸顶点的几何约束方程组,综合采用图解法及优化方法,求解单元内部可平折点,得到一系列基于不同对称单元的六折痕折纸结构构型。研究表明,该折痕设计方法精确可行,且具有并行性,能求得给定单元形状的所有内部可平折点。该折痕设计方法适用于任意边界条件的六折痕折纸结构,可为折纸结构创新与应用发挥积极作用。Recent years, origami structures develope rapidly and have been successfully applied in various engineering fields. However, there are still some fundamental scientific problems to be solved such as difficult construction of new origami patterns and difficult coordination between configurations and folding motions. In order to explore multi-fold origami structure, the origami crease configuration is described based on the graph theory method considering the regularity and foldability of the origami configuration, and the geometric constraint equations of origami vertices are established. Through flat foldability of each vertex, nodal coordinates of the inner points of basic units are evaluated using graphic and optimization methods. A series of novel six-fold origami structures based on different symmetrical units are proposed. The numerical results show that the proposed origami design method is not only accurate and feasible, but also parallel. All interior points of a given boundary shape can be effectively obtained to satisfy the flat-foldability of six-fold origami. The presented method is suitable for six-fold origami structures with arbitrary boundary conditions. It can play a positive role in design and engineering applications of origami structures.

关 键 词：Waterbomb折纸 折痕模式 对称 优化算法 平面可折叠 

分 类 号：TU357[建筑科学—结构工程]