Abstract

This study investigates the folding pattern design and deployment behavior of origami-based foldable conical structures. The geometric analysis is performed to design the six fold line pattern to obtain foldable conical structures. A single-story origami cone, modeled with pin-jointed framework, is selected for the analytical investigation. The axial strains, nodal forces, relative rotation of the fold polygons, and the strain energy during the deployment are obtained analytically. Moreover, the influence of design parameters ($m$ and ${\alpha }_1$) on the deployment behavior of a single story cone is investigated. The results indicate that several fold configurations exhibit a bistable behavior during the motion, and these bistable configurations undergo lesser deformations than other singly stable fold configurations. Then, the folding and deployment process is simulated numerically using FE software to verify the accuracy of the analytical approach. The numerical results are completely consistent with the analytical results. The existence of bistability is verified using the variation of elastic strain energy during the motion. An analytical approach to obtain the bistability points for any conical folding pattern is presented and verified using numerical simulations. The influence of design parameters, materials, and scaling on the bistability point is also investigated. The results show that the bistability is solely a geometrical phenomenon, and scaling does not change the deformation behavior of the cone. Finally, the deployment dynamics of both singly stable and bistable multistory conical structures are discussed, with their potential applications.

摘要

本研究调查了基于折纸的可折叠圆锥结构的折叠图案设计和部署行为。进行几何分析以设计六折线图案以获得可折叠的锥形结构。选择一个单层折纸圆锥体，用销接框架建模，用于分析研究。通过分析获得轴向应变、节点力、折叠多边形的相对旋转以及展开过程中的应变能。此外，设计参数的影响（$米$和${\alpha }_{\mathrm{1个}}$) 对单个故事锥体的部署行为进行了调查。结果表明，几种折叠配置在运动过程中表现出双稳态行为，并且这些双稳态配置比其他单稳定折叠配置经历更小的变形。然后，使用有限元软件对折叠和展开过程进行数值模拟，以验证分析方法的准确性。数值结果与解析结果完全一致。利用运动过程中弹性应变能的变化来验证双稳态的存在。提出了一种获得任何锥形折叠模式双稳态点的分析方法，并使用数值模拟对其进行了验证。还研究了设计参数、材料和缩放比例对双稳态点的影响。结果表明，双稳态仅仅是一种几何现象，缩放不会改变锥体的变形行为。最后，讨论了单稳态和双稳态多层锥形结构的部署动力学及其潜在应用。