折纸结构和折纸超材料动力学研究进展

方虹斌; 吴海平; 刘作林; 张琦炜; 徐鉴

doi:10.6052/0459-1879-21-478

折纸结构和折纸超材料动力学研究进展

doi: 10.6052/0459-1879-21-478

方虹斌^*,,
吴海平^*,
刘作林^{*, †},
张琦炜^†,
徐鉴^†,

*.
复旦大学智能机器人研究院, 上海 200433
†.
同济大学航空航天与力学学院, 上海 200092

基金项目: 国家重点研发计划“智能机器人”重点专项(2020YFB1312900), 国家自然科学基金(11932015, 11902078)和上海市“科技创新行动计划”启明星(20QA1400800)资助项目

详细信息

作者简介:
徐鉴, 教授, 主要研究方向: 非线性动力学与控制、时滞系统动力学、机器人动力学. E-mail: xujian@tongji.edu.cn

中图分类号: O313
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-16
- 录用日期: 2021-11-29
- 网络出版日期: 2021-12-02
- 刊出日期: 2022-01-05

ADVANCES IN THE DYNAMICS OF ORIGAMI STRUCTURES AND ORIGAMI METAMATERIALS

Fang Hongbin^*
,,
Wu Haiping^*,
Liu Zuolin^{*, †},
Zhang Qiwei^†,
Xu Jian^{†
,}

*.
Institute of AI and Robotics, Fudan University, Shanghai 200433, China
†.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

摘要

摘要: 折纸结构和折纸超材料由于其无穷的设计空间, 突出的变形状、变大小、变拓扑特性, 以及由折叠诱发的超常规力学特性, 在最近几年迅速成为数学、物理和工程学科的研究前沿和热点. 折纸结构和折纸超材料在航天、医疗、材料、机器人等众多工程领域具有广泛的应用前景, 其典型的代表包括大型空间可展开结构、自折叠可重构机器人、微型可折叠器械等. 随着应用范围的不断扩大, 折纸结构和折纸超材料的动力学问题日益突出, 不仅涉及其动力学建模和参数辨识, 还包括动力学机制分析与实验测试. 折纸结构复杂的空间几何关系、丰富的变形模式、折叠诱发的全局强非线性本构关系等给动力学研究带来了很多新挑战和新机遇. 本文首先阐述了折纸结构和折纸超材料的研究背景和意义, 并简要概述了折纸的基本定义、假设和分类, 以及折纸结构和折纸超材料的几何设计、静力学和运动学特性. 随后, 本文系统回顾了折纸结构和折纸超材料动力学研究中相关问题的最新进展, 包括: (1) 动力学建模及参数辨识方法; (2) 动力学理论、有限元和实验分析手段; (3) 折叠诱发的动力学行为, 包括双稳态和多稳态动力学行为、瞬态动力学行为和波传播动力学行为等; (4) 典型动力学应用. 本文最后提出了折纸结构和折纸超材料动力学研究中若干值得关注的问题.
- 折纸结构 /
- 折纸超材料 /
- 动力学建模 /
- 折叠动力学 /
- 多稳态动力学 /
- 瞬态动力学 /
- 波动力学
Abstract: Recently, due to the infinite design space, outstanding capability in changing shape, dimension, and topology, as well as the folding-induced extraordinary mechanical properties, origami structures and origami metamaterials have rapidly become the research frontiers and hot spots in the fields of mathematics, physics, and engineering. Origami structures and origami metamaterials have extensive application prospects in various fields, including aerospace, medical, and robotic engineering. Typical examples are the large-scale deployable aerospace structures, reconfigurable self-folding robots, and micro-scale foldable devices. As the scope of engineering applications continues to expand, the dynamics of origami structures and origami metamaterials become increasingly prominent, which not only involves dynamic modeling and parameter identification but also relates to the dynamic mechanism analyses and experimental tests. The origami dynamics research is facing many new challenges and opportunities brought by the complex spatial geometric relations, the rich deformation modes, and the folding-induced global strong nonlinear constitutive profiles. In this review, the research background and significance of origami structures and origami metamaterials are firstly surveyed, followed by a brief introduction to the fundamental definitions, assumptions, and categorization of origami. The geometric design, kinematic and static properties of the origami structures and origami metamaterials are also summarized in brief. Afterward, the recent research progress on the dynamics of origami structures and origami metamaterials are systematically reviewed, from the following aspects: (1) dynamic modeling and parameter identification methods; (2) theoretical, finite element, and experimental approaches for dynamic analysis; (3) folding-induced dynamic behaviors, including bi-stable and multi-stable dynamic behaviors, transient dynamic behaviors, and wave propagation dynamic behaviors, etc.; (4) typical dynamic applications. Finally, several open problems are addressed for future studies.
- origami structure /
- origami metamaterial /
- dynamic modeling /
- folding dynamics /
- multi-stable dynamics /
- transient dynamics /
- wave dynamics

HTML全文

图 1 2014—2021年间在顶级期刊上发表的以Origami为主题的论文

Figure 1. Papers on origami published in top journals during 2014—2021

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图 2 以Origami为主题的研究发展历程分析

Figure 2. Analysis of the development process of origami-themed research

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图 3 常见的折纸结构的折痕图和三维构型

Figure 3. Crease patterns and 3D configurations of classical origami structures

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图 4 折纸结构的超常规运动学和静力学特性^{[23,28,30,83]}

Figure 4. Extraordinary kinematic and mechanical properties of origami structures^{[23,28,30,83]}

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图 5 折纸结构和折纸超材料空间桁架等效动力学模型^{[33,39,90-92]}

Figure 5. Truss-based equivalent dynamic models of origami structures and origami metamaterials^{[33,39,90-92]}

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图 6 折纸结构和折纸超材料的非线性弹簧等效动力学模型^{[27,38,87,92]}

Figure 6. Nonlinear spring-based equivalent dynamic models of origami structures and origami metamaterials^{[27,38,87,92]}

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图 7 折纸结构和折纸超材料基于广义哈密顿原理等效建模研究进展^{[34,74,97,99-100,104]}

Figure 7. Equivalent dynamic modeling of origami structures and origami metamaterials based on generalized Hamilton principle^{[34,74,97,99-100,104]}

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图 8 折纸结构和折纸超材料约束及折面接触处理^{[102,106-107,110]}

Figure 8. Constraints and contact of origami structures and origami metamaterials

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9 折纸结构和折纸超材料的参数辨识和数据驱动动力学建模^{[131,140-141]}

9. Parameter identification and data-driven dynamic modeling of origami structures and origami metamaterials^{[131,140-141]}

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图 9 折纸结构和折纸超材料的参数辨识和数据驱动动力学建模^{[131,140-141]} (续)

Figure 9. Parameter identification and data-driven dynamic modeling of origami structures and origami metamaterials^{[131,140-141]} (continued)

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图 10 基于模型的折纸结构动力学分析方法^{[34,36,74,87,94]}

Figure 10. Model-based dynamic analysis methods of origami structures^{[34,36,74,87,94]}

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图 11 基于不同单元类型的折纸结构有限元模型^[30,78,148]

Figure 11. FE models of origami structures based on different types of elements^[30,78,148]

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图 12 折纸结构和折纸超材料动力学实验^{[27,34,39,151]}

Figure 12. Dynamic experiment of origami structures and origami metamaterials^{[27,34,39,151]}

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13 折纸结构和折纸超材料中的双稳态和多稳态动力学行为^[74,96,154]

13. Bistable and multi-stable dynamics of origami structures and origami metamaterials^[74,96,154]

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图 13 折纸结构和折纸超材料中的双稳态和多稳态动力学行为^[74,96,154] (续)

Figure 13. Bistable and multi-stable dynamics of origami structures and origami metamaterials^[74,96,154] (continued)

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图 14 折叠诱发的可编程刚度相关动力学行为^[18,30]

Figure 14. Programmable stiffness-dependent dynamics induced by folding^[18,30]

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图 15 折纸结构和折纸超材料展开瞬态动力学行为^{[33,102,144,159]}

Figure 15. Transient dynamic behaviors of origami structures and origami metamaterials during deployment^{[33,102,144,159]}

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图 16 折纸结构和折纸超材料波动力学行为^{[38-39,92,169]}

Figure 16. Wave dynamic behavior of origami structures and origami metamaterials^{[38-39,92,169]}

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图 17 折纸启发的隔振和能量吸收装置^{[18,62,174,176-178]}

Figure 17. Origami-inspired vibration isolation and energy absorption devices^{[18,62,174,176-178]}

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图 18 折纸启发的空间可展开结构^{[15,64-65,82]}

Figure 18. Origami-inspired space deployable structures^{[15,64-65,82]}

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图 19 折纸启发的波调控装置^[20,169,173]

Figure 19. Origami-inspired wave tailoring devices^[20,169,173]

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图 20 折纸机器人设计和实验原型^{[6,186-187,189-191]}

Figure 20. Designs and prototypes of origami robots^{[6,186-187,189-191]}

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表 1 EFRI-ODISSEI资助的项目^[13]

Table 1. Projects funded by EFRI-ODISSEI^[13]

No.	Project title	Awarded amount	Execution period
1	Multi-field Responsive Origami Structures—Advancing the Emerging Frontier of Active Compliant Mechanisms	$2,124,000	2012.8—2017.7
2	Externally-triggered Origami of Responsive Polymer Sheets	$1,846,358	2012.8—2018.4
3	Uniting Principles of Folding and Compliant Mechanisms to Create Engineering Systems with Unprecedented Performance	$2,400,000	2012.8—2019.7
4	Synthesizing Complex Structures from Programmable Self-folding Active Materials	$2,398,106	2012.8—2019.7
5	Photo-origami	$1,999,377	2012.8—2014.5
6	Programmable Origami for Integration of Self-assembling Systems in Engineered Structures	$2,000,000	2012.8—2018.7
7	Mechanical Meta-materials from Self-folding Polymer Sheets	$2,008,500	2012.8—2017.7
8	Multi-scale origami for Novel Photonics, Energy Conversion	$2,404,013	2012.8—2021.7
9	Photomorphon Networks: Intelligent Shape Changing Structures	$2,409,749	2013.8—2020.7
10	Novel Perpetual Reconfigurable & Multi-band "Origami Folding/Unfolding" Electromagnetic Systems for Cognitive Intelligence Applications	$2,530,890	2013.8—2021.1
11	Origami and Assembly Techniques for Human-tissue-engineering (OATH)	$2,240,328	2013.8—2019.7
12	Foldable Self-replicating DNA Nanostructures for Organization of Functional Nanomaterials and 3D Meta-material Assembly	$2,260,585	2013.8—2019.7
13	Cutting and Pasting—Kirigami in Architecture, Technology, and Science	$2,399,000	2013.8—2020.7
Total funding		$29,020,953
Average funding		$2,232,379

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