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Research Papers: Design Automation

Bistable Behavior of the Cylindrical Origami Structure With Kresling Pattern

[+] Author and Article Information
Cai Jianguo

Mem. ASME
Key Laboratory of C & PC Structures
of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Si Pai Lou No. 2,
Nanjing 210096, China
e-mail: j.cai@seu.edu.cn

Deng Xiaowei

Department of Structural Engineering,
University of California,
San Diego, CA 92093
e-mail: x8deng@eng.ucsd.edu

Zhou Ya

Wuxi Architectural Design
& Research Institute Co. Ltd,
Wuxi, Jiangsu 214001, China
e-mail: zhouya5166@126.com

Feng Jian

Key Laboratory of
C & PC Structures of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Si Pai Lou No. 2,
Nanjing 210096, China
e-mail: fengjian@seu.edu.cn

Tu Yongming

Department of Civil, Environmental
and Natural Resources Engineering,
Luleå University of Technology,
Luleå SE-971 87, Sweden
e-mail: yongming.tu@ltu.se

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 10, 2014; final manuscript received March 12, 2015; published online April 21, 2015. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 137(6), 061406 (Jun 01, 2015) (8 pages) Paper No: MD-14-1230; doi: 10.1115/1.4030158 History: Received April 10, 2014; Revised March 12, 2015; Online April 21, 2015

The deployment of a cylinder based on origami with Kresling pattern, whose basic mechanisms are formed by the buckling of a thin cylindrical shell under torsional loading, is studied in this paper. The model consists of identical triangular panels with cyclic symmetry and has a small displacement internal inextensional mechanism. First, geometric formulation of the design problem is presented. Then, assuming that the deployment and folding process is uniform, the bistable behavior of the cylinder is discussed. It can be found that, during the deployment, the dimensionless strain energy increases first and then reduces to zero but followed by another sharp increase. Moreover, the limit condition of geometry parameters for the bistable phenomenon is also discussed. Finally, the bistable behavior is also studied by using numerical simulations for simple and more complex case of the cylinder with multistory. The numerical results agree well with the analytical predictions. Therefore, comparisons with finite element predictions have shown that the analytical solutions given in this paper are accurate and have validated the assumptions made in the derivations.

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References

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Figures

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Fig. 1

The construction process and the deployable process

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Fig. 2

Geometric parameters of the flat paper strip

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Fig. 3

The movement between the adjacent elements (a) deployed state and (b) folded state

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Fig. 4

The sides of the regular polygon formed by the upper lines of the paper strip

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Fig. 5

The relation between two regular polygons formed by the upper and lower lines of the paper strip

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Fig. 6

The cylindrical shell during the motion

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Fig. 7

Plots of c/a against b/a

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Fig. 8

Plots of the folding property length ratio c/a versus δ

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Fig. 9

The dimensionless strain energy of unit length during the motion

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Fig. 10

The deployment of one segment (a) the folded configuration and (b) the deployable configuration

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Fig. 11

The energy during the deployment of one segment

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Fig. 12

The folding process

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Fig. 13

The folding process of one segment (a) the initial configuration and (b) the flat configuration

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Fig. 14

The energy during the folding process of one segment

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Fig. 15

The deployment process of the cylinder with four segments

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Fig. 16

The vertical nodal displacement during the deployment

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Fig. 17

The dimensionless element stresses of bar c

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