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Research Papers

Folding Behavior of a Foldable Prismatic Mast With Kresling Origami Pattern

[+] Author and Article Information
Cai Jianguo

Mem. ASME
Key Laboratory of C and PC Structures
of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Si Pai Lou 2#,
Nanjing 210096, China
e-mails: j.cai@seu.edu.cn;
caijg_ren@hotmail.com

Deng Xiaowei

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

Zhang Yuting

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: 472661724@qq.com

Feng Jian

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: fengjian@seu.edu.cn

Zhou Ya

School of Civil Engineering,
Southeast University,
Nanjing 210096, China;
Wuxi Architectural Design and
Research Institute Co. Ltd.,
Wuxi, Jiangsu 214001, China
e-mail: zhouya5166@126.com

1Corresponding author.

Manuscript received June 29, 2015; final manuscript received October 27, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.

J. Mechanisms Robotics 8(3), 031004 (Mar 07, 2016) (12 pages) Paper No: JMR-15-1160; doi: 10.1115/1.4032098 History: Received June 29, 2015; Revised October 27, 2015

The folding behavior of a prismatic mast based on Kresling origami pattern is studied in this paper. The mast consists of identical triangles with cyclic symmetry. Bar stresses and necessary external nodal loads of the mast during the motion are studied analytically. The results show that the mechanical behaviors are different when the initial height of the mast is different. Then the numerical analysis is used to prove the accuracy of the analytical results. The influence of the geometry and the number of sides of the polygon on the folding behavior of the basic segment is also investigated. The folding process of the mast with multistories was discussed. The effect of the imperfection based on the eigenvalue buckling modes on the folding behavior is also studied. It can be found that when the number of sides of the polygon is small, the imperfection in the axial direction affects the energy seriously by changing the folding sequence of the mast. When the number of sides of the polygon is larger, the imperfection in the horizontal plane has significant effect on the folding pattern, which leads to the sudden change of energy curve.

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Figures

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Fig. 1

Cylinder with Kresling pattern: (a) cylinder, (b) regular polygon A, (c) Helix B, and (d) Helix C

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Fig. 2

Coordinate system of cylinder and parameters defining Polygon A and Helix B: (a) coordinate cylinder and (b) plan view

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Fig. 3

Equilibrium path of one segment: (a) external forces (in the negative direction), (b) nodal equilibrium, and (c) nodal equilibrium in the xy plan

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Fig. 4

Plots of bar stress and nodal vertical forces versus nodal displacements (a) bar stresses and (b) nodal vertical forces

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Fig. 5

Folding process of the model

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Fig. 6

Bar stress during the folding process

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Fig. 7

Force–displacement diagram of one segment

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Fig. 8

Influence of b/a on bar stresses and external nodal load (a) bar a, (b) bar b, (c) bar c, and (d) necessary external load

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Fig. 9

Influence of b/a on energy of the system

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Fig. 10

Influence of n on bar stresses and external nodal load (a) stresses of bar a, (b) stresses of bar b, (c) stresses of bar c, and (d) necessary external load

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Fig. 11

Influence of n on energy of the system

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Fig. 12

The folding process of four-story mast

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Fig. 13

First ten eigenvalue buckling modes when n = 5

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Fig. 14

Effects of imperfections when n = 5

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Fig. 15

First ten eigenvalue buckling modes when n = 6

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Fig. 16

Effects of imperfections when n = 6

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Fig. 17

Effects of imperfections when n = 8

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Fig. 18

First ten eigenvalue buckling modes when n = 9

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Fig. 19

Effects of imperfections when n = 9

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Fig. 20

Folding process of the imperfect mast based on 9th buckling mode

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Fig. 21

Bar stress with different Young’s modulus of bars: (a) E = 2.1 × 105  MPa, (b) E = 2.1 × 104  MPa, and (c) E = 2.1 × 103  MPa

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Fig. 22

Folding process of steel mast

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Fig. 23

Folding process of mast considering local buckling of bars

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