Research Papers

Folding Behavior of a Foldable Prismatic Mast With Kresling Origami Pattern

[+] Author and Article Information
Cai Jianguo

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;

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Sorguc, A. G. , Hagiwara, I. , and Selcuk, S. A. , 2009, “ Origami in Architecture: A Medium of Inquiry for Design in Architecture,” Metu Jfa, 26(2), pp. 235–247. [CrossRef]
Kwan, A. S. K. , and Pellegrino, S. , 1991, “ The Pantographic Deployable Mast: Design, Structural Performance and Deployment Tests,” Rapidly Assembled Structures, P. S. Bulson , ed., Computational Mechanics Publications, Southampton, UK, pp. 213–224.
You, Z. , and Pellegrino, S. , 1997, “ Cable-Stiffened Pantographic Deployable Structures. Part 2: Mesh Reflector,” AIAA J., 35(8), pp. 1348–1355. [CrossRef]
Guest, S. D. , 1996, “ Deployable Structures: Concepts and Analysis,” Ph.D. thesis, Cambridge University, Cambridge, UK.
Gunnar, T. , 2002, “ Deployable Tensegrity Structures for Space Applications,” Ph.D. thesis, Royal Institute of Technology Department of Mechanics, Stockholm, Sweden.
Hagiwara, I. , 2008, “ From Origami to Origamics,” Sci. Jpn. J., 5(2) pp. 22–25.
Miura, K. , 1980, “ Method of Packaging and Deployment of Large Membranes in Space,” Proceedings of 31st Congress of International Astronautics Federation (IAF-80-A31), Tokyo, Japan, pp. 1–10.
Yoshimura, Y. , 1951, “ On the Mechanism of Buckling of a Circular Cylindrical Shell Under Axial Compression and Bending,” Reports of the Institute of Science and Technology of the University of Tokyo, National Advisory Committee on Aeronautics, Washington, DC, Report No. NACA-TM-1390.
Hunt, G. W. , Lord, G. J. , and Peletier, M. A. , 2003, “ Cylindrical Shell Buckling: A Characterization of Localization and Periodicity,” Discrete Contin. Dyn. Syst. B, 3(4), pp. 505–518. [CrossRef]
Thompson, J. M. T. , and Hunt, G. W. , 1984, Elastic Instability Phenomena, Wiley, Chichester.
Hegedüs, I. , 1986, “ Analysis of Lattice Single Layer Cylindrical Structures,” Space Struct., 2, pp. 87–91.
Friedman, N. , Weiner, M. , Farkas, G. , Hegedüs, I. , and Ibrahimbegovic, A. , 2013, “ On the Snap-Back Behavior of a Self-Deploying Antiprismatic Column During Packing,” Eng. Struct., 50, pp. 74–89. [CrossRef]
Guest, S. D. , and Pellegrino, S. , 1994, “ The Folding of Triangulated Cylinders, Part I: Geometric Considerations,” ASME J. Appl. Mech., 61(4), pp. 773–777. [CrossRef]
Guest, S. D. , and Pellegrino, S. , 1994, “ The Folding of Triangulated Cylinders, Part II: The Folding Process,” ASME J. Appl. Mech., 61(4), pp. 778–783. [CrossRef]
Guest, S. D. , and Pellegrino, S. , 1996, “ The Folding of Triangulated Cylinders, Part III: Experiments,” ASME J. Appl. Mech., 63(1), pp. 77–83. [CrossRef]
Nojima, T. , 2002, “ Modelling of Folding Patterns in Flat Membranes and Cylinder by Origami,” JSME Int. J. Ser. C, 45(1), pp. 364–370. [CrossRef]
Ma, J. , and You, Z. , 2014, “ Energy Absorption of Thin-Walled Square Tubes With a Prefolded Origami Pattern—Part I: Geometry and Numerical Simulation,” ASME J. Appl. Mech., 81(1), p. 011003. [CrossRef]
Ma, J. , and You, Z. , 2013, “ Energy Absorption of Thin-Walled Beams With a Pre-Folded Origami Pattern,” Thin-walled Struct., 73, pp. 198–206. [CrossRef]
Schenk, M. , Kerr, S. , Smyth, A. M. , and Guest, S. D. , 2013, “ Inflatable Cylinders for Deployable Space Structures,” First Conference Transformables, Seville, Spain.
Schenk, M. , Viquerat, A. D. , Seffen, K. A. , and Guest, S. D. , 2014, “ Review of Inflatable Booms for Deployable Space Structures: Packing and Rigidisation,” J. Spacecr. Rockets, 51(3), pp. 762–778. [CrossRef]
Miura, K. , and Tachi, T. , 2010, “ Synthesis of Rigid-Foldable Cylindrical Polyhedral,” Symmetry: Art and Science, International Society for the Interdisciplinary Study of Symmetry, Gmuend, Austria.
Tachi, T. , 2010, “ Geometric Considerations for the Design of Rigid Origami Structures,” International Association for Shell and Spatial Structures (IASS) Symposium, Shanghai, China.
Liu, S. , Lv, W. , Chen, Y. , and Lu, G. , 2014, “ Deployable Prismatic Structures With Origami Patterns,” ASME Paper No. DETC2014-34567.
Kresling, B. , 1995, “ Plant “Design”: Mechanical Simulations of Growth Patterns and Bionics,” Biomimetics, 3(3), pp. 105–222.
Kresling, B. , 2001, “ Folded Tubes as Compared to Kikko (“Tortoise-Shell”) Bamboo,” Origami, T. Hull , ed., AK Peters, Natick, MA, pp. 197–207.
Kresling, B. , 2008, “ Natural Twist Buckling in Shells: From the Hawkmoth’s Bellows to the Deployable Kresling-Pattern and Cylindrical Miura-Ori,” 6th International Conference on Computation of Shell & Spatial Structures (IASS-IACM 2008), Ithaca, NY, May 28–31.
Hunt, G. W. , and Ichiro, A. , 2005, “ Twist Buckling and the Foldable Cylinder: An Exercise in Origami,” Int. J. Non-Linear Mech., 40(6), pp. 833–843. [CrossRef]
Cai, J. G. , Deng, X. W. , Zhou, Y. , Feng, J. , and Tu, Y. M. , 2015, “ Bistable Behavior of the Cylindrical Origami Structure With Kresling Pattern,” ASME J. Mech. Des., 137(6), p. 061404. [CrossRef]
You, Z. , and Cole, N. , 2006, “ Self-Locking Bi-Stable Deployable Booms,” AIAA Paper No. 2006-1685.
Nagase, K. , and Skelton, R. E. , 2014, “ Double-Helix Tensegrity Structures,” AIAA J., 53(4), pp. 847–862. [CrossRef]
Cai, J. G. , Gu, L. M. , Xu, Y. X. , Feng, J. , and Zhang, J. , 2012, “ Nonlinear Stability of a Single-Layer Hybrid Grid Shell,” J. Civil Eng. Manage., 18(5), pp. 752–760. [CrossRef]
Cai, J. G. , Zhou, Y. , Xu, Y. X. , and Feng, J. , 2013, “ Non-Linear Stability Analysis of a Hybrid Barrel Vault Roof,” Steel Compos. Struct., 14(6), pp. 571–586. [CrossRef]
Wang, Y. , Ameer, G. A. , Sheppard, B. J. , and Langer, R. , 2002, “ A Tough Biodegradable Elastomer,” Nat. Biotechnol., 20(6), pp. 602–606. [CrossRef] [PubMed]
Sonnenschein, M. F. , Ginzburg, V. V. , Schiller, K. S. , and Wendt, B. L. , 2013, “ Design, Polymerization, and Properties of High Performance Thermoplastic Polyurethane Elastomers From Seed-Oil Derived Soft Segments,” Polymer, 54(4), pp. 1350–1360. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

Folding process of the model

Grahic Jump Location
Fig. 6

Bar stress during the folding process

Grahic Jump Location
Fig. 7

Force–displacement diagram of one segment

Grahic Jump Location
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

Grahic Jump Location
Fig. 9

Influence of b/a on energy of the system

Grahic Jump Location
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

Grahic Jump Location
Fig. 11

Influence of n on energy of the system

Grahic Jump Location
Fig. 12

The folding process of four-story mast

Grahic Jump Location
Fig. 13

First ten eigenvalue buckling modes when n = 5

Grahic Jump Location
Fig. 14

Effects of imperfections when n = 5

Grahic Jump Location
Fig. 15

First ten eigenvalue buckling modes when n = 6

Grahic Jump Location
Fig. 16

Effects of imperfections when n = 6

Grahic Jump Location
Fig. 17

Effects of imperfections when n = 8

Grahic Jump Location
Fig. 18

First ten eigenvalue buckling modes when n = 9

Grahic Jump Location
Fig. 19

Effects of imperfections when n = 9

Grahic Jump Location
Fig. 20

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 22

Folding process of steel mast

Grahic Jump Location
Fig. 23

Folding process of mast considering local buckling of bars




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In