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.

References

References
1.
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
.10.4305/METU.JFA.2009.2.12
2.
Hagiwara
,
I.
,
2008
, “
From Origami to Origamics
,”
Sci. Jpn. J.
,
5
(
2
) pp.
22
25
.
3.
Guest
,
S. D.
,
1996
, “
Deployable Structures: Concepts and Analysis
,” Ph.D. thesis, Cambridge University, Cambridge.
4.
Gunnar
,
T.
,
2002
, “
Deployable Tensegrity Structures for Space Applications
,” Ph.D. thesis, Royal Institute of Technology Department of Mechanics, Stockholm.
5.
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
.10.1115/1.4024405
6.
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
.10.1016/j.tws.2013.08.001
7.
Miura
,
K.
,
1980
, “
Method of Packaging and Deployment of Large Membranes in Space
,”
Proceedings of 31st Congress of International Astronautics Federation
, Tokyo, Japan, pp.
1
10
, No. IAF-80-A31.
8.
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, Tokyo.
9.
Hunt
,
G. W.
,
Lord
,
G. J.
, and
Peletier
,
M. A.
,
2003
, “
Cylindrical Shell Buckling: A Characterization of Localization and Periodicity
,”
Discrete Contin. Dyn. Syst., Ser. B
,
3
(
4
), pp.
505
518
.
10.
Thompson
,
J. M. T.
, and
Hunt
,
G. W.
,
1984
,
Elastic Instability Phenomena
,
Wiley
,
Chichester
.
11.
Lord
,
G. J.
,
Champneys
,
A. R.
, and
Hunt
,
G. W.
,
1999
, “
Computation of Homoclinic Orbits in Partial Differential Equations: An Application to Cylindrical Shell Buckling
,”
SIAM J. Sci. Comput.
,
21
(
2
), pp.
591
619
.10.1137/S1064827597321647
12.
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
.10.1115/1.2901553
13.
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
.10.1115/1.2901554
14.
Guest
,
S. D.
, and
Pellegrino
,
S.
,
1996
, “
The Folding of Triangulated Cylinders, Part III: Experiments
,”
ASME J. Appl. Mech.
,
63
(
1
), pp.
77
83
.10.1115/1.2787212
15.
Tachi
,
T.
,
2009
, “
One-DOF Cylindrical Deployable Structures With Rigid Quadrilateral Panels
,”
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium
, Valencia.
16.
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
.
17.
Tachi
,
T.
,
2010
, “
Geometric Considerations for the Design of Rigid Origami Structures
,”
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium
, Shanghai.
18.
Schenk
,
M.
,
Kerr
,
S.
,
Smyth
,
A. M.
, and
Guest
,
S. D.
,
2013
, “
Inflatable Cylinders for Deployable Space Structures
,”
Proceedings of the First Conference Transformables
, Sept. 18–20, Seville.
19.
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
.10.2514/1.A32598
20.
Viquerat
,
A.
,
Schenk
,
M.
,
Sanders
,
B.
, and
Lappas
,
V. J.
,
2014
, “
Inflatable Rigidisable Mast For End-of-Life Deorbiting System
,”
European Conference on Spacecraft Structures, Materials and Environmental Testing (SSMET)
, Apr. 1–4, Braunschweig.
21.
Kresling
,
B.
,
1995
, “
Plant “Design”: Mechanical Simulations of Growth Patterns and Bionics
,”
Biomimetics
,
3
(
3
), pp.
105
222
.
22.
Kresling
,
B.
,
2001
, “
Folded Tubes as Compared to Kikko (“Tortoise-Shell”) Bamboo
,”
Origami
,
T.
Hull
, ed.,
A K Peters
, pp.
197
207
.
23.
Kresling
,
B.
,
2008
, “
Natural Twist Buckling in Shells: From the Hawkmoth's Bellows to the Deployable Kresling-Pattern and Cylindrical Miura-ori
,”
Proceedings of the 6th International Conference on Computation of Shell and Spatial Structures
, John F. Abel and J. Robert Cooke, eds., Ithaca.
24.
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
.10.1016/j.ijnonlinmec.2004.08.011
You do not currently have access to this content.