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Research Papers

Coupling of Creases and Shells

[+] Author and Article Information
Wei Wang

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Xinming Qiu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: qxm@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 27, 2017; final manuscript received November 10, 2017; published online November 28, 2017. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 85(1), 011009 (Nov 28, 2017) (7 pages) Paper No: JAM-17-1537; doi: 10.1115/1.4038470 History: Received September 27, 2017; Revised November 10, 2017

In the analysis of origami structures, the deformation of shells usually couples with the rotation of creases, which leads to the difficulty of solving high-order differential equations. In this study, first the deformation of creased shell is solved analytically. Then, an approximation method named virtual crease method (VCM) is employed, where virtual creases are used to approximate the deformation of shells, and then a complex structure can be simplified into rigid shells connected by real and virtual creases. Then, VCM is used to analyze the large deflection of shells as well as the bistable states of origami structures, such as single creased shell and cell of Miura-Ori. Compared with experiment results, the deformed states given by VCM are quite accurate. Therefore, this generalized method may have potential applications in the analysis of origami structures.

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Topics: Deformation , Shells
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References

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Figures

Grahic Jump Location
Fig. 1

The single creased shell under uniform pulling: (a) Initial profile and deformed profile and (b) the contribution ratio of the crease rotation to total deformation (L=80 mm, φ0=3π/2, k=B/(200h) and α=0.1)

Grahic Jump Location
Fig. 2

The rotation methods: (a) the initial shape, (b) rotate with respect to O1O2 of angle ϕ1, (c) rotate with respect to O1O4 of angle −ϕ2, and (d) rotate with respect to O1O6 of angle ϕ3

Grahic Jump Location
Fig. 3

A circular paper under central compression (r = 24.8 mm, ψ = 75 deg). The results of VCM with (a) both equality and inequality constraints and (b) only equality constraints. The experimental results with the support of (c) an intact cylinder, (d) a defected cylinder, and (e) the convergence of VCM.

Grahic Jump Location
Fig. 4

Möbius strip with b = 5 mm and L = 120 mm: (a) VCM result of nv=36, (b) experiment result, (c) the oblique creases on the Möbius strip, (d) comparison between VCM and experiment

Grahic Jump Location
Fig. 5

The single creased shell under a concentrated force along z direction. (a) The deformation profile and (b) the normalized strain energy versus displacement (φ0=2.22 and kr=kv,ϕ=π/2).

Grahic Jump Location
Fig. 6

The response of the bistability of a creased shell (W = 20 mm, L = 80 mm, φ0=2.22, kr=kv): (a)–(c) VCM results of nv=4,12,28, respectively, and (d) experimental result

Grahic Jump Location
Fig. 7

The bistable state of Miura-ori structure (l1=20 mm, l2=37 mm, α=1.03, β=1.09, kr=kv): (a)–(c) VCM results of nv=4,12,28, respectively, and (d) experimental result

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