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Stiffener Insertion Based Variance in Radial Stiffness of Multi-Concentric Hollow Tubes

Published online by Cambridge University Press:  08 August 2013

Motohiro Sato ,
Hiroyuki Shima  and
S.-J. Park
Motohiro Sato
Affiliation:
Division of Engineering and Policy for Sustainable Environment, Faculty of Engineering, Hokkaido University, Kita-13, Nishi-8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan
Hiroyuki Shima
Affiliation:
Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Takeda, Kofu, Yamanashi 400-8510, Japan
S.-J. Park*
Affiliation:
Department of Urban and Environment Engineering, Incheon National University12-1, Songdo-dong, Yeonsu-gu, Incheon 406-772, Korea
*
*[email protected]
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Abstract

Shell theory solutions for radial buckling of multiply-concentric hollow cylinders are presented. Multi-cylindrical systems are those composed of two or more concentically mounted hollow tubes, wherein the annular space mediates inter-tube forces, attractive or repulsive depending on structural details of composites. Reflecting the multiple core-shell structures, the systems often exhibit peculiar radial buckling modes, which should be relevant to macro scale applications for deep water oil and gas transportation andmicroscale realization in lipid bilayer tubes. In this article, we focus on an illustrative example of such the multiply-tubular systems with nanometric dimension, the so-called multiwalled carbon nanotubes (MWNTs). Theoretical analysis based on a thin shell theory allows us to find anomalous radial buckling behaviors of MWNTs driven by hydrostatic pressure. The obtained buckling modes are characterized by petal-like wavy cross sections, which is what we call the radial corrugation of MWNTs. An important observation is the mechanical consequence of stiff core-tube insertion into the innermost hollow region of a given MWNT. The insertion results in a significant variance in the critical buckling pressure, above which the MWNT undergoes radial corrugation. The insertion-induced-variance in the critical pressure is due to the primary role of inter-tube interaction between adjacent constituent tubes, as explained within our theoretical model.

Keywords

Carbon nanotubeBucklingRadial corrugationHigh pressure phenomenonPipe in pipe systemSandwich pipeThin shell theory
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 583 - 588
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Kyriakides, S., “Buckle Propagation in Pipe-In-Pipe Systems: Part I. Experiments,” International Journal of Solids and Structure, 30, pp. 351–366 (2002).CrossRefGoogle Scholar
2.Kyriakides, S., “Buckle Propagation in Pipe-In-Pipe Systems: Part II. Analysis,” International Journal of Solids and Structures, 30, pp. 367–392 (2002).CrossRefGoogle Scholar
3.Han, J. H., Kardmateas, G. A. and Simitses, G. J., “Elasticity, Shell Theory and Finite Element Results for the Buckling of Long Sandwich Cylindrical Shells under External Pressure,” Composites PartB, 35, pp. 591–598.CrossRefGoogle Scholar
4.Kardmateas, G. A. and Simitses, G. J., “Buckling of Long Sandwich Cylindrical Shells Under External Pressure,” Journal of Applied Mechanics, 72, pp. 493–499.Google Scholar
5.Sato, M. and Patel, M. H., “Exact and Simplified Estimations for Elastic Buckling Pressures of Structural Pipe-In-Pipe Cross Sections Under External Hydrostatic Pressure,” Journal of Marine Science and Technology, 12, pp. 251–262 (2007).Google Scholar
6.Sato, M., Patel, M. H. and Trarieux, F., “Static Displacement and Elastic Buckling Characteristics of Structural Pipe-In-Pipe Cross-Sections,” Structural Engineering and Mechanics, 30, pp. 263–278 (2008).Google Scholar
7.Shimizu, T., Masuda, M. and Minamikawa, H., “Supramolecular Nanotube Architectures Based on Amphiphilic Molecules,” Chemical Reviews, 105, pp. 1401–1444 (2005).CrossRefGoogle ScholarPubMed
8.Li, H., De Rosier, D. J., Nicholson, W. V., Nogales, E. and Downing, K. H., “Microtubule Structure at 8 Å Resolution,” Structure, 10, pp. 1317–1328 (2002).CrossRefGoogle Scholar
9.Saito, R., Dresselhaus, M. S. and Dresselhaus, G., Physical Properties of Carbon Nanotubes, World Scientific Publishing Company (1998).CrossRefGoogle Scholar
10.Loiseau, A., Launois, P., Petit, P., Roche, S. and Salvetat, J. P., Understanding Carbon Nanotubes: From Basics to Application, Springer-Verlag (2006).Google Scholar
11.Sato, M. and Shima, H., “Buckling Characteristics of Multiwalled Carbon Nanotubes under External Pressure,” Interaction and Multiscale Mechanics, 2, pp. 209–222 (2009).Google Scholar
12.Kim, P., Shi, L., Majumdar, A. and McEuen, P. L., “Thermal Transport Measurements of Individual Multiwalled Nanotubes,” Physical Review Letters, 87, p. 215502 (4 pages) (2001).CrossRefGoogle ScholarPubMed
13.Shima, H., “Buckling of Carbon Nanotubes: A State of the Art Review,” Materials, 5, pp. 47–84 (2012).CrossRefGoogle Scholar
14.Shima, H., Umeno, Y. and Sato, M., Molecular Dynamics Study of Radial Corrugation in Carbon Nanotubes, Mechanics of Advanced Materials and Structures, in press (2013).Google Scholar
15.Pantano, A., Parks, D. M. and Boyce, M. C., “Mechanics of Deformation of Single- and Multi-Wall Carbon Nanotubes,” Journal of the Mechanics and Physics of Solids, 52, pp. 789–821 (2004).Google Scholar
16.Shima, H. and Sato, M., “Multiple Radial Corrugations in Multiwall Carbon Nanotubes Under Pressure,” Nanotechnology, 19, p. 495705 (8 pages) (2008).Google Scholar
17.Shima, H., Sato, M., Iiboshi, K., Ghosh, S. and Arroyo, M., “Diverse Corrugation Pattern in Radially Shrinking Carbon Nanotubes,” Physical Review B, 82, p. 085401 (7 pages) (2010).Google Scholar
18.Huang, X., Liang, W. and Zhang, S., “Radial Corrugations of Multi-Walled Carbon Nanotubes Driven by Inter-Wall Nonbonding Interactions,” Nanoscale Research Letters, 6, p. 53 (6 pages) (2011).Google Scholar
19.Shima, H., Ghosh, S., Arroyo, M., Iiboshi, K. and Sato, M., “Thin-Shell Theory Based Analysis of Radially Pressurized Multiwall Carbon Nano tubes,” Computational Materials Science, 52, pp. 90–94 (2012).Google Scholar
20.Shima, H. and Yoshioka, H., “Electronic Spectral Shift of Oxygen-Filled (6,6) Carbon Nanotubes,” Chemical Physics Letters, 513, pp. 224–228 (2011).CrossRefGoogle Scholar
21.Sato, M., Shima, H. and Iiboshi, K., “Core-Tube Morphology of Multiwall Carbon Nanotubes,” International Journal of Modern Physics B, 24, pp. 288–294 (2010).CrossRefGoogle Scholar
22.Girifalco, L. A., Hodak, M. and Lee, R. S., “Carbon Nanotubes, Bucky Balls, Ropes, and a Universal Graphitic Potential,” Physical Review B, 62, pp. 13104–13110 (2000).CrossRefGoogle Scholar
23.Ru, C. Q., “Column Buckling of Multiwalled Carbon Nanotubes with Interlayer Radial Displacements,” Physical Review B, 62, pp. 16962–16967 (2000).CrossRefGoogle Scholar
24.Shen, H. S., “Postbuckling Prediction of DoubleWalled Carbon Nanotubes under Hydrostatic Pressure,” International Journal of Solids and Structures, 41, pp. 2643–2657 (2004).Google Scholar
25.He, X. Q., Kitipornchai, S. and Liew, K. M., “Buckling Analysis of Multiwalled carbon Nano-tubes: A Continuum Model Accounting for Van Der Waals interaction,” Journal of the Mechanics and Physics Solids, 53, pp. 303–326 (2005).CrossRefGoogle Scholar
26.Silvestre, N., Wang, C. M., Zhang, Y. Y. and Xiang, Y., “Sanders Shell Model for Buckling of SingleWalled Carbon Nanotubes with Small Aspect Ratio,” Composite Structures, 93, pp. 1683–1691 (2011).Google Scholar
27.Shima, H. and Sato, M., “Pressure-Induced Structural Transitions Inmulti-Walled Carbon Nano-tubes,” Physica Status Solidi A, 206, pp. 2228–2233 (2009).Google Scholar
28.Kudin, K. N., Scuseria, G. E. and Yakobson, B. I., “C2F, BN, and C Nanoshell Elasticity from Ab Initio Computations,” Physical Review B, 64, p. 235406 (10 pages) (2001).Google Scholar
29.Park, S. J., Sato, M., Ikeda, T. and Shima, H., “Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders,” World Journal of Mechanics, 2, pp. 42–50 (2012).Google Scholar
30.Shima, H. and Sato, M., Elastic and Plastic Deformation of Carbon Nanotubes, Pan Stanford Publishing, Singapore (2013).Google Scholar