Research Papers

Buckling of a Clamped-Free Double-Walled Carbon Nanotube by the Bubnov-Galerkin Method

[+] Author and Article Information
Isaac Elishakoff

Department of Mechanical Engineering,
Florida Atlantic University,
Boca Raton, FL 33431-0991
e-mail: elishako@fau.edu

French Institute for Advanced Mechanics,
Aubière, 63175 cedex, France
e-mail: simon.bucas@ifma.fr

Manuscript received December 29, 2010; final manuscript received April 20, 2012; accepted manuscript posted June 6, 2012; published online October 29, 2012. Assoc. Editor: Wei-Chau Xie.

J. Appl. Mech 80(1), 011004 (Oct 29, 2012) (5 pages) Paper No: JAM-10-1471; doi: 10.1115/1.4006937 History: Received December 29, 2010; Revised April 20, 2012; Accepted June 06, 2012

This study deals with the Bubnov-Galerkin method applied to the buckling of clamped-free double-walled carbon nanotubes (DWCNTs) subjected to a concentrated compressive load at the free end. It was found that at least four comparison functions are needed in order to obtain accurate results.

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Ru, C. Q., 2000, “Effect of van der Waals Forces on Axial Buckling of a Double-Walled Carbon Nanotubes,” J. Appl. Phys., 87(10), pp. 7227–7231. [CrossRef]
He, X. Q., Kitipornchai, S., and Liew, K. M., 2004, “Buckling Analysis of Multi-Walled Carbon Nanotubes: A Continuum Model Accounting for van der Waals Interaction,” J. Mech. Phys. of Solids, 53(2), pp. 303–326. [CrossRef]
Elishakoff, I., and Pentaras, D., 2009, “Buckling of a Double-Walled Carbon Nanotube,” Adv. Sci. Lett., 2(3), pp. 372–376. [CrossRef]
Elishakoff, I., Dujat, K., and Lemaire, M., 2010, “Buckling of Double-Walled Clamped-Free Carbon Nanotubes by the Finite Difference Method,” ASME J. Appl. Mech. (submitted).
Chang, T., Li, G., and Guo, X., 2005, “Elastic Axial Buckling of Carbon Nanotubes via a Molecular Mechanics Model,” Carbon, 43(2), pp. 287–294. [CrossRef]
Li, C., and Chan, T. W., 2005, “Modeling of Elastic Buckling of Carbon Nanotubes by Molecular Structural Mechanics Approach,” Mech. Mater., 36(11), pp. 1047–1055. [CrossRef]
Sudak, L. J., 2003, “Column Buckling of Multiwalled Carbon Nanotubes Using Nonlocal Continuum Mechanics,” J. Appl. Phys., 94(11), pp. 7281–7287. [CrossRef]
Adali, S., 2008, “Variational Principles for Multi-Walled Carbon Nanotubes Undergoing Buckling Based on Nonlocal Elasticity Theory,” Phys. Lett. A, 372(35), pp. 5701–5705. [CrossRef]
Kumar, D., Heinrich, C., and Waas, A. M., “Buckling Analysis of Carbon Nanotubes Modeled Using Nonlocal Continuum Theories,” J. Appl. Phys., 103(7), p. 073521. [CrossRef]
Artan, R., and Tepe, A., 2008, “The Initial Values Method for Buckling of Nonlocal Bars With Application in Nanotechnology,” Eur. J. Mech. A/Solids, 27(3), pp. 469–477. [CrossRef]
Waters, J. F., Riester, L., Jouzi, M., Guduru, P. R., and Xu, J. M., 2004, “Buckling Instabilities in Multiwalled Carbon Nanotubes Under Uniaxial Compression,” Appl. Phys. Lett., 85(10), pp. 1787–1789. [CrossRef]
Sears, A., and Batra, R. C., 2006, “Buckling of Multiwalled Carbon Nanotubes Under Axial Compression,” Phys. Rev. B, 73(8), p. 085410. [CrossRef]
Aydoğdu, M., and Ece, M. C., 2007, “Vibration and Buckling of In-Plane Loaded Double-Walled Carbon Nano-Tubes,” Turk. J. Eng. Environ. Sci., 31(5), pp. 305–310, http://journals.tubitak.gov.tr/engineering/issues/muh-07-31-5/muh-31-5-5-0704-1.pdf
Hu, N., Nunoya, K., Pan, D., Okabe, T., and Fukunaga, H., 2007, “Prediction of Buckling Characteristics of Carbon Nanotubes,” Int. J. Solids Struct., 44(20), pp. 6535–6550. [CrossRef]
Wang, Z., Zu, X., Yang, L., GaoF., and Weber, W. J., 2008, “Buckling of GaN Nanotubes Under Uniaxial Compression,” Solid State Commun., 146(7–8), pp. 293–297. [CrossRef]
Lu, J.-M., Hwang, C.-C., Kuo, Q.-Y., and Wang, Y.-C., 2008, “Mechanical Buckling of Multi-Walled Carbon Nanotubes: The Effects of Slenderness Ratio,” Physica E, 40(5), pp. 1305–1308. [CrossRef]
Tong, F. M., Wang, C. Y., and Adhikari, S., 2009, “Axial Buckling of Multiwall Carbon Nanotubes With Heterogeneous Boundaries,” J. Appl. Phys., 105(9), p. 094325. [CrossRef]
Zhang, Y. Q., Lu, Y., Wang, S. L., and Liu, X., 2008, “Vibration and Buckling of a Double-Beam System Under Compressive Axial Loading,” J. Sound Vib., 318(1-2), pp. 341–352. [CrossRef]
Zhang, Y. Y., Wang, C. M., and Tan, V. B. C., 2009, “Mechanical Properties and Buckling Behaviors of Condensed Double-Walled Carbon Nanotubes,” J. Nanosci. Nanotechnol., 9(8), pp. 4870–4879. [CrossRef] [PubMed]
Wang, C. Y., Zhang, Y. Y., Wang, C. M., and Tan, V. B. C., 2007, “Buckling of Carbon Nanotubes: A Literature Survey,” J. Nanosci. Nanotechnol., 7(12), pp. 4221–4247. [CrossRef] [PubMed]
Wang, C. M., Zhang, Y. Y., Xiang, Y., and Reddy, J. N., 2010, “Recent Studies on Buckling of Carbon Nanotubes,” Appl. Mech. Rev., 63(3), p. 030804. [CrossRef]
Zhang, Y. Q., Lu, Y., Wang, S. L., and Liu, X., 2008, “Vibration and Buckling of a Double-Beam System Under Compressive Axial Loading,” J. Sound Vib., 318(1-2), pp. 341–352. [CrossRef]
Challamel, N., Mechab, I., El Meiche, N., and Krour, B., 2011, “Buckling of Composite Nonlocal or Gradient Connected Beams,” Int. J. Struct. Stab. Dyn., 11(6), pp. 1015–1033. [CrossRef]





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