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An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes

Leta, James V.
http://rave.ohiolink.edu/etdc/view?acc_num=akron1312166451

Abstract Details

2011, Master of Science, University of Akron, Applied Mathematics.
Multi-walled carbon nanotubes (MWNT) are well-known for their superior mechanical properties. Their size, tensile strength, and flexibility make them an attractive choice for a variety of practical applications. Thus numerous studies have been conducted in an effort to better understand the response of MWNT to applied loading. In this paper, we develop a nonlinear continuum model that describes equilibrium configurations of double-walled carbon nanotubes (DWNT). The DWNT is assumed to deform in such a way that enables us to reduce our analysis to a single cross-section perpendicular to the axis of the DWNT. We model the cross-section of a DWNT as 2 circular concentric rings that interact through a van der Waals body force. Utilizing our continuum assumption and the Lennard-Jones 12-6 potential function, we derive an expression for the body force. We apply Euler's elastica theory to derive a two-point boundary value problem that consist of a system of 4 nonlinear ordinary differential equations with periodic boundary conditions. Using standard techniques of bifurcation theory, we establish a trivial branch of circular solutions and give a complete description of the critical radii at which buckled solutions bifurcate from the trivial branch.
J. Patrick Wilber, Dr. (Advisor)
Gerald Young, Dr. (Committee Member)
Dmitry Golovaty, Dr. (Committee Member)
63 p.
Applied Mathematics; Mechanics; Nanoscience
nanomechanics; nonlinear elasticty; continuum mechanics; elastica; buckling; bifurcation theory

Recommended Citations

Citations

  • Leta, J. V. (2011). An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1312166451

    APA Style (7th edition)

  • Leta, James. An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes. 2011. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1312166451.

    MLA Style (8th edition)

  • Leta, James. "An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes." Master's thesis, University of Akron, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1312166451

    Chicago Manual of Style (17th edition)

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© 2011, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.