Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory

Abstract

The small-scale effect on the torsional buckling of a double-walled carbon nanotube (DWCNT) embedded on Winkler and Pasternak foundations is investigated in this study using the theory of nonlocal elasticity. The effects of the surrounding elastic medium, such as the spring constant of the Winkler type and the shear constant of the Pasternak type, as well as the van der Waals (vdW) forces between the inner and the outer nanotubes are taken into account. Finally, based on the theory of nonlocal elasticity and by employing the continuum models, an elastic double-shell model is presented for the nonlocal torsional buckling load of a DWCNT. It is seen from the results that the shear constant of the Pasternak type increases the nonlocal critical torsional buckling load, while the difference between the presence and the absence of the shear constant of the Pasternak type becomes large. It is shown that the nonlocal critical buckling load is lower than the local critical buckling load. Moreover, a simplified analysis is carried out to estimate the nonlocal critical torque for the torsional buckling of a DWCNT.

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Correspondence to A. Ghorbanpour Arani.

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This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho

Mehdi Mohammadimehr received his B.Sc. degree from the University of Kashan in Kashan, Iran, in 2002. He then received his M.Sc. degree from Shahid Bahonar University of Kerman in Kerman, Iran, in 2004. He is currently a Ph.D student at Shahid Bahonar University of Kerman. His research interests are buckling and vibration analyses of carbon nanotubes and functionally graded materials (FGMs).

Ali Reza Saidi received his B.Sc. degree from Amirkabir University of Technology in Tehran, Iran, in 1993. He received his M.Sc. and Ph.D degrees from Sharif University of Technology in Tehran, Iran, in 1996 and 2003, respectively. Dr Ali Reza Saidi is currently an Associate Professor at the Department of Mechanical Engineering, Shahid Bahonar University of Kerman in Kerman, Iran. His research interests include elasticity, plasticity, nonlinear continuum mechanics, large deformation analysis of solids, nanomechanics, composite materials, functionally graded materials (FGMs), and plates and shells.

Ali Ghorbanpour Arani received his B.Sc. degree from Sharif University of Technology in Tehran, Iran, in 1988. He then received his M.Sc. degree from Amirkabir University of Technology in Tehran, Iran, in 1991 and his Ph.D degree from the Esfahan University of Technology in Esfahan, Iran, in 2001. Dr Ali Ghorbanpour Arani is currently a Professor at the Mechanical Engineering Department of University of Kashan in Kashan, Iran. His current research interests are stress analyses, stability and vibration of nanotubes, and FGMs.

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Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A. et al. Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory. J Mech Sci Technol 24, 1289–1299 (2010). https://doi.org/10.1007/s12206-010-0331-6

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Keywords

  • DWCNT
  • Small scale effect
  • Torsional buckling
  • VdW force
  • Winkler and Pasternak foundations