Pasternak effect on the buckling of embedded single-walled carbon nanotubes using non-local cylindrical shell theory

Abstract

In this article, the buckling analysis of a single-walled carbon nanotube using the non-local cylindrical shell theory under general loading embedded on the Winkler- and Pasternak-type foundations is presented. The effect of the surrounding elastic medium such as the Winkler-type spring constant and the Pasternak-type shear constant is taken into account in the present formulations. The non-local and local critical buckling loads are obtained under general loading such as the axial compression, lateral pressure, and torsional loading, and it is concluded from the results that the non-local critical buckling load under general loading is lower than the local critical buckling load. It is seen that the Winkler-type spring constant and Pasternak-type shear constant increase the non-local critical buckling load under general loading, therefore the difference between the presence and the absence of the Pasternak-type shear constant is large.

Keywords

small-scale effect Winkler and Pasternak foundations single-walled carbon nanotube buckling analysis general loading

Get full access to this article

View all access options for this article.

References

Iijima

Helical microtubes of graphitic carbon. Nature, 1991, 354, 56–58.

C. Q.

Axially compressed buckling of a double-walled carbon nanotube embedded elastic medium. J. Mech. Phys. Solids, 2001, 49, 1265–1279.

Han

Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium. Eur. J. Mech. A Solids, 2003, 22, 875–883.

Wang

C. Y.

C. Q.

Mioduchowski

Axially compressed buckling of pressured multi-walled carbon nanotubes. Int. J. Solids Struct., 2003, 40, 3893–3911.

Zhang

Y. Q.

Liu

G. R.

Qiang

H. F.

G. Y.

Investigation of buckling of double- walled carbon nanotubes embedded in an elastic medium using the energy method. Int. J. Mech. Sci., 2006, 48, 53–61.

Yang

H. K.

Wang

Torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium. Compos. Struct., 2007, 77, 182–192.

Sohi

A. N.

Naghdabadi

Torsional buckling of carbon nano peapods. Carbon, 2007, 45, 952–957.

Ranjbartoreh

A. R.

Ghorbanpour

Soltani

Double-walled carbon nanotube with surrounding elastic medium under axial pressure. Physica E, 2007, 39, 230–239.

Ranjbartoreh

A. R.

Wang

G. X.

Ghorbanpour Arani

Loghman

Comparative consideration of axial stability of single- and double-walled carbon nanotube and its inner and outer tubes. Physica E, 2008, 41, 202–208.

10.

Yao

Han

The thermal effect on axially compressed buckling of a double-walled carbon nanotube. Eur. J. Mech. A Solids, 2007, 26, 298–312.

11.

Zhang

Y. Q.

Liu

G. R.

Han

Effect of small length scale on elastic buckling of multi walled carbon nanotubes under radial pressure. Phys. Lett. A, 2006, 349, 370–376.

12.

Wang

Varadan

V. K.

Quek

S. T.

Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models. Phys. Lett. A, 2006, 357, 130–135.

13.

Wang

Liew

K. M.

Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Phys. Lett. A, 2007, 363, 236–242.

14.

Ghorbanpour Arani

Rahmani

Arefmanesh

Golabi

Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale. J. Mech. Sci. Technol., 2008, 22, 429–439.

15.

Ghorbanpour Arani

Mohammadimehr

Arefmanesh

Ghasemi

Transverse vibration of short carbon nanotube using cylindrical shell and beam models. Proc. IMechE, Part C: J.Mechanical Engineering Science, 2010, 224, 745–756.

16.

Ghorbanpour Arani

Rahmani

Arefmanesh

Elastic buckling analysis of single-walled carbon nanotube under combined loading by using the ANSYS software. Physica E, 2008, 40, 2390–2395.

17.

Ghorbanpour Arani

Mohammadimehr

Saidi

A. R.

Shogaei

Arefmanesh

Thermal buckling analysis of double-walled carbon nanotube considering small scale effect. Proc. IMechE, Part C: J. Mechanical Engineering Science, 2011, 225, 248–256.

18.

Mohammadimehr

Saidi

A. R.

Ghorbanpour Arani

Effect of small length scale on elastic buckling of double-walled carbon nanotube using Timoshenko beam theory. 16th Annual (International) Conference on Mechanical engineering (ISME 2008)

2008 (Kerman, Iran, Shahid Bahonar University of Kerman14–16 May.

19.

Eringen

A. C.

On differential equations of nonlocalelasticity and solutions of screw dislocationand surface waves. J. Appl. Phys., 1983, 54, 4703–4710.

20.

Yoon

C. Q.

Mioduchowskil

Vibration of an embedded multiwall carbon nanotube. Compos. Sci. Technol., 2003, 63, 1533–1545.

21.

Brush

D. O.

Almroth

B. O.

Buckling of bars, plates, and shells, 1975 (New York, McGraw-Hill).

22.

Paliwal

D. N.

Pendey

R. K.

Nath

Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations. Int. J. Press. Vessels Pip., 1996, 69, 79–89.

23.

Yakobson

B. I.

Brabec

C. J.

Bernholc

Nanomechanics of carbon nanotubes: instabilities beyond linear range. Phys. Rev. Lett., 1996, 76, 2511–2514.