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.
S. Iijima, Helical micro tubes of graphitic carbon, Nature, 354 (1991) 56-58.
C. Q. Ru, Axially compressed buckling of a DWCNT embedded in an elastic medium, J. Mech. Phys. Solids, 49 (2001) 1265-1279.
A. R. Ranjbartoreh, A. Ghorbanpour and B. Soltani, DWCNT with surrounding elastic medium under axial pressure, Physica E, 39 (2007) 230-239.
Q. Han and G. Lu, Torsional buckling of a DWCNT embedded in an elastic medium, Eur. J. Mech. A/Solids, 22 (2003) 875-883.
X. Q. He, S. Kitipomchai, C. M. Wang and K. M. Liew, Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells, Int. J. Solids Stuct., 42 (2005) 6032-6047.
Q. Han, G. Lu and L. Dai, Bending instability of an embedded DWCNT based on Winkler and van der Waals forces, Compos. Sci. Technol., 65 (2005) 1337-1346.
X. Wang, H. K. Yang and K. Dong, Torsional buckling of multi-walled carbon nanotubes, Mater. Sci. Eng. A, 404 (2005) 314-322.
H. K. Yang and X. Wang, Torsional buckling of multiwalled carbon nanotubes embedded in an elastic medium, Compos. Struct., 77 (2007) 182-192.
X. Yao and Q. Han, Investigation of axially compressed buckling of a multi-walled carbon nanotube under temperature field, Compos. Sci. Technol., 67 (2007) 125-134.
X. Wang, Guoxing Lu and Y. J. Lu, Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading, Int. J. Solids Stuct., 44 (2007) 336-351.
A. N. Sohi and R. Naghdabadi, Torsional buckling of carbon nanopeapods, Carbon, 45 (2007) 952-957.
Y. Q. Zhang, G. R. Liu and X. Han, Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure, Phys. Lett. A, 349 (2006) 370-376.
Q. Wang, V. K. Varadan and S. T. Quek, Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models, Phys. Lett. A, 357 (2006) 130-135.
Q. Wang and K. M. Liew, Application of non local continuum mechanics to static analysis of micro- and nanostructures, Phys. Lett. A, 363 (2007) 236-242.
A. C. Eringen, On differential equations of non local elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54 (1983) 4703-4710.
A.Ghorbanpour Arani, M. Moharnmadimehr, A. Arefinanesh and A. Ghasemi, Transverse Vibration of Short Carbon Nanotube using Cylindrical Shell and Beam Models, Proc. ImechE, Part C: J. Mech. Eng. Sci., 224 (C3) (2010) 745-756.
M. Sadeghi, M. Ozmaian and R. Naghdabadi, Stability analysis of carbon nanotubes under electric fields and compressive loading, J. Phys. D: Appl. Phys., 41 (2008) 205411.
A. Ghorbanpour Arani, R. Rahmani, A. Arefinanesh and S. Golabi, Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale, J. Mech. Sci. Technol., 22 (2008) 429-439.
A. Ghorbanpour Arani, R. Rahmani and A. Arefinanesh, Elastic buckling analysis of single-walled carbon nanotube under combined loading by using the ANSYS software, Physica E, 40 (2008) 2390-2395.
M. Mohammadimehr, A. R. Saidi and A. Ghorbanpour Arani, Effect of small length scale on elastic buckling of DWCNT using Timoshenko beam theory, 16th Annual (International) Conference on Mechanical Engineering (ISME 2008), Shahid Bahonar University of Kerman, Kerman, Iran.
D. O. Brush and B. O. Almroth, Buckling of bars, plates and shells, McGraw-Hili, New York, USA, (1975).
D. N. Paliwal, R. K. Pendey and T. Nath, Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations, Int. J. Pres. Ves. Pip., 69 (1996) 79-89.
B. I. Yakobson, C. J. Brabec and J. Bernholc, Nanomechanics of Carbon Tubes: Instabilities beyond Linear Response, Phys. Rev. Lett., 76 (1996) 2511-2514.
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