Thermal Effect on the Torsional Buckling of Double Walled Carbon Nanotube Embedded in Pasternak Foundation

Document Type: Persian


1 Associate Professor, Faculty of Engineering, Kashan University, Kashan

2 Ph.D. Student, Faculty of Engineering, Kashan University, Kashan

3 Assistant Professor, Faculty of Engineering, Kashan University, Kashan


In this study the effect of thermal stress on the torsional buckling of double walled carbon nanotubes is investigated. Moreover based on nonlocal continuum mechanic the buckling governing equations are obtained and equilibrium of Equations is generalized to double wall nanotubes. Also in this study the elastic medium, small scale effect and van der Walls force are considered. Also for simulation of the interaction between the polymer matrix and external tube Pasternak model is used. The numerical results indicate that critical buckling load occurs in the middle modes. Moreover for the Winkler related the Pasternak model the buckling occurs earlier. Results show that for rigid elastic medium in both case of Pasternak and Winkler models the buckling load is independent of their values Moreover from the result it can be seen that the buckling load has been increase as the thermal effect change.


[1] S. Iijima, Helical Micro Tubes of Graphitic Carbon, Nature, 354, 1991, pp. 56-58.

[2] S. Rodney Ruoff, Q. Dong, L. Wing Kam, Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements, C. R. Physique,4, 2003, pp.  993-1008

[3] A. Ghorbanpour Arani, R. Rahmani, A. Arefmanesh, S. Golabi, Buckling Analysis of Multi-Walled Carbon Nanotubes under Combined Loading Considering the Effect of Small Length Scale, Journal of Mechanical Science  and  Technology, 22, 2008, pp. 429-439.


[4] Ru CQ., Elastic buckling of single-walled carbon nanotube ropes under high pressure, Physics Review B, 62, ‌2000, pp. 10405–10408.

[5] M.J. Hao, X.M. Guo, Q. Wang., Small-scale effect on torsional buckling of multi-walled carbon nanotubes, European Journal of Mechanics A/Solids, 29, 2010, pp. 49-55.

[6] Y.C. Zhang, X. Chen, X. Wang., Effects of temperature on mechanical properties of multi-walled, Composites Science and Technology, 68, 2008, pp.  572-581.

[7] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 1983, pp. 4703-4710.

[8] S. Kitipornchai, X. Q. He, and K. M., Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix, Journal of Applied Physics., 97, 2005, pp.114318-114325.

[9] T. Murmu, S.C. Pradhan., Thermal effects on the stability of embedded carbon nanotubes, Computational Materials Science, 47, 2010, pp. 721-726.

[10]S. Chengqi, L. Kaixin, Dynamic torsional buckling of a double-walled carbon nanotube embedded in an elastic medium, European Journal of Mechanics A/Solids, 27, 2008, pp. 40–49.

[11]A.C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002

[12]            Mohammadimehr  M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A. , Torsional buckling of a DWCNT embeddedon winkler and pasternak foundations using nonlocal theory, Journal of Mechanical Science and Technology,24(6)‌‌‌,‌‌ 2010, pp.1289-1299

[13]Y. Xiaohu, H. Qiang, The thermal effect on axially compressed buckling of a double-walled carbon nanotube, European Journal of Mechanics A/Solids, 26, 2007, pp. 298–312.