Mechanical Buckling Analysis of Single-Walled Carbon Nanotube with Nonlocal Effects

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In this work Differential Transform Method (DTM) is used to study the buckling behavior of the single walled carbon nanotube (SWCNT). The critical buckling load is being found out up to fourth degree accuracy for different boundary conditions, i.e. Clamped-Clamped, Simply Supported at ends, Clamped Hinged, and Clamped Free. Effect of different nonlocal parameters, different L/d ratio on critical buckling load is being discussed. The DTM is implemented for the nonlocal SWCNT analysis and this yields results with high degree of accuracy. Further, present method can be applied to linear and nonlinear problems.

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85-94

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B. Ravi Kumar, "Mechanical Buckling Analysis of Single-Walled Carbon Nanotube with Nonlocal Effects", Journal of Nano Research, Vol. 48, pp. 85-94, 2017

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July 2017

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[1] Iijima, Sumio. Helical microtubules of graphitic carbon., nature 354. 6348 (1991): 56-58.

DOI: https://doi.org/10.1038/354056a0

[2] Thostenson, Erik T., Zhifeng Ren, and Tsu-Wei Chou. Advances in the science and technology of carbon nanotubes and their composites: a review., Composites science and technology 61. 13 (2001): 1899-(1912).

DOI: https://doi.org/10.1016/s0266-3538(01)00094-x

[3] D. Qian, G.J. Wagner, W.K. Liu, M.F. Yu, R.S. Ruoff, Appl. Mech. Rev. 55 (2002) 495.

[4] Eringen, A. Cemal. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves., Journal of applied physics 54. 9 (1983): 4703-4710.

DOI: https://doi.org/10.1063/1.332803

[5] Zhou, S. J., and Z. Q. Li. Length scales in the static and dynamic torsion of a circular cylindrical micro-bar., Journal of Shandong university of technology 31. 5 (2001): 401-407.

[6] N.A. Fleck, J.W. Hutchinson, Adv. Appl. Mech. 33 (1997) 295.

[7] Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Int. J. Solids Struct. 39 (2002) 2731.

[8] L.J. Sudak, J. Appl. Phys. 94 (2003) 7281.

[9] Q. Wang, V.K. Varadhan, Smart Mater. Struct. 14 (2005) 281.

[10] B.I. Yakobson, C.J. Brabec, J. Bernholc, Phys. Rev. Lett. 76 (1996) 2511.

[11] A. Sears, R.C. Batra, Phys. Rev. B 73 (2006) 085410.

[12] Reddy, J. N. Nonlocal theories for bending, buckling and vibration of beams., International Journal of Engineering Science 45. 2 (2007): 288-307.

DOI: https://doi.org/10.1016/j.ijengsci.2007.04.004

[13] Pradhan, S. C., and G. K. Reddy. Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM., Computational Materials Science 50. 3 (2011): 1052-1056.

DOI: https://doi.org/10.1016/j.commatsci.2010.11.001

[14] T. Murmu, S.C. Pradhan, Comput. Mater. Sci. 47 (2010) 721.

[15] Kumar, R. and S. Deol, 2016. Vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium using DTM (Differential Transformation Method). Int. J. Eng. Sci. Invent. Res. Dev., Vol. 2 ( 2016).

[16] T. Murmu, S.C. Pradhan, Mech. Res. Commun. 36 (2009) 933.

[17] S.C. Pradhan, T. Murmu, Comput. Mater. Sci. 47 (2009) 268.

[18] S.C. Pradhan, Phys. Lett. A 373 (2009) 4182.

[19] S.C. Pradhan, J.K. Phadikar, Struct. Eng. Mech. Int. J. 33 (2009) 193.

[20] S.C. Pradhan, A. Sarkar, Struct. Eng. Mech. Int. J. 32 (2009) 811.

[21] T. Murmu, S.C. Pradhan, Physica E: Low-Dim. Syst. NanoStruct. 41 (2009) 1628.

[22] S.C. Pradhan, T. Murmu, J. Appl. Phys. 105 (2009) 124306.

[23] S.C. Pradhan, J.K. Phadikar, G. Karthik, J. Inst. of Eng. (India), Met. Mater. Eng. Div. 90 (2009) 16.

[24] T. Murmu, S.C. Pradhan, Physica E: Low-Dim. Syst. NanoStruct. 41 (2009) 1232.

[25] S.C. Pradhan, J.K. Phadikar, Phys. Lett. A 373 (2009) 1062.

[26] T. Murmu, S.C. Pradhan, J. Appl. Phys. 105 (2009) 064319.

[27] J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, (1986).

[28] Ayaz, Fatma. Applications of differential transform method to differential-algebraic equations., Applied Mathematics and Computation 152. 3 (2004): 649-657.

DOI: https://doi.org/10.1016/s0096-3003(03)00581-2

[29] A. Arıkog˘lu, Appl. Math. Comput. 168 (2005) 1145.

[30] Q. Wang, V.K. Varadhan, S.T. Quek, Phys. Lett. A 357 (2006) 130.

[31] C.M. Wang, Y.Y. Zhang, S.S. Ramesh, S. Kitipornchai, J. Phys. D: Appl. Phys. 39 (2006) 3904.

[32] Kumar, R. and D. Sumit, Nonlocal buckling analysis of single-walled carbon nanotube using Differential Transform Method (DTM). Int. J. Sci. Res., (2016)Vol 5: 1768-1773.

DOI: https://doi.org/10.21275/v5i3.nov162343

[33] Wang, Xueshen, et al. Fabrication of ultralong and electrically uniform single-walled carbon nanotubes on clean substrates., Nano letters 9. 9 (2009): 3137-3141.

DOI: https://doi.org/10.1021/nl901260b

[34] Belluci, S. (19 January 2005). Carbon nanotubes: physics and applications,.: 34–47.

[35] Reddy, J. N., and S. D. Pang. Nonlocal continuum theories of beams for the analysis of carbon nanotubes., Journal of Applied Physics 103. 2 (2008): 023511.

DOI: https://doi.org/10.1063/1.2833431