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On the static stability of nonlocal nanobeams using higher-order beam theories
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  • Journal title : Advances in nano research
  • Volume 4, Issue 1,  2016, pp.51-64
  • Publisher : Techno-Press
  • DOI : 10.12989/anr.2016.4.1.051
 Title & Authors
On the static stability of nonlocal nanobeams using higher-order beam theories
Eltaher, M.A.; Khater, M.E.; Park, S.; Abdel-Rahman, E.; Yavuz, M.;
This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.
buckling;nanobeams;higher-order beam theories;nonlocal elasticity;thermal loads;
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Adali, S. (2008), "Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory", Phys. Lett. A, 372(35), 5701-5705. crossref(new window)

Adali, S. (2012), "Variational formulation for buckling of multi-walled carbon nanotubes modelled as nonlocal Timoshenko beams", J. Theo. Appl. Mech., 50 (1), 321-333.

Ansari, R., Gholami, R. and Sahmani, S. (2013), "Prediction of compressive post-buckling behavior of single-walled carbon nanotubes in thermal environments", Appl. Phys. A, 113(1), 145-153. crossref(new window)

Amirian, B., Hosseini-Ara, R. and Moosavi, H. (2013), "Thermo-mechanical vibration of short carbon nanotubes embedded in pasternak foundation based on nonlocal elasticity theory", Shock Vib., 20(4), 821-832. crossref(new window)

Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B: Eng., 60, 274-283. crossref(new window)

Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B: Eng., 57, 21-24. crossref(new window)

Benzair, A., Besseghier, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 029. crossref(new window)

Bessaim, A., Houari, M.S., Tounsi, A. and Mahmoud, S.R., (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703. crossref(new window)

Chang, T. (2011), "Thermal-nonlocal vibration and instability of single-walled carbon nanotubes conveying fluid", J. Mech., 27 (04), 567-573. crossref(new window)

Chang, T. (2012), "Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Appl. Math. Model., 36(5), 1964-1973. crossref(new window)

Eltaher, M., Khater, M., Abdel-Rahman, E. and Yavuz, M. (2014), "A Model for Nano Bonding Wires under Thermal Loading", IEEE-Nano 2014, Toronto, Canada.

Eltaher, M., Emam, S. and Mahmoud, F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. crossref(new window)

Eltaher, M., Khairy, A., Sadoun, A. and Omar, F. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295.

Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. crossref(new window)

Emam, S. (2013), "A general nonlocal nonlinear model for buckling of nanobeams", Appl. Math. Model., 37(10), 6929-6939. crossref(new window)

Eringen, A. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. crossref(new window)

Ghasemi, A., Dardel, M., Ghasemi, M. and Barzegari, M. (2013), "Analytical analysis of buckling and postbuckling of fluid conveying multi-walled carbon nanotubes", Appl. Math. Model., 37(7), 4972-4992. crossref(new window)

Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. crossref(new window)

Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E, 40(8), 2791-2799. crossref(new window)

Houari, M.S.A., Tounsi, A. and Beg, O.A. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. crossref(new window)

Janghorban, M. (2012), "Two different types of differential quadrature methods for static analysis of microbeams based on nonlocal thermal elasticity theory in thermal environment", Arch. Appl. Mech., 82(5), 669-675. crossref(new window)

Lim, C., Yang, Q. and Zhang, J. (2012), "Thermal buckling of nanorod based on non-local elasticity theory", Int. J. Nonlin. Mech., 47(5), 496-505. crossref(new window)

Narendar, S. and Gopalakrishnan, S. (2011), "Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics", Physica E, 43(6), 1185-1191. crossref(new window)

Nayfeh, A. and Emam, S. (2008), "Exact solution and stability of postbuckling configurations of beams", Nonlin. Dyn., 54(4), 395-408. crossref(new window)

Meziane, M.A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. crossref(new window)

Murmu, T. and Pradhan, S. (2010), "Thermal effects on the stability of embedded carbon nanotubes", Comput. Mater. Sci., 47(3), 721-726. crossref(new window)

Peddieson, J., Buchanan, G. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312. crossref(new window)

Pradhan, S. and Mandal, U. (2013), "Finite element analysis of CNTs based on nonlocal elasticity and Timoshenko beam theory including thermal effect", Physica E, 53, 223-232. crossref(new window)

Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. crossref(new window)

Reddy, J.N. and El-Borgi, S. (2014), "Eringen's nonlocal theories of beams accounting for moderate rotations", Int. J. Eng. Sci., 82, 159-177. crossref(new window)

Setoodeh, A., Khosrownejad, M. and Malekzadeh, P. (2011), "Exact nonlocal solution for postbuckling of single-walled carbon nanotubes", Physica E, 43(9), 1730-1737. crossref(new window)

Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. crossref(new window)

Sudak, L. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281-7287. crossref(new window)

Tounsi, A., Semmah, A. and Bousahla, A. (2013), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech., 3(3), 37-42. crossref(new window)

Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24(1), 209-220. crossref(new window)

Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. crossref(new window)

Wang, C., Zhang, Y., Xiang, Y. and Reddy, J. (2010), "Recent studies on buckling of carbon nanotubes", Appl. Mech. Rev., 63(3), 030804. crossref(new window)

Wang, L., Ni, Q., Li, M. and Qian, Q. (2008), "The thermal effect on vibration and instability of carbon nanotubes conveying fluid", Physica E, 40(10), 3179-3182. crossref(new window)

Zhen, Y. and Fang, B. (2010), "Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nanotubes conveying fluid", Comput. Mater. Sci., 49(2), 276-282. crossref(new window)

Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygrothermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. crossref(new window)