Abstract
As a first attempt, the thermal buckling and post-buckling behaviors of moderately thick nanobeams subject to uniform temperature rise are investigated via employing the differential quadrature method (DQM). Considering the von-Kármán’s assumptions, governing equations of the nanobeams are derived using the Eringen’s nonlocal elasticity theory in conjunction with the first-order shear deformation beam theory. The differential quadrature method is used to discretize the governing equations. The direct iterative displacement control method is coupled with the DQM to solve the nonlinear system of algebraic equations. Rapid rate of convergence and accuracy of the method for solving the problem are shown, and effects of the small-scale parameters on the thermal buckling and post-buckling behaviors of the nanobeams for different boundary conditions and length-to-thickness ratios are demonstrated.
Similar content being viewed by others
References
Abdelouahed T, Benguediab S, Bedia EAA, Semmah A, Zidour M (2013) Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes. Adv Nano Res 1:1–11
Adda Bedia W, Benzair A, Semmah A, Tounsi A (2015) On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in anelastic medium based on nonlocal continuum elasticity. Braz J Phys 45:225–233
Ansari R, Gholami R, Darabi MA (2011) Thermal buckling analysis of embedded single-walled carbon nanotubes with arbitrary boundary conditions using the nonlocal Timoshenko beam theory. J Therm Stresses 34(12):1271–1281
Ansari R, Oskouie MF, Gholami R, Sadeghi F (2016) Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory. Compos Part B Eng 89:316–327
Darabi A, Vosoughi AR (2016) A hybrid inverse method for small scale parameter estimation of FG nanobeams. Steel Compos Struct 20(5):1119–1131
Eltahera MA, Khater ME, Emam SA (2016) A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl Math Model 40:4109–4128
Lim CW, Yang Q, Zhang JB (2012) Thermal buckling of nanorod based on non-local elasticity theory. Int J Non-Linear Mech 47(5):496–505
Liu C, Ke LL, Wang YS, Yang J, Kitipornchai S (2014) Buckling and post-buckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings. Int J Str Stab Dyn 14:1350067
Malekzadeh P, Vosoughi AR (2008) Large amplitude free vibration analysis of composite plates with rotationally restrained edges using DQM. J Reinf Plast Comp 27(4):409–430
Malekzadeh P, Vosoughi AR, Sadeghpour M, Vosoughi HR (2014) Thermal buckling optimization of temperature-dependent laminated composite skew plates. ASCE J Aerosp Eng 27:64–75
Narendar S, Gopalakrishnan S (2011) Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics. Phys E Low-Dims Syst Nanostruct 43(6):1185–1191
Rafiee M, Yang J, Kitipornchai S (2013) Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams. Comput Math Appl 66(7):1147–1160
Reddy JN (2004) Mechanics of laminated composite plates and shells, theory and analysis. CRC Press, New Yourk
Reddy JN (2007) Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 45:288–307
Shen HS (2012) Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells. Compos B Eng 43(3):1030–1038
Shen HS, Xiang Y (2015) Thermal postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations. Compos Struct 123:383–392
Shen HS, Zhang CL (2010) Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Mater Des 31:3403–3411
Vosoughi AR (2014) Thermal postbuckling analysis of functionally graded beams. J Therm Stress 37:532–544
Vosoughi AR (2016) Nonlinear free vibration of functionally graded nanobeams on nonlinear elastic foundation. IJST Trans Civil Eng 40:45–58
Vosoughi AR, Nikoo MR (2015) Maximum fundamental frequency and thermal buckling temperature of laminated composite plates by a new hybrid multi-objective optimization technique. Thin-Wall Struct 95:408–415
Vosoughi AR, Malekzadeh P, Banan MR, Banan MR (2011) Thermal postbuckling of laminated composite skew plates with temperature-dependent properties. Thin-Walled Struct 49(7):913–922
Vosoughi AR, Malekzadeh P, Banan MR, Banan MR (2012) Thermal buckling and postbuckling of laminated composite beams with temperature-dependent properties. Int J Nonlin Mech 47:96–102
Wang YZ, Li FM, Kishimoto K (2010) Scale effects on thermal buckling properties of carbon nanotube. Phys Lett A 374:4890–4893
Yu YJ, Xue Z, Li C, Tian X (2016) Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity. Compos Struct 146:108–113
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vosoughi, A.R., Anjabin, N. & Amiri, S.M. Thermal Post-buckling Analysis of Moderately Thick Nanobeams. Iran J Sci Technol Trans Civ Eng 42, 33–38 (2018). https://doi.org/10.1007/s40996-017-0084-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-017-0084-x