Thermo-mechanical Buckling Analysis of Non-homogeneous Open Circular Cylindrical Shells Reinforced with Single-walled Carbon Nanotubes

Document Type : Original Research Paper


Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran.



 In this paper, the thermo-mechanical buckling analysis of a non-homogeneous open cylindrical shell reinforced with single-walled carbon nanotubes with a uniform/non-uniform distribution on an elastic foundation under thermal and
mechanical loads has been addressed. Using the minimum energy principle, the governing differential equations of this system are derived and in order to determine the properties of the reinforced composite shell, the modified mixtures law has been used. It is assumed that the properties of single-walled carbon nanotubes are acquired from molecular dynamics simulation. It is also assumed that the material properties of the reinforced carbon nanotube composites are linear in the thickness and are defined based on mixture law via a micro-mechanical model in which the nanotube performance parameter is considered. After solving these equations, the effects of geometric characteristics of the shell and material properties on the critical load and critical temperature of shell buckling are investigated.


 [1] C.H. Sun, F. Li, H.M. Cheng, G.Q. Lu, Axial Young’s modulus prediction of single walled carbon nanotube arrays with diameters from nanometer to meter scales, Appl. Phys. Lett., 87(19) (2005) 193201.
[2] J.D. Fidelus, E. Wiesel, F.H. Gojny, K. Schulte, H.D. Wagner, Thermo mechanical properties of randomly riented carbon/epoxy nanocomposites, Composites, Part A, 36(11) (2005) 1555-1561.
[3] Y.S. Song, J.R. Youn, Modeling of effective elastic properties for polymer based carbon nanotube composites, Polymer, 47(5) (2006) 1741-1748.
[4] Y. Han, J. Elliott, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Comput. Mater. Sci., 39(2) (2007) 315-323.
[5] R. Zhu, E. Pan, A.K. Roy, Molecular dynamics study of the stress-strain behavior of carbonnanotube reinforced Epon862 composites, Mater. Sci. Eng. A, 447(1-2) (2007) 51-57.
[6] M. Gribel, J.M. Hamaekers, Molecular dynamic simulation of the elastic moduli of polymer-carbon nanotube composites, Comput. Methods Appl. Mech. Eng., 193(17-20) (2004) 1773-1788.
[7] N. Kordani, A. Fereidoon, S. Sadoddin, M. Ghorbanzadeh Ahangari, Investigation of mechanical and thermal behavior of reinforced polypropylene with single walled Carbon nanotube, Aerospace Mech. J., 6(4) (2011) 1-10. (In Persian).
[8] T. Vodenitcharova, L.C. Zhang, Bending and local buckling of a nanocomposite beam reinforced by a single-walled Carbon nanotube, Int. J. Solids Struct., 43(10) (2006) 3006-3024.
[9] G. Formica, W. Lacarbonara, R. Alessi, Vibrations of carbon nanotube-reinforced composites, Sound Vib. J., 329(10) (2010) 1875-1889. [10] G.D. Seidel, D.C. Lagoudas, Micromechanical analysis of the effective elastic properties of carbon
nanotube reinforced composites, Mech. Mater., 38(8-10) (2006) 884-907.
[11] D. Qian, E.C. Dickey, R. Andrews, T. Rantell, Load transfer and deformation mechanismsin carbon nanotube-polystyrene composites, Appl. Phys. Lett., 76(20) (2000) 2868-2870.
[12] H.S. Shen, Nonlinear bending of functionally graded Carbon nanotube-reinforce composite plates in thermal environments, Compos. Struct., 91(1) (2009) 9-19.
[13] H.S. Shen, Z.H. Zhu, Buckling and postbuckling behavior of functionally graded nanotubereinforced composite plates in thermal environments, Comput. Mater, Continua, 18(2) (2010) 155-182.
[14] L.L. Ke, J. Yang, S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotubereinforced composite beams, Compos. Struct, 92(3) (2010) 676-683.
[15] M. Raoufi, S. Jafari Mehrabadi, S. Satouri, Free vibration analysis of 2D-FGM annular sectorial moderately thick plate resting on elastic foundation using 2D-DQM solution, Modares Mech. Eng., 14(15) (2015) 299-306.
[16] M. Mohammadimehr, M. Salami, H. Nasiri, H. Afshari, Thermal effect on deflection, critical buckling load and vibration of nonlocal Euler-Bernoulli beam on Pasternak foundation using Ritz method, Modares Mech. Eng., 13(11) (2013) 64-76.
[17] A. Pourasghar, R. Moradi-Dastjerdi, M.H. Yas, A. Ghorbanpour Arani, S. Kamarian, Three-dimensional analysis of carbon nanotubereinforced cylindrical shells with temperaturedependent properties under thermal environment, Polym. Compos., 39(4) (2018) 1161-1171.
[18] A. Ghorbanpour Arani, S. Shams, S. Amir, M.J. Maboudi, Buckling of piezoelectric composite cylindrical shell under electro-thermo-mechanical loading, J. Solid Mech., 4(3) (2012) 296-306.
[19] A.A. Mosallaie Barzoki, A. Ghorbanpour Arani, R. Kolahchi, M.R. Mozdianfard, A. Loghman, Non-linear buckling response of embedded piezoelectric cylindrical shell reinforced with BNNT under electro-thermomechanical loadings using HDQM, Compos. Part B, 44(1) (2013) 722-727.
[20] H.S. Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells, Compos. Struct., 93(8) (2011) 2096-2108.
[21] M. Mohammadi, M. Arefi, R. Dimitri, F. Tornabene, Higher-order thermo-elastic analysis of FG-CNTRC cylindrical vessels surrounded by a pasternak foundation, Nanomaterials, 9(1) (2019) 79.
[22] M. Arefi, M. Mohammadi, A. Tabatabaeian, R. Dimitri, F. Tornabene, Two-dimensional thermoelastic analysis of FG-CNTRC cylindrical pressure vessels, Steel Compos. Struct., 27(4) (2018) 525-536.
[23] M. Arefi, M. Pourjamshidian, A. Ghorbanpour Arani, Application of non-local strain gradient theory and various shear deformation theories to non-linear vibration analysis of sandwich nanobeam with FGCNTRCs face-sheets in electrothermal environment, Appl. Phys. A, 123(5) (2017) 323.
[24] M. Arefi, E. Mohammad-Rezaei Bidgoli, R. Dimitri, M. Bacciocchi, F. Tornabene, Non-local bending analysis of curved nano-beams reinforced by graphene nanoplatelets, Composites, Part B, 166 (2019) 1-12.
[25] M. Arefi, E. Mohammad-Rezaei Bidgoli, R. Dimitri, F. Tornabene, J.N. Reddy, Sizedependent free vibrations of FG polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on pasternak foundations, Appl. Sci., 9(8) (2019) 1580.
[26] M. Arefi, E. Mohammad-Rezaei Bidgoli, R. Dimitri, F. Tornabene, Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets, Aerosp. Sci. Technol., 81 (2018) 108-117.
[27] Y. Tadi Beni, F. Mehralian, H. Razavi, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Compos. Struct., 120 (2015) 65-78.
[28] F. Mehralian, Y. Tadi Beni, Size-dependent torsional buckling analysis of functionally graded cylindrical shell, Composites, Part B, 94 (2016) 11-25.
[29] F. Mehralian, Y. Tadi Beni, R. Ansari, Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell, Compos. Struct., 152 (2016) 45-61.
[30] H. Zeighampour, Y. Tadi Beni, Size dependent analysis of wave propagation in functionally graded composite cylindrical microshell reinforced by carbon nanotube, Compos. Struct., 179 (2017) 124-131.
[31] P. Mohammadi Dashtaki, Y. Tadi Beni, Effects of Casimir force and thermal stresses on the buckling of electrostatic nanobridges based on couple stress theory, Arabian J. Sci. Eng., 39(7) (2014) 5753-5763.
[32] J. Song, B. Karami, D. Shahsavari, Ö. Civalek, Wave dispersion characteristics of graphene reinforced nanocomposite curved viscoelastic panels, Compos. Struct., 277 (2021) 114648.
[33] M. Khorasani, Z. Soleimani-Javid, E. Arshid, S. Amir, Ö. Civalek, Vibration analysis of graphene nanoplatelets’ reinforced composite plates integrated by piezo-electromagnetic patches on the piezo-electromagnetic media, Waves Random Complex Medium, (2021) 1-31.
[34] M. Karimi Zeverdejani, Y. Tadi Beni, Y. Kiani, Multi-scale buckling and post-buckling analysis of functionally graded laminated composite plates reinforced by defective graphene sheets, Int. J. Struct. Stab. Dyn., 20(01) (2020) 2050001.
[35] M. Karimi Zeverdejani, Y. Tadi Beni, Effect of laminate configuration on the free vibration/buckling of FG Graphene/PMMA composites, Adv. Nano Res., 8(2) (2020) 103-114.
[36] E. Bagherizadeh, Y. Kiani, M.R. Eslami, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Compos. Struct., 93(11) (2011) 3063-3071.
[37] H. Babaei, M.R. Eslami, Nonlinear analysis of thermal-mechanical coupling bending of FGP infinite length cylindrical panels based on PNS and NSGT, Appl. Math. Modell., 91 (2021) 1061-1080.
[38] A. Nosier, M. Ruhi, Three dimensional analysis of laminated cylindrical panels with piezoelectric layers, Int. J. Eng., 19(1) (2006) 61-72.
[39] A.H. Sofiyev, K. Yucel, M. Avcar, Z. Zerin, The dynamic stability of orthotropic cylindrical shells with nonhomogenous material properties under axial compressive load varying as a parabolic function of time, J. Reinf. Plast. Compos., 25(18) (2006) 1877-1886.
[40] D.O. Brush, B.O. Almorth, Buckling of Bars, Plates, and Shells, New York, McGraw-Hill Publisher, (1975).
[41] A.M. Zenkour, Maupertuis-lagrange mixed variational formula for laminated composite structures with a refined higher-order beam theory, Int. J. of Non Linear Mech., 32(5) (1997) 989-1001.
[42] M. Arefi, A.M. Zenkour, A simplified shear and normal deformations non-local theory for bending of functionally graded piezomagnetic sandwich nano-beams in magneto-thermo-electric environment, J. Sandwich Struct. Mater., 18(5) (2016) 624-651.
[43] M. Arefi, A.M. Zenkour, Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory, Steel Compos. Struct., 26(4) (2018) 421-437.
[44] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, Second Edition, Boca Raton, CRC Press LLC, (2004).
[45] S. Abolghasemi, H.R. Eipakchi, M. Shariati, Analytical solution for buckling of rectangular plates subjected to nonuniform in-plane loadig based on first order shear deformation theory, Modares Mech. Eng., 14(13) (2014) 37-46.
[46] F. Sohani, H.R. Eipakchi, A survey on free vibration and buckling of a beam with moderately large deflection using first order shear deformation theory, Modares Mech. Eng., 13(14) (2014) 1-14.
[47] H.S. Shen, C.L. Zhang, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Mater. Des., 31(7) (2010) 3403-3411.
[48] A. Bakhsheshy, K. Khorshidi, Free vibration of functionally graded rectangular nanoplates in thermal environment based on the modified couple stress theory, Modares Mech. Eng., 14(15) (2015) 323-330.
[49] M. Nejati, R. Dimitri, F. Tornabene, M.H. Yas, Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by functionally graded wavy carbon nanotubes with temperaturedependent properties, J. Appl. Sci., 7(12) (2017) 1223.
[50] B. Mirzavand, M.R. Eslami, Thermal buckling of imperfect functionally graded cylindrical shells based on the Wan-Donnell model, J. Therm., Stress, 29(1) (2006) 37-55.
[51] O. Miraliyari, M. Bohloli, Thermal buckling of short and long cylindrical shells reinforced with single wall carbon nanotubes using first order shear deformation theory, 2st National Conference on Development of Civil Engineering, Architecure, Electricity and Mechanical in Iran, Gorgan, 17 November (2015).