DOI QR코드

DOI QR Code

On axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets

  • Gao, Yang (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Xiao, Wan-shen (State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University) ;
  • Zhu, Haiping (School of Computing, Engineering and Mathematics, Western Sydney University)
  • 투고 : 2019.05.11
  • 심사 : 2019.10.01
  • 발행 : 2019.10.25

초록

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

키워드

과제정보

연구 과제 주관 기관 : Hunan Provincial Innovation Foundation

참고문헌

  1. Allahyari, E. and Kiani, A. (2018), "Employing an analytical approach to study the thermo-mechanical vibration of a defective size-dependent graphene nanosheet", Eur. Phys. J. Plus., 133(6), 223. https://doi.org/10.1140/epjp/i2018-12058-2
  2. Apuzzo, A., Barretta, R., Faghidian, S.A., Luciano, R. and de Sciarra, F.M. (2018), "Free vibrations of elastic beams by modified nonlocal strain gradient theory", Int. J. Eng. Sci., 133, 99-108. https://doi.org/10.1016/j.ijengsci.2018.09.002
  3. Bao, W., Miao, F., Chen, Z., Zhang, H., Jang, W., Dames, C. and Lau, C.N. (2009), "Controlled ripple texturing of suspended graphene and ultrathin graphite membranes", Nature Nanotechnol., 4, 562-566. https://doi.org/10.1038/nnano.2009.191
  4. Barati, M.R. (2017), "A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous nanoporous plates", Eur. J. Mech. A-Solid., 67, 215-230. https://doi.org/10.1016/j.euromechsol.2017.09.001
  5. Barati, M.R. and Zenkour, A.M. (2017a), "Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection", Compos. Struct., 181, 194-202. https://doi.org/10.1016/j.compstruct.2017.08.082
  6. Barati, M.R. and Zenkour, A.M. (2017b), "Investigating postbuckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions", Compos. Struct., 182, 91-98. https://doi.org/10.1016/j.compstruct.2017.09.008
  7. Barati, M.R. and Zenkour, A.M. (2018a), "Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions", Mech. Adv. Mater. Struct., 26(18), 1580-1588. https://doi.org/10.1080/15376494.2018.1444235
  8. Barati, M.R. and Zenkour, A.M. (2018b), "Post-buckling analysis of imperfect multi-phase nanocrystalline nanobeams considering nanograins and nanopores surface effects", Compos. Struct., 184, 497-505. https://doi.org/10.1016/j.compstruct.2017.10.019
  9. Barati, M.R. and Zenkour, A.M. (2018c), "Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection", Mech. Adv. Mater. Struct., 26(17), 1482-1490. https://doi.org/10.1080/15376494.2018.1432821
  10. Barati, M.R. and Zenkour, A.M. (2018d), "Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection", Mech. Adv. Mater. Struct., 26(6), 503-511. https://doi.org/10.1080/15376494.2017.1400622
  11. Barati, M.R. and Zenkour, A.M. (2019), "Analysis of postbuckling behavior of general higher-order functionally graded nanoplates with geometrical imperfection considering porosity distributions", Mech. Adv. Mater. Struct., 26(12), 1081-1088. https://doi.org/10.1080/15376494.2018.1430280
  12. Barretta, R. and Sciarra, F.M.D. (2018), "Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams", Int. J. Eng. Sci., 130, 187-198. https://doi.org/10.1016/j.ijengsci.2018.05.009
  13. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable mode", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  14. Christy, P.A., Peter, A.J. and Lee, C.W. (2018), "Density functional theory on 13C NMR chemical shifts of fullerene", Solid State Commun., 283, 22-26. https://doi.org/10.1016/j.ssc.2018.08.001
  15. Cong, P.H. and Duc, N.D. (2018), "New approach to investigate the nonlinear dynamic response and vibration of a functionally graded multilayer graphene nanocomposite plate on a viscoelastic Pasternak medium in a thermal environment", Acta Mech., 229(9), 3651-3670. https://doi.org/10.1007/s00707-018-2178-3
  16. Ebrahimi, F. and Barati, M.R. (2016), "Vibration analysis of piezoelectrically actuated curved nanosize fg beams via a nonlocal strain-electric field gradient theory", Mech. Adv. Mater. Struct., 25(4), 350-359. https://doi.org/10.1080/15376494.2016.1255830
  17. Ebrahimi, F. and Barati, M.R. (2017), "Hygrothermal effects on vibration characteristics of viscoelastic fg nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  18. Ebrahimi, F. and Barati, M.R. (2018a), "Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory", Compos. Struct., 185, 241-253. https://doi.org/10.1016/j.compstruct.2017.10.021
  19. Ebrahimi, F. and Barati, M.R. (2018b), "Vibration analysis of biaxially compressed double-layered graphene sheets based on nonlocal strain gradient theory", Mech. Adv. Mater. Struct., 26(10), 854-865. https://doi.org/10.1080/15376494.2018.1430267
  20. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  21. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  22. Farokhi, H. and Ghayesh, M.H. (2015), "Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory", Int. J. Mech. Sci., 90, 133-144. https://doi.org/10.1016/j.ijmecsci.2014.11.002
  23. Farokhi, H. and Ghayesh, M.H. (2017), "Nonlinear resonant response of imperfect extensible Timoshenko microbeams", Int. J. Mech. Mater. Des., 13(1), 43-55. https://doi.org/10.1007/s10999-015-9316-z
  24. Farokhi, H. and Ghayesh, M.H. (2018a), "Supercritical nonlinear parametric dynamics of Timoshenko microbeams", Commun. Nonlinear Sci., 59, 592-605. https://doi.org/10.1016/j.cnsns.2017.11.033
  25. Farokhi, H. and Ghayesh, M.H. (2018b), "Nonlinear mechanics of electrically actuated microplates", Int. J. Eng. Sci., 123, 197-213. https://doi.org/10.1016/j.ijengsci.2017.08.017
  26. Farokhi, H., Ghayesh, M.H. and Amabili, M. (2013), "Nonlinear resonant behavior of microbeams over the buckled state", Appl. Phys. A., 113, 297-307. https://doi.org/10.1007/s00339-013-7894-x
  27. Farokhi, H., Ghayesh, M.H. and Hussain, S. (2016), "Largeamplitude dynamical behaviour of microcantilevers", Int. J. Eng. Sci., 106, 29-41. https://doi.org/10.1016/j.ijengsci.2016.03.002
  28. Fasolino, A., Los, J.H. and Katsnelson, M.I. (2007), "Intrinsic ripples in graphene", Nature Mater., 6, 858-861. https://doi.org/10.1038/nmat2011
  29. Ghavanloo, E. (2017), "Axisymmetric deformation of geometrically imperfect circular graphene sheets", Acta Mech., 228(9), 3297-3305. https://doi.org/10.1007/s00707-017-1891-7
  30. Ghayesh, M.H. (2013), "Subharmonic dynamics of an axially accelerating beam", Arch App. Mech., 82(9), 1169-1181. https://doi.org/10.1007/s00419-012-0609-5
  31. Ghayesh, M.H. (2018a), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004
  32. Ghayesh, M.H. (2018b), "Functionally graded microbeams: Simultaneous presence of imperfection and viscoelasticity", Int. J. Mech. Sci., 140, 339-350. https://doi.org/10.1016/j.ijmecsci.2018.02.037
  33. Ghayesh, M.H. (2018c), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Math. Model., 59, 583-596. https://doi.org/10.1016/j.apm.2018.02.017
  34. Ghayesh, M.H. (2019a), "Viscoelastic dynamics of axially FG microbeams", Int. J. Eng. Sci., 135, 75-85. https://doi.org/10.1016/j.ijengsci.2018.10.005
  35. Ghayesh, M.H. (2019b), "Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams", Compos. Struct., 225, 110974. https://doi.org/10.1016/j.compstruct.2019.110974
  36. Ghayesh, M.H. (2019c), "Mechanics of viscoelastic functionally graded microcantilevers", Eur. J. Mech. A/Solid., 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001
  37. Ghayesh, M.H. (2019d), "Asymmetric viscoelastic nonlinear vibrations of imperfect AFG beams", Appl. Acoust., 154, 121-128. https://doi.org/10.1016/j.apacoust.2019.03.022
  38. Ghayesh, M.H. (2019e), "Nonlinear oscillations of FG cantilevers", Appl. Acoust., 145, 393-398. https://doi.org/10.1016/j.apacoust.2018.08.014
  39. Ghayesh, M.H. (2019f), "Resonant vibrations of FG viscoelastic imperfect Timoshenko beams", J. Vib. Control, 25(12), 1823-1832. https://doi.org/10.1177/1077546318825167
  40. Ghayesh, M.H. (2019g), "Viscoelastic nonlinear dynamic behaviour of Timoshenko FG beams", Eur. Phys. J. Plus, 134, 401. https://doi.org/10.1140/epjp/i2019-12472-x
  41. Ghayesh, M.H. and Farokhi, H. (2015), "Chaotic motion of a parametrically excited microbeam", Int. J. Eng. Sci., 96, 34-45. https://doi.org/10.1016/j.ijengsci.2015.07.004
  42. Ghayesh, M.H. and Moradian, N. (2011), "Nonlinear dynamic response of axially moving, stretched viscoelastic strings", Arch. App. Mech., 81, 781-799. https://doi.org/10.1007/s00419-010-0446-3
  43. Ghayesh, M.H., Yourdkhani, M., Balar, S. and Reid, T. (2010), "Vibrations and stability of axially traveling laminated beams", Appl. Math. Compos., 217(2), 545-556. https://doi.org/10.1016/j.amc.2010.05.088
  44. Ghayesh, M.H., Kazemirad, S. and Darabi, M.A. (2011), "A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions", J. Sound Vib., 330(22), 5382-5400. https://doi.org/10.1016/j.jsv.2011.06.001
  45. Ghayesh, M.H., Kazemirad, S. and Reid, T. (2012), "Nonlinear vibrations and stability of parametrically exited systems with cubic nonlinearities and internal boundary conditions: A general solution procedure", Appl. Math. Model., 36(7), 3299-3311. https://doi.org/10.1016/j.apm.2011.09.084
  46. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013a), "Coupled global dynamics of an axially moving viscoelastic beam", Int. J. Non-linear Mech., 51, 54-74. https://doi.org/10.1016/j.ijnonlinmec.2012.12.008
  47. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013b), "Threedimensional nonlinear size-dependent behaviour of Timoshenko microbeams", Int. J. Eng. Sci., 71, 1-14. https://doi.org/10.1016/j.ijengsci.2013.04.003
  48. Ghayesh, M.H., Farokhi, H. and Alici, G. (2016), "Size-dependent performance of microgyroscopes", Int. J. Eng. Sci., 100, 99-111. https://doi.org/10.1016/j.ijengsci.2015.11.003
  49. Ghayesh, M.H., Farokhi, H. and Gholipour, A. (2017), "Vibration analysis of geometrically imperfect three-layered sheardeformable microbeams", Int. J. Mech. Sci., 122, 370-383. https://doi.org/10.1016/j.ijmecsci.2017.01.001
  50. Gholipour, A., Farokhi, H. and Ghayesh, M.H. (2015), "In-plane and out-of-plane nonlinear size-dependent dynamics of microplates", Nonlinear Dyn., 79, 1771-1785. https://doi.org/10.1007/s11071-014-1773-7
  51. Guo, H., Cao, S., Yang, T. and Chen, Y. (2018), "Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method", Int. J. Mech. Sci., 142, 610-621. https://doi.org/10.1016/j.ijmecsci.2018.05.029
  52. Hashemi, S.H. and Samaei, A.T. (2011), "Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory", Physica E, 43(7), 1400-1404. https://doi.org/10.1016/j.physe.2011.03.012
  53. Hosseini, S.M. and Zhang, C. (2018), "Elastodynamic and wave propagation analysis in a FG graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel Compos. Struct., Int. J., 27(3), 255-271. https://doi.org/10.12989/scs.2018.27.3.255
  54. Hosseini, M., Gorgani, H.H., Shishesaz, M. and Hadi, A. (2017), "Size-dependent stress analysis of single-wall carbon nanotube based on strain gradient theory", Int. J. App. Mech., 9(6), 1750087. https://doi.org/10.1142/S1758825117500879
  55. Hussein, A. and Kim, B. (2018), "Graphene/polymer nanocomposites: The active role of the matrix in stiffening mechanics", Compos. Struct., 202, 170-181. https://doi.org/10.1016/j.compstruct.2018.01.023
  56. Karami, B., Janghorban, M. and Li, L. (2018), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  57. Kazemirad, S., Ghayesh, M.H. and Amabili, M. (2012), "Thermomechanical nonlinear dynamics of a buckled axially moving beam", Arch App. Mech., 83(1), 25-42. https://doi.org/10.1007/s00419-012-0630-8
  58. Kiani, Y. (2017), "Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation", Comput. Method. Appl. M., 332, 86-101. https://doi.org/10.1016/j.cma.2017.12.015
  59. Korobeynikov, S.N., Alyokhin, V.V. and Babichev, A.V. (2018), "On the molecular mechanics of single layer graphene sheets", Int. J. Eng. Sci., 133, 109-131. https://doi.org/10.1016/j.ijengsci.2018.09.001
  60. Kumar, D. and Srivastava, A. (2016), "Elastic properties of CNTand graphene-reinforced nanocomposites using RVE", Steel Compos. Struct., Int. J., 21(5), 1085-1103. https://doi.org/10.12989/scs.2016.21.5.1085
  61. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021
  62. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  63. Liu, H., Lv, Z. and Wu, H. (2018), "Nonlinear free vibration of geometrically imperfect functionally graded sandwich nanobeams based on nonlocal strain gradient theory", Compos. Struct., 214, 47-61. https://doi.org/10.1016/j.compstruct.2019.01.090
  64. Lu, L., Guo, X. and Zhao, J. (2017a), "A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms", Int. J. Eng. Sci., 119, 265-277. https://doi.org/10.1016/j.ijengsci.2017.06.024
  65. Lu, L., Guo, X. and Zhao, J. (2017b), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006
  66. Ma, H.M., Gao, X.L. and Reddy, J.N. (2008), "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solid., 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  67. Malikan, M. and Nguyen, V.B. (2018), "Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory", Physica E., 102, 8-28. https://doi.org/10.1016/j.physe.2018.04.018
  68. Malikan, M., Nguyen, V.B. and Tornabene, F. (2018), "Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory", Mater. Res. Express, 5(7), 075031. https://doi.org/10.1088/2053-1591/aad144
  69. Mcfarland, A.W. and Colton, J.S. (2005), "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng., 15(5), 1060-1067. https://doi.org/10.1088/0960-1317/15/5/024
  70. Meyer, J.C., Geim, A.K., Katsnelson, M.I., Novoselov, K.S., Booth, T.J. and Roth, S. (2007), "The structure of suspended graphene sheets", Nature, 446, 60-63. https://doi.org/10.1038/nature05545
  71. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2018a), "Postbuckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technol., 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3
  72. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2018b), "Transient response of porous fg nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", Eur. J. Mech. A-Solid., 74, 210-220. https://doi.org/10.1016/j.euromechsol.2018.11.004
  73. Mirjavadi, S.S., Forsat, M., Hamouda, A.M.S. and Barati, M.R. (2019), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552
  74. Nematollahi, M.S. and Mohammadi, H. (2019), "Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory", Int. J. Mech. Sci., 156, 31-45. https://doi.org/10.1016/j.ijmecsci.2019.03.022
  75. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A.A. (2004), "Electric field effect in atomically thin carbon films", Science, 306(5696), 666-669. https://doi.org/10.1126/science.1102896
  76. Pradhan, S.C. (2009), "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", Phys. Lett. A, 373(45), 4182-4188. https://doi.org/10.1016/j.physleta.2009.09.021
  77. Pradhan, S.C. and Murmu, T. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Compos. Mater. Sci., 47(1), 268-274. https://doi.org/10.1016/j.commatsci.2009.08.001
  78. Sadeghirad, A., Su, N. and Liu, F. (2015), "Mechanical modeling of graphene using the three-layer-mesh bridging domain method", Comput. Method. Appl. Mech. Eng., 294, 278-298. https://doi.org/10.1016/j.cma.2015.06.001
  79. Sahmani, S. and Aghdam, M.M. (2017a), "Nonlinear instability of hydrostatic pressurized hybrid FGM exponential shear deformable nanoshells based on nonlocal continuum elasticity", Compos. Part B: Eng., 114, 404-417. https://doi.org/10.1016/j.compositesb.2017.01.038
  80. Sahmani, S. and Aghdam, M.M. (2017b), "Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells", Compos. Part B Eng., 132, 258-274. https://doi.org/10.1016/j.compositesb.2017.09.004
  81. Sahmani, S., Bahrami, M. and Aghdam, M.M. (2015), "Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions", Int. J. Mech. Sci., 100, 1-22. https://doi.org/10.1016/j.ijmecsci.2015.06.004
  82. Sahmani, S., Bahrami, M. and Aghdam, M.M. (2016), "Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to axial compression", Int. J. Eng. Sci., 99, 92-106. https://doi.org/10.1016/j.ijengsci.2015.10.010
  83. Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", Int. J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004
  84. Shahsavari, D., Karami, B. and Mansouri, S. (2017), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech. A-Solid., 67(C), 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  85. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3d shear deformation theory", Acta Mech., 229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7
  86. She, G.L., Yuan, F.G. and Ren, Y.R. (2017a), "Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory", Compos. Struct., 165, 74-82. https://doi.org/10.1016/j.compstruct.2017.01.013
  87. She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017b), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005
  88. She, G.L., Yuan, F.G. and Ren, Y.R. (2017c), "Research on nonlinear bending behaviors of FGM infinite cylindrical shallow shells resting on elastic foundations in thermal environments", Compos. Struct., 170, 111-121. https://doi.org/10.1016/j.compstruct.2017.03.010
  89. She, G.L., Yuan, F.G. and Ren, Y.R. (2017d), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357. https://doi.org/10.1016/j.apm.2017.03.014
  90. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005
  91. Shen, H.S. (2007), "Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties", Int. J. Mech. Sci., 49(4), 466-478. https://doi.org/10.1016/j.ijmecsci.2006.09.011
  92. Shen, H.S. (2013), A two-step perturbation method in nonlinear analysis of beams, plates and shells, Higher Education Press.
  93. Shen, H.S. and Zhang, J.W. (1988), "Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression", App. Math. Mech., 9(8), 793-804. https://doi.org/10.1007/BF02465403
  94. Shen, H.S., Xiang, Y., Lin, F. and Hui, D. (2017), "Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments", Compos. Part B Eng., 119, 67-78. https://doi.org/10.1016/j.compositesb.2017.03.020
  95. Shen, H.S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear bending analysis of FG-GRC laminated cylindrical panels on elastic foundations in thermal environments", Compos. Part B: Eng., 15, 148-157. https://doi.org/10.1016/j.compositesb.2017.12.048
  96. Singh, S. and Patel, B.P. (2018), "A computationally efficient multiscale finite element formulation for dynamic and postbuckling analyses of carbon nanotubes", Comput. Struct., 195, 126-144. https://doi.org/10.1016/j.compstruc.2017.10.003
  97. Soleimani, A., Dastani, K., Hadi, A. and Naei, M.H. (2019), "Effect of out-of-plane defects on the postbuckling behavior of graphene sheets based on nonlocal elasticity theory", Steel Compos. Struct., Int. J., 30(6), 517-534. https://doi.org/10.12989/scs.2019.30.6.517
  98. Tahouneh, V., Naei, M.H. and Mashhadi, M.M. (2018), "The effects of temperature and vacancy defect on the severity of the SLGS becoming anisotropic", Steel Compos. Struct., Int. J., 29, 647-657. https://doi.org/10.12989/scs.2018.29.5.647
  99. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124301. https://doi.org/10.1063/1.2141648
  100. Wang, J., Xie, H. and Guo, Z. (2017), "First-principles investigation on thermal properties and infrared spectra of imperfect graphene", Appl. Therm. Eng., 116, 456-462. https://doi.org/10.1016/j.applthermaleng.2016.12.087
  101. Wang, Y., Feng, C., Zhao, Z. and Yang, J. (2018), "Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL)", Compos. Struct., 202, 38-46. https://doi.org/10.1016/j.compstruct.2017.10.005
  102. Wu, C.P. and Chen, Y.J. (2018), "Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium", Int. J. Struct. Stab. Dyn., 19(4), 1950035. https://doi.org/10.1142/S0219455419500354
  103. Wu, X., Mu, F., Wang, Y. and Zhao, H. (2018), "Application of atomic simulation methods on the study of graphene nanostructure fabrication by particle beam irradiation: A review", Compos. Mater. Sci., 149, 98-106. https://doi.org/10.1016/j.commatsci.2018.03.022
  104. Xu, X.J., Zheng, M.L. and Wang, X.C. (2017), "On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics", Int. J. Eng. Sci., 119, 217-231. https://doi.org/10.1016/j.ijengsci.2017.06.025
  105. Yan, J.W. and Lai, S.K. (2018), "Superelasticity and wrinkles controlled by twisting circular graphene", Comput. Method. Appl. Mech. Eng., 338, 634-656. https://doi.org/10.1016/j.cma.2018.04.049
  106. Yang, J., Wu, H. and Kitipornchai, S. (2016), "Buckling and postbuckling of functionally graded multilayer graphene plateletreinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048
  107. Yang, J., Dong, J. and Kitipornchai, S. (2018a), "Unilateral and bilateral buckling of functionally graded corrugated thin plates reinforced with graphene nanoplatelets", Compos. Struct., 209, 789-801. https://doi.org/10.1016/j.compstruct.2018.11.025
  108. Yang, Z., Liew, K.M. and Hui, D. (2018b), "Characterizing nonlinear vibration behavior of bilayer graphene thin films", Compos. Part B Eng., 145, 197-205. https://doi.org/10.1016/j.compositesb.2018.03.004
  109. Yengejeh, S.I., Kazemi, S.A., Ivasenko, O. and O chsner, A. (2017), "Simulations of Graphene Sheets Based on the Finite Element Method and Density Functional Theory: Comparison of the Geometry Modeling under the Influence of Defects", J. Nano. Res-sew., 47, 128-135. https://doi.org/10.4028/www.scientific.net/JNanoR.47.128
  110. Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to timedependent heat flux", Steel Compos. Struct., Int. J., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909
  111. Zhan, H.Z., Yang, F.P. and Wang, X. (2018), "Nonlinear dynamic characteristics of bi-graphene sheets/piezoelectric laminated films considering high order van der Walls force and scale effect", Appl. Math. Model., 56, 289-303. https://doi.org/10.1016/j.apm.2017.11.038
  112. Zhang, J., Zhang, W., Ragab, T. and Basaran, C. (2018), "Mechanical and electronic properties of graphene nanomesh heterojunctions", Comp. Mater. Sci., 153, 64-72. https://doi.org/10.1016/j.commatsci.2018.06.026
  113. Zhu, X. and Li, L. (2017), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019

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