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Thermal buckling analysis of embedded graphene-oxide powder-reinforced nanocomposite plates

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Nouraei, Mostafa (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Dabbagh, Ali (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Rabczuk, Timon (Institute of Structural Mechanics (ISM), Bauhaus-University Weimar)
  • Received : 2018.12.29
  • Accepted : 2019.05.08
  • Published : 2019.09.25

Abstract

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

Keywords

thermal buckling;graphene oxide powder;refined higher-order plate theory;elastic foundations

References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693
  2. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., Int. J., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195 https://doi.org/10.12989/sem.2013.48.2.195
  3. Anlas, G. and Goker, G. (2001), "Vibration analysis of skew fibre-reinforced composite laminated plates", J. Sound Vib., 242, 265-276. https://doi.org/10.1006/jsvi.2000.3366 https://doi.org/10.1006/jsvi.2000.3366
  4. Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods", J. Mech. Sci. Technol., 25, 809-820. https://doi.org/10.1007/s12206-011-0127-3 https://doi.org/10.1007/s12206-011-0127-3
  5. Arefi, M., Bidgoli, E.M.-R., Dimitri, R., Bacciocchi, M. and Tornabene, F. (2019), "Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets", Compos. Part B: Eng., 166, 1-12. https://doi.org/10.1021/nl0731872 https://doi.org/10.1016/j.compositesb.2018.11.092
  6. Bakhadda, B., Bouiadjra, M.B., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., Int. J., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311
  7. Balandin, A.A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F. and Lau, C.N. (2008), "Superior thermal conductivity of single-layer graphene", Nano Letters, 8, 902-907. https://doi.org/10.1021/nl0731872 https://doi.org/10.1021/nl0731872
  8. Baltacioglu, A., Civalek, O., Akgoz, B. and Demir, F. (2011), "Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution", Int. J. Press. Vessels Pip., 88, 290-300. https://doi.org/10.1016/j.ijpvp.2011.06.004 https://doi.org/10.1016/j.ijpvp.2011.06.004
  9. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., Int. J., 5(4), 393-414. https://doi.org/10.12989/anr.2017.5.4.393 https://doi.org/10.21474/IJAR01/4731
  10. Barati, M.R. and Zenkour, A.M. (2017), "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 https://doi.org/10.1016/j.compstruct.2017.08.082
  11. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695
  12. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
  13. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., Int. J., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061
  14. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  15. Cai, W., Moore, A.L., Zhu, Y., Li, X., Chen, S., Shi, L. and Ruoff, R.S. (2010), "Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition", Nano Lett., 10, 1645-1651. https://doi.org/10.1021/nl9041966 https://doi.org/10.1021/nl9041966
  16. Ebrahimi, F. and Barati, M.R. (2016a), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 7(3), 119-143. https://doi.org/10.1080/19475411.2016.1223203 https://doi.org/10.1080/19475411.2016.1223203
  17. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177/1077546316646239 https://doi.org/10.1177/1077546316646239
  18. Ebrahimi, F. and Barati, M.R. (2016c), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9 https://doi.org/10.1007/s00339-016-0441-9
  19. Ebrahimi, F. and Barati, M.R. (2016d), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014 https://doi.org/10.1088/0964-1726/25/10/105014
  20. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intel. Mater. Syst. Struct., 28(11), 1472-1490. https://doi.org/10.1177/1045389X16672569 https://doi.org/10.1177/1045389X16672569
  21. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4 https://doi.org/10.1007/s13369-015-1930-4
  22. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y https://doi.org/10.1140/epjp/i2016-16279-y
  23. Ebrahimi, F." and Barati, M.R. (2016h), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18. https://doi.org/10.1007/s00339-016-0001-3
  24. Ebrahimi, F. and Barati, M.R. (2016i), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2 https://doi.org/10.1007/s00339-016-0322-2
  25. Ebrahimi, F. and Barati, M.R. (2016j), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001 https://doi.org/10.1016/j.ijengsci.2016.08.001
  26. Ebrahimi, F. and Barati, M.R. (2016k), "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
  27. Ebrahimi, F. and Barati, M.R. (2016l), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 39(3), 937-952. https://doi.org/10.1007/s40430-016-0551-5 https://doi.org/10.1007/s40430-016-0551-5
  28. Ebrahimi, F. and Barati, M.R. (2016m), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16238-8 https://doi.org/10.1140/epjp/i2016-16001-3
  29. Ebrahimi, F. and Barati, M.R. (2016n), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11. https://doi.org/10.1017/jmech.2016.46
  30. Ebrahimi, F. and Barati, M.R. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058 https://doi.org/10.1016/j.compstruct.2016.09.058
  31. Ebrahimi, F. and Barati, M.R. (2019), "On static stability of electro-magnetically affected smart magneto-electro-elastic nanoplates", Adv. Nano Res., Int. J., 7(1), 63-75. https://doi.org/10.12989/anr.2019.7.1.063
  32. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293. https://doi.org/10.1016/j.compstruct.2016.11.058
  33. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24, 820-829. https://doi.org/10.1080/15376494.2016.1196786 https://doi.org/10.1080/15376494.2016.1196786
  34. Ebrahimi, F. and Haghi, P. (2018a), "Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment", Adv. Nano Res., Int. J., 6(3), 201-217. https://doi.org/10.12989/anr.2018.6.3.201 https://doi.org/10.21474/IJAR01/7662
  35. Ebrahimi, F. and Haghi, P. (2018b), "A nonlocal strain gradient theory for scale-dependent wave dispersion analysis of rotating nanobeams considering physical field effects", Coupl. Syst. Mech., Int. J., 7(4), 373-393. https://doi.org/10.12989/csm.2018.7.4.373
  36. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Thermal Stresses, 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684 https://doi.org/10.1080/01495739.2016.1160684
  37. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16160-1 https://doi.org/10.1140/epjp/i2016-16001-3
  38. Ebrahimi, F. and Rostami, P. (2018), "Wave propagation analysis of carbon nanotube reinforced composite beams", Eur. Phys. J. Plus, 133, 285. https://doi.org/10.1140/epjp/i2018-12069-y https://doi.org/10.1140/epjp/i2018-12069-y
  39. 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 https://doi.org/10.1016/j.ijengsci.2016.07.008
  40. Ebrahimi, F., Barati, M.R. and Haghi, P. (2018a), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, 24, 3809-3818. https://doi.org/10.1177/1077546317711537 https://doi.org/10.1177/1077546317711537
  41. Ebrahimi, F., Haghi, P. and Zenkour, A.M. (2018b), "Modelling of thermally affected elastic wave propagation within rotating Mori-Tanaka-based heterogeneous nanostructures", Microsyst. Technol., 24, 2683-2693. https://doi.org/10.1007/s00542-018-3800-y https://doi.org/10.1007/s00542-018-3800-y
  42. Ebrahimi, F., Dehghan, M. and Seyfi, A. (2019), "Eringen's nonlocal elasticity theory for wave propagation analysis of magneto-electro-elastic nanotubes", Adv. Nano Res., Int. J., 7(1), 1-11. https://doi.org/10.12989/anr.2019.7.1.001
  43. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)", Compos. Part B: Eng., 110, 132-140. https://doi.org/10.1016/j.compositesb.2016.11.024 https://doi.org/10.1016/j.compositesb.2016.11.024
  44. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020 https://doi.org/10.1016/j.jsv.2009.11.020
  45. Gomez-Navarro, C., Burghard, M. and Kern, K. (2008), "Elastic properties of chemically derived single graphene sheets", Nano Letters, 8, 2045-2049. https://doi.org/10.1021/nl801384y https://doi.org/10.1021/nl801384y
  46. Kant, T. and Babu, C. (2000), "Thermal buckling analysis of skew fibre-reinforced composite and sandwich plates using shear deformable finite element models", Compos. Struct., 49, 77-85. https://doi.org/10.1016/S0263-8223(99)00127-0 https://doi.org/10.1016/S0263-8223(99)00127-0
  47. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361
  48. Kiani, Y. (2019), "Buckling of functionally graded graphene reinforced conical shells under external pressure in thermal environment", Compos. Part B: Eng., 156, 128-137. https://doi.org/10.1016/j.compstruct.2012.11.006 https://doi.org/10.1016/j.compositesb.2018.08.052
  49. Lei, Z., Liew, K. and Yu, J. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006 https://doi.org/10.1016/j.compstruct.2012.11.006
  50. Liew, K., Lei, Z., Yu, J. and Zhang, L. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Methods Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001 https://doi.org/10.1016/j.cma.2013.09.001
  51. Liu, G., Chen, X. and Reddy, J. (2002), "Buckling of symmetrically laminated composite plates using the element-free Galerkin method", Int. J. Struct. Stabil. Dyn., 2, 281-294. https://doi.org/10.1142/S0219455402000634 https://doi.org/10.1142/S0219455402000634
  52. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002 https://doi.org/10.1016/j.compstruct.2019.03.002
  53. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157
  54. Mikoushkin, V., Shnitov, V., Nikonov, S.Y., Dideykin, A., Vul, A.Y., Sakseev, D., Vyalikh, D. and Vilkov, O.Y. (2011), "Controlling graphite oxide bandgap width by reduction in hydrogen", Techn. Phys. Lett., 37, 942. https://doi.org/10.1134/S1063785011100257 https://doi.org/10.1134/S1063785011100257
  55. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52, 5-25. https://doi.org/10.1016/j.polymer.2010.11.042 https://doi.org/10.1016/j.polymer.2010.11.042
  56. Pradhan, S.C. and Phadikar, J.K. (2011), "Nonlocal theory for buckling of nanoplates", Int. J. Struct. Stabil. Dyn., 11(3), 411-429. https://doi.org/10.1142/S021945541100418X https://doi.org/10.1142/S021945541100418X
  57. Qaderi, S., Ebrahimi, F. and Seyfi, A. (2019), "An investigation of the vibration of multi-layer composite beams reinforced by graphene platelets resting on two parameter viscoelastic foundation", SN Applied Sciences, 1, 399. https://doi.org/10.1007/s42452-019-0252-7 https://doi.org/10.1007/s42452-019-0252-7
  58. Qiao, P., Zou, G. and Davalos, J.F. (2003), "Flexural-torsional buckling of fiber-reinforced plastic composite cantilever I-beams", Compos. Struct., 60, 205-217. https://doi.org/10.1016/S0263-8223(02)00304-5 https://doi.org/10.1016/S0263-8223(02)00304-5
  59. Safarpour, H., Ghanbari, B. and Ghadiri, M. (2019), "Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell", Appl. Math. Model., 65, 428-442. https://doi.org/10.1016/j.apm.2018.08.028 https://doi.org/10.1016/j.apm.2018.08.028
  60. Shan, L. and Qiao, P. (2005), "Flexural-torsional buckling of fiber-reinforced plastic composite open channel beams", Compos. Struct., 68, 211-224. https://doi.org/10.1016/j.compstruct.2004.03.015 https://doi.org/10.1016/j.compstruct.2004.03.015
  61. Shariyat, M. (2010), "A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads", Int. J. Mech. Sci., 52, 495-514. https://doi.org/10.1016/j.ijmecsci.2009.11.010 https://doi.org/10.1016/j.ijmecsci.2009.11.010
  62. Shen, H.-S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025
  63. Shen, H.-S. and Zhang, C.-L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31, 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048 https://doi.org/10.1016/j.matdes.2010.01.048
  64. Shen, H.-S., Xiang, Y. and Lin, F. (2017a), "Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments", Compos. Struct., 170, 80-90. https://doi.org/10.1016/j.compstruct.2017.03.001 https://doi.org/10.1016/j.compstruct.2017.03.001
  65. Shen, H.-S., Xiang, Y. and Lin, F. (2017b), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments", Comput. Methods Appl. Mech. Eng., 319, 175-193. https://doi.org/10.1016/j.matdes.2010.01.048 https://doi.org/10.1016/j.cma.2017.02.029
  66. Shojaee, S., Valizadeh, N., Izadpanah, E., Bui, T. and Vu, T.-V. (2012), "Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method", Compos. Struct., 94, 1677-1693. https://doi.org/10.1016/j.compstruct.2012.01.012 https://doi.org/10.1016/j.compstruct.2012.01.012
  67. Sobhani, A., Saeedifar, M., Najafabadi, M.A., Fotouhi, M. and Zarouchas, D. (2018), "The study of buckling and post-buckling behavior of laminated composites consisting multiple delaminations using acoustic emission", Thin-Wall. Struct., 127, 145-156. https://doi.org/10.1016/j.tws.2018.02.011 https://doi.org/10.1016/j.tws.2018.02.011
  68. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B: Eng., 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043 https://doi.org/10.1016/j.compositesb.2017.09.043
  69. Suk, J.W., Piner, R.D., An, J. and Ruoff, R.S. (2010), "Mechanical properties of monolayer graphene oxide", ACS Nano, 4, 6557-6564. https://doi.org/10.1021/nn101781v https://doi.org/10.1021/nn101781v
  70. Thai, C.H., Nguyen-Xuan, H., Nguyen-Thanh, N., Le, T.H., Nguyen-Thoi, T. and Rabczuk, T. (2012), "Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach", Int. J. Numer. Methods Eng., 91, 571-603. https://doi.org/10.1002/nme.4282 https://doi.org/10.1002/nme.4282
  71. Thai, C.H., Ferreira, A., Tran, T. and Phung-Van, P. (2019), "Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation", Compos. Struct., 220, 749-759. https://doi.org/10.1016/j.compstruct.2019.03.100 https://doi.org/10.1016/j.compstruct.2019.03.100
  72. Torabi, J., Ansari, R. and Hassani, R. (2019), "Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory", Eur. J. Mech.-A/Solids, 73, 144-160. https://doi.org/10.1016/j.euromechsol.2018.07.009 https://doi.org/10.1016/j.euromechsol.2018.07.009
  73. Tornabene, F., Fantuzzi, N., Viola, E. and Carrera, E. (2014), "Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method", Compos. Struct., 107, 675-697. https://doi.org/10.1016/j.compstruct.2013.08.038 https://doi.org/10.1016/j.compstruct.2013.08.038
  74. 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., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001 https://doi.org/10.12989/anr.2013.1.1.001
  75. Urthaler, Y. and Reddy, J. (2008), "A mixed finite element for the nonlinear bending analysis of laminated composite plates based on FSDT", Mech. Adv. Mater. Struct., 15, 335-354. https://doi.org/10.1080/15376490802045671 https://doi.org/10.1080/15376490802045671
  76. Van Es, M. (2001), "Polymer-clay nanocomposites", Ph.D. Thesis; Delft University, Delft, Netherlands.
  77. Wang, Z.-X. and Shen, H.-S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Computat. Mater. Sci., 50, 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005 https://doi.org/10.1016/j.commatsci.2011.03.005
  78. Wang, Q., Shi, D., Liang, Q. and Pang, F. (2017), "Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints", Appl. Math. Model., 46, 227-262. https://doi.org/10.1016/j.apm.2017.01.070 https://doi.org/10.1016/j.apm.2017.01.070
  79. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Computat. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028 https://doi.org/10.1016/j.commatsci.2013.01.028
  80. Wu, H., Yang, J. and Kitipornchai, S. (2016), "Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections", Compos. Part B: Eng., 90, 86-96. https://doi.org/10.1016/j.compositesb.2015.12.007 https://doi.org/10.1016/j.compositesb.2015.12.007
  81. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048 https://doi.org/10.1016/j.compstruct.2016.11.048
  82. Yas, M. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Vessels Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012 https://doi.org/10.1016/j.ijpvp.2012.07.012
  83. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015
  84. Zhang, L., Lei, Z. and Liew, K. (2015), "Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates", Compos. Struct., 122, 172-183. https://doi.org/10.1016/j.ijpvp.2012.07.012 https://doi.org/10.1016/j.compstruct.2014.11.070
  85. Zhang, Z., Li, Y., Wu, H., Zhang, H., Wu, H., Jiang, S. and Chai, G. (2018), "Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the first-order shear deformation theory", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1444216
  86. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, 799-808. https://doi.org/10.1016/j.compstruct.2017.08.044 https://doi.org/10.1016/j.compstruct.2017.08.044
  87. Zhen, W. and Wanji, C. (2006), "Free vibration of laminated composite and sandwich plates using global-local higher-order theory", J. Sound Vib., 298, 333-349. https://doi.org/10.1016/j.jsv.2006.05.022 https://doi.org/10.1016/j.jsv.2006.05.022
  88. Zhu, P., Lei, Z. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94, 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010 https://doi.org/10.1016/j.compstruct.2011.11.010