DOI QR코드

DOI QR Code

Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle

  • Tayeb, Tayeb Si (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science University of Sidi Bel Abbes) ;
  • Zidour, Mohamed (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science University of Sidi Bel Abbes) ;
  • Bensattalah, Tayeb (Universite of tiaret) ;
  • Heireche, Houari (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science University of Sidi Bel Abbes) ;
  • Benahmed, Abdelillah (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science University of Sidi Bel Abbes) ;
  • Bedia, E.A. Adda (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2019.07.19
  • 심사 : 2019.10.21
  • 발행 : 2020.02.25

초록

The incorporation of carbon nanotubes in a polymer matrix makes it possible to obtain nanocomposite materials with exceptional properties. It's in this scientific background that this work was based. There are several theories that deal with the behavior of plates, in this research based on the Mindlin-Reissner theory that takes into account the transversal shear effect, for analysis of the critical buckling load of a reinforced polymer plate with parabolic distribution of carbon nanotubes. The equations of the model are derived and the critical loads of linear and parabolic distribution of carbon nanotubes are obtained. With different disposition of nanotubes of carbon in the polymer matrix, the effects of different parameters such as the volume fractions, the plate geometric ratios and the number of modes on the critical load buckling are analysed and discussed. The results show that the critical buckling load of parabolic distribution is larger than the linear distribution. This variation is attributed to the concentration of reinforcement (CNTs) at the top and bottom faces for the X-CNT type which make the plate more rigid against buckling.

키워드

과제정보

연구 과제 주관 기관 : Directorate General for Scientific Research and Technological Development (DGRSDT)

Authors would like to acknowledge the support provided by the Directorate General for Scientific Research and Technological Development (DGRSDT).

참고문헌

  1. Abdelaziz, H.H., Ait Amar Meziane, M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. 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. Abualnour, M., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Addou, F.Y., Meradjah, M., M.A.A, Bousahla, Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, Int. J., 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347
  4. Ait Atmane, H, Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x
  5. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  6. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magnetoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  7. Anumandla, V. and Gibson, R.F. (2006), "A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites", Compos. Part A: Appl. Sci. Manuf., 37(12), 2178-2185. https://doi.org/10.1016/j.compositesa.2005.09.016
  8. Asadi, H. and Beheshti, A.R. (2018), "On the nonlinear dynamic responses of FG-CNTRC beams exposed to aerothermal loads using third- order piston theory", Acta Mechanica, 229(6), 2413-2430. https://doi.org/10.1007/s00707-018-2121-7
  9. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  10. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453
  11. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  12. Avcar, M. and Alwan, A.S. (2017), "Free vibration of functionally graded Rayleigh beam", Int. J. Eng. Appl. Sci., 9(2), 127-127. https://doi.org/10.24107/ijeas.322884
  13. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2
  14. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (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
  15. 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
  16. Barber, A.H., Cohen, S.R. and Wagner, H.D. (2003), "Measurement of carbon nanotube-polymer interfacial strength", Appl. Phys. Lett., 82, 4140-4142. https://doi.org/10.1063/1.1579568
  17. Beik Mohammadlou, H. and Ekhteraei Toussi, H. (2017), "Parametric studies on elastoplastic buckling of rectangular FGM thin plates", Aerosp. Sci. Technol., 69, 513-525. https://doi.org/10.1016/j.ast.2017.07.015
  18. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., Int. J., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103
  19. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  20. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257
  21. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "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
  22. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., Int. J., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
  23. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Int. J., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019
  24. Berghouti, H., Adda Bedia, E.A. Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  25. Biercuk, M.J., Llaguno, M.C., Radosavljevic, M., Hyun, J.K., Johnson, A.T. and Fischer, J.E. (2002), "Carbon nanotube composites for thermal management", Appl. Phys. Lett., 80(15), 2767-2769. https://doi.org/10.1063/1.1469696
  26. Bonnet, P., Sireude, D., Garnier, B. and Chauvet, O. (2007), "Thermal properties and percolation in carbonnanotube-polymer composites", J. Appl. Phys., 91, 2019-2010. https://doi.org/10.1063/1.2813625
  27. 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
  28. Bouanati, S., Benrahou, K.H., Ait Atmane, H., Ait Yahia, S., Bernard, F., Tounsi, A. and Adda Bedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., Int. J., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085
  29. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (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
  30. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  31. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  32. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  33. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  34. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  35. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., Int. J., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  36. 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
  37. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  38. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., Int. J., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197
  39. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191
  40. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  41. Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., Int. J., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193
  42. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1
  43. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  44. Civalek, O. (2017), "Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method", Compos. Part B: Eng., 111, 45-59. https://doi.org/10.1016/j.compositesb.2016.11.030
  45. Cooper, C.A., Cohen, S.R., Barber, A.H. and Wagner, H.D. (2002), "Detachment of nanotubes from a polymer matrix", Appl. Phys. Lett., 81, 3873-3875. https://doi.org/10.1063/1.1521585
  46. Daouadji, T.H. and Adim, B. (2016), "An analytical approach for buckling of functionally graded plates", Adv. Mater. Res., Int. J., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141
  47. Diamanti, K. and Soutis, C. (2010), "Structural health monitoring techniques for aircraft composite structures", Prog. Aerosp. Sci., 46(8), 342-352. https://doi.org/10.1016/j.paerosci.2010.05.001
  48. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  49. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  50. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  51. Ebrahimi, F. and Jafari, A. (2016), "A four-variable refined sheardeformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities", Mech. Adv. Mater. Struct., 25(3), 12-224. http://dx.doi.org/10.1080/15376494
  52. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., Int. J., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141
  53. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585
  54. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Des., 28, 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  55. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., Int. J., 13(3), 385-410. https://doi.org/10.12989/gae.2017.13.3.385
  56. Fellah, M., Draiche, K., Houar, M.S.A., Tounsi, A., Saeed, T., Alhodaly, M.S. and Benguediab, M. (2019), "A novel refined shear deformation theory for the buckling analysis of thick isotropic plates", Struct. Eng. Mech., Int. J., 69(3), 335-345. https://doi.org/10.12989/sem.2019.69.3.335
  57. Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A: Appl. Sci. Manuf., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  58. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., Int. J., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109
  59. Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer carbon nanotube composites", Comput. Meth. Appl. Mech. Eng., 193, 1773-1788. https://doi.org/10.1016/j.cma.2003.12.025
  60. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., Int. J., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115
  61. Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., Int. J., 6(4), 299-321. https://doi.org/10.12989/anr.2018.6.4.299
  62. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39, 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  63. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636219845841
  64. Hwang, J.T. and Steeves, C.A. (2015), "Optimization of 3D lattice cores in composite sandwich structures", J. Compos. Mater., 49(17), 2041-2055. https://doi.org/10.1177/0021998314541537
  65. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  66. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621
  67. Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., 55, 42-56. https://doi.org/10.4028/www.scientific.net/JNanoR.55.42
  68. Kar, V.R. and Panda, S.K. (2016), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014
  69. Kar, V.R. and Panda, S.K. (2017), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Thermal Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  70. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., Int. J., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  71. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  72. 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
  73. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018a), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 233(1), 287-301. https://doi.org/10.1177/0954406218756451
  74. Karami, B., Shahsavari, D. and Janghorban, M. (2018b), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  75. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  76. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018d), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099
  77. Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201
  78. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019a), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036
  79. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., Int. J., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487
  80. Karami, B., Janghorban, M. and Tounsi, A. (2019c), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., Int. J., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055
  81. Karami, B., Janghorban, M. and Tounsi, A. (2019d), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9
  82. Katariya, P.V. and Panda, S.K. (2014), "Thermo-Mechanical Stability Analysis of Composite Cylindrical Panels", Proceedings of ASME 2013 Gas Turbine India Conference, American Society of Mechanical Engineers Digital Collection.
  83. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp. Technol.: Int. J., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  84. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017a), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595
  85. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017b), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., Int. J., 6(4), 349-361. https://doi.org/10.12989/amr.2017.6.4.349
  86. Katariya, P.V., Das, A. and Panda, S.K. (2018), "Buckling analysis of SMA bonded sandwich structure-using FEM", Proceedings of IOP Conference Series: Materials Science and Engineering (Vol. 338, No. 1, p. 012035), IOP Publishing. https://doi.org/10.1088/1757-899X/338/1/012035
  87. Katnam, K.B., Da Silva, L.F.M. and Young, T.M. (2013), "Bonded repair of composite aircraft structures: Areview of scientific challenges and opportunities", Prog. Aerosp. Sci., 61, 26-42. https://doi.org/10.1016/j.paerosci.2013.03.003
  88. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a fourvariable quasi 3D HSDT", Eng. Comput. https://doi.org/10.1007/s00366-019-00732-1
  89. Kolahchi, R. (2017), "A comparative study on the bending,vibration and buckling of viscoelastic sandwich nanoplatesbased on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248 https://doi.org/10.1016/j.ast.2017.03.016
  90. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017), "Optimization of dynamic buckling for sandwichnanocomposite plates with sensor and actuator layer based onsinusoidal-viscopiezoelasticity theories using grey wolf algorithm", J. Sandw. Struct. Mater., 22(1), 3-27. https://doi.org/10.1177/1099636217731071
  91. Lei, Z.X., Liew, K.M. and Yu, J.L. (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
  92. Li, X., Gao, H., Scrivens, W.A., Fei, D., Xu, X., Sutton, M.A., Reynolds, A.P. and Myrick, M.L. (2007), "Reinforcing mechanisms of single-walled carbon nanotube-reinforced polymer composites", J. Nanosci. Nanotech., 7(7), 2309-2317. https://doi.org/10.1166/jnn.2007.410
  93. Ma, R.Z., Wu, J., Wei, B.Q., Liang, J. and Wu, D.H. (1998), "Processing and properties of carbon nanotubes-nano SiC ceramics", J. Mater. Sci., 33, 5243-5246. https://doi.org/10.1023/A:1004492106337
  94. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  95. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577
  96. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., Int. J., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  97. Mehar, K. and Panda, S.K. (2017), "Thermoelastic analysis of FGCNT reinforced shear deformable composite plate under various loading", Int. J. Computat. Methods, 14(2), 1750019. https://doi.org/10.1142/S0219876217500190
  98. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., Int. J., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181
  99. Mehar, K., Panda, S.K. and Patle, B.K. (2017), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466
  100. 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
  101. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443
  102. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (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
  103. 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. https://doi.org/10.1177/1099636214526852
  104. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", Meccanica, 51(9), 2185-2201. https://doi.org/10.1007/s11012-015-0348-0
  105. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397
  106. Nethercot, D.A. and Kirby, P.A. (1979), Design for Structural Stability, John Wiley and Sons, New York.
  107. Nethercot, D.A. and Trahair, N.S. (1976), "Lateral buckling approximations for elastic beams", Struct. Engr., 54, 197-204.
  108. Odegard, G.M., Gates, T.S., Wise, K.E., Park, C. and Siochi, E.J. (2003), "Constitutive modelling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63, 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0
  109. Ould Youcef, D., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., Int. J., 3(4), 177-191. https://doi.org/10.12989/anr.2015.3.4.177
  110. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Computat. Mathe., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  111. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004
  112. Panda, S.K. and Singh, B.N. (2010), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  113. Panda, S.K. and Singh, B.N. (2013a), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  114. Panda, S.K. and Singh, B.N. (2013b), "Thermal Postbuckling Behavior of Laminated Composite Spherical Shell Panel Using NFEM#", Mech. Based Des. Struct. Mach., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  115. Panda, S.K., Mahapatra, T.R. and Kar, V.R. (2017), Nonlinear Finite Element Solution of Post-buckling Responses of FGM Panel Structure under Elevated Thermal Load and TD and TID Properties.
  116. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., Int. J., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061
  117. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), Taylor & Francis eBooks, CRC Press.
  118. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082
  119. Seidel, G.D. and Lagoudas, D.C. (2006), "Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38(8-10), 884-907. https://doi.org/10.1016/j.mechmat.2005.06.029
  120. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., Int. J., 64(6), 737-749. https://doi.org/10.12989/sem.2017.64.6.737
  121. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  122. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  123. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  124. Shokravi, M. (2017a), "Buckling of sandwich plates with FG-CNT reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., Int. J., 23(6), 623-631. https://doi.org/10.12989/scs.2017.23.6.623
  125. Shokravi, M. (2017b), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., Int. J., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327
  126. Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102
  127. Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation", Engineering, 2(4), 228-236. https://doi.org/10.4236/eng.2010.24033
  128. Thess, A., Lee, R., Nikolaev, P., Dai, H., Petit, P., Robert, J., Xu, C., Lee, Y.H., Kim, S.G., Rinzler, A.G. and Colbert, D.T. (1996), "Crystalline ropes of metallic carbon nanotubes", Science, 273(5274), 483-487. https://doi.org/10.1126/science.273.5274.483
  129. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A. Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637
  130. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  131. Van Lier, G., Van Alsenoy, C., Van Doren, V. and Geerlings, P. (2000), "Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene", Chem. Phys. Lett., 326(1-2), 181-185. https://doi.org/10.1016/S0009-2614(00)00764-8
  132. Vodenitcharova, T. and Zhang, L.C. (2006), "Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube", Int. J. Solids Struct., 43, 3006-3024. https://doi.org/10.1016/j.ijsolstr.2005.05.014
  133. Wan, H., Delale, F. and Shen, L. (2005), "Effect of CNT length and CNT-matrix inter phase in carbon nanotube (CNT) reinforced composites", Mech. Res. Commun., 32, 481-489. https://doi.org/10.1016/j.mechrescom.2004.10.011
  134. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50, 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005
  135. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotubereinforced composite plates with Pasternak elastic foundation", Appl. Mathe. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058
  136. Wu, H., Kitipornchai, S. and Yang, J. (2016), "Thermo-electromechanical postbuckling of piezoelectric FG-CNTRC beams with geometric imperfections", Smart Mater. Struct., 25(9), 095022. https://doi.org/10.1088/0964-1726/25/9/095022
  137. 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
  138. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., Int. J., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065
  139. Younsi, A., Tounsi, A, Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., Int. J., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519
  140. Yu, M.F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F. and Ruoff, R.S. (2000), "Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load", Science, 287(5453), 637-640. https://doi.org/10.1126/science.287.5453.637
  141. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  142. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  143. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element- free approach", Compos. Part B: Eng., 75, 36-46. https://doi.org/10.1016/j.compositesb.2015.01.033
  144. Zhu, P., Lei, Z.X. 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
  145. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., Int. J., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125

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