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Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation

  • Bakhadda, Boumediene (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Bouiadjra, Mohamed Bachir (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Bourada, Fouad (Departement de Genie Civil, Institut de Technologie, Centre Universitaire de Ain Temouchent) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2017.11.19
  • Accepted : 2018.02.02
  • Published : 2018.11.25
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Abstract

This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

Keywords

Acknowledgement

Supported by : Agency of Research in Science and Technology (ATRST)

References

  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., 5(6), 693-704.
  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. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct.Environ., 4(2), 59-64.
  4. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016) "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  5. Ait Amar Meziane, M., 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 boundaryconditions", J. Sandw. Struct. Mate., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  6. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A, (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  7. Ajayan, P.M., Stephen, O., Colliex, C. and Trauth, D. (1994), "Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite", Science, 256, 1212-1214.
  8. 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
  9. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded be am", Appl. Phys.A, 123, 296. https://doi.org/10.1007/s00339-017-0854-0
  10. Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  11. 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., (In press).
  12. 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., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  13. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  14. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  15. 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., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  16. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  17. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017b), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  18. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017a), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  19. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  20. Benadouda, M., AitAtmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/EAS.2017.13.3.255
  21. 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., 65(1), 19-31.
  22. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater.Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  23. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15, 671-703. https://doi.org/10.1177/1099636213498888
  24. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/SSS.2017.19.6.601
  25. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  26. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126 https://doi.org/10.12989/sss.2017.19.2.115
  27. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  28. Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  29. 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., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  30. 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., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  31. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  32. 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., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  33. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A.(2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  34. 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., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  35. 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., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  36. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  37. 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., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  38. Esawi, A.M. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Des., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  39. Fadelus, 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, 36, 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  40. 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., 13(3), 385-410. https://doi.org/10.12989/GAE.2017.13.3.385
  41. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014),"A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  42. Ghorbanpour Arani, A., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., 60(3), 489-505. https://doi.org/10.12989/sem.2016.60.3.489
  43. Griebel, M. and Hamaekers, J. (2004), "Moleculardynamics simulations of the elastic moduli of polymer carbon nanotube composites", Comput. Method. Appl. M., 193, 1773-1788. https://doi.org/10.1016/j.cma.2003.12.025
  44. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/SCS.2017.25.6.717
  45. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., (In press).
  46. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  47. 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
  48. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech.- ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  49. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  50. Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proc. R. Soc. A, 461, 1685-1710. https://doi.org/10.1098/rspa.2004.1422
  51. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/SCS.2017.25.3.361
  52. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A., S.R. Mahmoud, (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/SEM.2017.64.4.391
  53. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S.R. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., 63(4), 439-446. https://doi.org/10.12989/SEM.2017.63.4.439
  54. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based 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
  55. Kolahchi, R. and Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech., 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  56. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlinear Dynam., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x
  57. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  58. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017b), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., (In press).
  59. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  60. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017c), "Wave propagation of embedded viscoelastic FG-CNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039
  61. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017a), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Walled Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  62. Kolahchi, R.,Safari, M., Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Composite Structures, 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  63. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  64. Lau, A.K.T. and Hui, D. (2002), "The revolutionary creation of new advanced materials-carbon nanotube composites", Compos. Part B: Engineering, 33(4), 263-277. https://doi.org/10.1016/S1359-8368(02)00012-4
  65. Lau, K.T. et al. (2004), "Stretching process of single-and multiwalled carbon nanotubes for nanocomposite applications", Carbon, 42(2), 426-428. https://doi.org/10.1016/j.carbon.2003.10.040
  66. 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
  67. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  68. 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
  69. Mahmoud, S.R., Abd-Alla, A.M., Tounsi, A. and Marin, M. (2015), "The problem of wave propagation in magneto-rotating orthotropic non-homogeneous medium", J. Vib. Control, 21(16), 3281-3291. https://doi.org/10.1177/1077546314521443
  70. Mehar, K. and Panda, S. (2017b), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005
  71. Mehar, K. and Panda, S.K. (2017a), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loading", Int. J. Comput. Meth., 14(2), 1750019. https://doi.org/10.1142/S0219876217500190
  72. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2018), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw . Struct. Mater., 1099636217698443. https://doi.org/10.1177/1099636217698443
  73. 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., 25(2), 157-175. https://doi.org/10.12989/SCS.2017.25.2.157
  74. Mokashi, V.V., Qian, D. and Liu, Y.J. (2007), "A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics", Compos. Sci. Technol., 67, 530-540. https://doi.org/10.1016/j.compscitech.2006.08.014
  75. Mouffoki, A., AddaBedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/SSS.2017.20.3.369
  76. 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
  77. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017a), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/SCS.2017.25.4.389
  78. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/SEM.2017.64.6.737
  79. 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
  80. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotubereinforced composite plates", Mater. Des., 31, 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  81. Shokravi, M. (2017a), "Dynamic pull-in and pull-out analysis of viscoelastic nanoplates under electrostatic and Casimir forces via sinusoidal shear deformation theory", Microelectron. Reliab., 71, 17-28. https://doi.org/10.1016/j.microrel.2017.02.006
  82. Shokravi, M. (2017b), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  83. Shokravi, M. (2017c), "Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM", Geomech. Eng., 12(2), 327-346. https://doi.org/10.12989/gae.2017.12.2.327
  84. Shokravi, M. (2017d)," Buckling of sandwich plates with FGCNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., 23(6), 623-631. https://doi.org/10.12989/SCS.2017.23.6.623
  85. Taibi, F.Z., Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct Mater., 17(2), 99-129. https://doi.org/10.1177/1099636214554904
  86. Thai. H.T. and Kim. S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025
  87. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  88. 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
  89. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotubereinforced composite plates with Pasternak elastic foundation", Appl. Math. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058
  90. Xie, X.L., Mai, Y.W. and Zhou, X.P. (2005), "Dispersion and alignment of carbon nanotubes in polymer matrix: a review", Mater. Sci. Eng.,49, 89-112. https://doi.org/10.1016/j.mser.2005.04.002
  91. 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., 21(1), 15-25. https://doi.org/10.12989/SSS.2018.21.1.015
  92. 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., 21(1), 65-74. https://doi.org/10.12989/SSS.2018.21.1.065
  93. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  94. Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO2 nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009
  95. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710 https://doi.org/10.12989/sem.2015.54.4.693
  96. 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
  97. Zhu, R., Pan, E. and Roy, A.K. (2007), "Molecular dynamics study of the stress-strain behavior of carbon-nanotube reinforced Epon 862 composites", Mater. Sci. Eng. A, 447, 51-57. https://doi.org/10.1016/j.msea.2006.10.054
  98. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., 64(2), 145-153. https://doi.org/10.12989/sem.2017.64.2.145
  99. Zidi, M., Tounsi, A., Houari M.S.A., AddaBedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  100. 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., 26(2), 125-137. https://doi.org/10.12989/SCS.2018.26.2.125

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