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Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation

  • Benahmed, Abdelillah (Laboratory de Modelisation et Simulation Multi-echaelle, Departement de Physique, Faculte des Science Exactes Universite de Sidi Bel Abbes) ;
  • Fahsi, Bouazza (Laboratory de Modelisation et Simulation Multi-echaelle, Departement de Physique, Faculte des Science Exactes Universite de Sidi Bel Abbes) ;
  • Benzair, Abdelnour (Laboratory de Modelisation et Simulation Multi-echaelle, Departement de Physique, Faculte des Science Exactes Universite de Sidi Bel Abbes) ;
  • Zidour, Mohamed (Civil Engineering Department, Universite Ibn Khaldoun) ;
  • Bourada, Fouad (Civil Engineering Department, Laboratory of Materials et Hydrology, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Civil Engineering Department, Laboratory of Materials et Hydrology, University of Sidi Bel Abbes)
  • 투고 : 2018.10.09
  • 심사 : 2019.01.10
  • 발행 : 2019.02.25

초록

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.

키워드

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., 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. 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
  4. 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 boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  5. 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
  6. 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
  7. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by $SiO_2$ nanoparticles subjected to blast load experimentally and theoretically", Constr. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
  8. 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
  9. 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., 65(4), 453-464. https://doi.org/10.12989/SEM.2018.65.4.453
  10. 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., 27(5), 311-324. https://doi.org/10.12989/WAS.2018.27.5.311
  11. Barati, M.R. and Zenkour, A. (2018), "Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments", Mech. Adv. Mater. Struct., 25(8), 669-680. https://doi.org/10.1080/15376494.2017.1308603
  12. 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., 14(2), 103-115. https://doi.org/10.12989/EAS.2018.14.2.103
  13. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-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
  14. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  15. 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., 25(3), 257-270. https://doi.org/10.12989/SCS.2017.25.3.257
  16. 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., 62(6), 695-702. https://doi.org/10.12989/SEM.2017.62.6.695
  17. 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. https://doi.org/10.12989/SEM.2018.65.1.019
  18. 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
  19. Bensaid, I. (2017), "A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., 5(2), 113-126. https://doi.org/10.12989/anr.2017.5.2.113
  20. Bensattalah, T., Daouadji, T. H., Zidour, M., Tounsi, A. and Bedia, E.A. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568. https://doi.org/10.1007/s11029-016-9606-z
  21. 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
  22. 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., 6(2), 147-162. https://doi.org/10.12989/ANR.2018.6.2.147
  23. Bouazza, M., Amara, K., Zidour, M., Abedlouahed, T. and El Abbas, A.B. (2014), "Thermal effect on buckling of multiwalled carbon nanotubes using different gradient elasticity theories", Nanosci. Nanotechnol., 4(2), 27-33.
  24. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Bedia, E.A. (2015), "Postbuckling analysis of nanobeams using trigonometric Shear deformation theory", Appl. Sci. Rep., 10, 112-121.
  25. 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., 66(1), 61-73. https://doi.org/10.12989/SEM.2018.66.1.061
  26. Boukhari, A., Ait Atmane, H., Houari, M.S.A., 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
  27. 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
  28. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybridand symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  29. 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
  30. 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.
  31. 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
  32. 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
  33. Doan, D.H., Van Do, T., Pham, P.M. and Duc, N.D. (2018), "Validation simulation for free vibration and buckling of cracked Mindlin plates using phase-field method", Mech. Adv. Mater. Struct., 1-10.
  34. 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
  35. Ebrahimi, F. and Barati, M.R. (2018a), "Stability analysis of functionally graded heterogeneous piezoelectric nanobeams based on nonlocal elasticity theory", Adv. Nano Res., 6(2), 93-112. https://doi.org/10.12989/ANR.2018.6.2.093
  36. Ebrahimi, F. and Jafari, A. (2017), "Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory", Adv. Nano Res., 5(4), 281-301. https://doi.org/10.12989/anr.2017.5.4.281
  37. Ebrahimi, F. and Jafari, A. (2018b), "A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities", Mech. Adv. Mater. Struct.
  38. 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
  39. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size dependent nanobeams", Appl. Math. Comput., 218, 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  40. 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., 27(1), 109-122. https://doi.org/10.12989/SCS.2018.27.1.109
  41. Ghaffari, I., Yaghoobi, M.P. and Ghannad, M. (2018), "Complete mechanical behavior analysis of FG nano beam under non-uniform loading using non-local theory", Mater. Res. Expr., 5(1), 015016.
  42. Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by $SiO_2$ nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/CAC.2018.21.4.431
  43. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/SEM.2018.67.2.115
  44. Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018b), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004
  45. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018a), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002
  46. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017b), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
  47. Hajmohammad, M.H., Zarei, M.S., Nouri, A. And Kolahchi, R. (2017a), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373.
  48. Hasanyan, D.J., Batra, R.C. and Harutyunyan, S. (2008), "Pull-In instabilities in functionally graded microthermo electro mechanical systems", J. Therm. Stress., 31, 1006-1021. https://doi.org/10.1080/01495730802250714
  49. Janghorban, M. and Zare, A. (2011), "Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method", Phys. E, 43, 1602-1604. https://doi.org/10.1016/j.physe.2011.05.002
  50. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/SEM.2018.65.5.621
  51. 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
  52. 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
  53. Kar, V.R. and Panda, S. K. (2017). "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Therm. Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  54. 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
  55. 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., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  56. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/SCS.2018.27.2.201
  57. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "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
  58. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., In Press.
  59. Karami, B., Shahsavari, D. and Janghorban, M. (2018a), "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
  60. Karami, B., Shahsavari, D. and Li, L. (2018b), "Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499 https://doi.org/10.1080/01495739.2017.1393781
  61. Katariya, P.V., Das, A. and Panda, S.K. (2018), "Buckling analysis of SMA bonded sandwich structure-using FEM", IOP Conf. Ser.: Mater. Sci. Eng., 338(1), 012035.
  62. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017a), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., 6(4), 349-361. https://doi.org/10.12989/AMR.2017.6.4.349
  63. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017b), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/SSS.2017.20.5.595
  64. Khetir, H., Bachir Bouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (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
  65. 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
  66. 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
  67. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90(1), 479-492. https://doi.org/10.1007/s11071-017-3676-x
  68. 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
  69. Kolahchi, R., Safari, M. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  70. 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
  71. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017c), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  72. 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-Wall. Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016
  73. 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
  74. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory", Int. J. Sol. Struct., 46, 1176-1185. https://doi.org/10.1016/j.ijsolstr.2008.10.012
  75. 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
  76. Mahinzare, M., Barooti, M.M. and Ghadiri, M. (2018a), "Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment", Microsyst. Technol., 24(3), 1695-1711. https://doi.org/10.1007/s00542-017-3544-0
  77. Mahinzare, M., Ranjbarpur, H. and Ghadiri, M. (2018b), "Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate", Mech. Syst. Sign. Proc., 100, 188-207. https://doi.org/10.1016/j.ymssp.2017.07.041
  78. Mahmoudpour, E., Hosseini-Hashemi, S.H. and Faghidian, S.A. (2018), << Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model", Appl. Math. Modell., 57, 302-315. https://doi.org/10.1016/j.apm.2018.01.021
  79. Maryam, S. (2017), "Buckling of sandwich plates with FG-CNT-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
  80. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  81. 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., In Press.
  82. 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
  83. Mohammadi-Alasti, B., Rezazadeh, G., Borgheei, A.M., Minaei, S. and Habibifar, R. (2011), "On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure", Compos. Struct., 93, 1516-1525. https://doi.org/10.1016/j.compstruct.2010.11.013
  84. 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., 21(4), 397-405. https://doi.org/10.12989/SSS.2018.21.4.397
  85. Morimoto, K., Janssen, W.J., Fessler, M.B., McPhillips, K.A., Borges, V.M., Bowler, R.P. and Vandivier, R.W. (2006), "Lovastatin enhances clearance of apoptotic cells (efferocytosis) with implications for chronic obstructive pulmonary disease", J. Immunol., 176(12), 7657-7665. https://doi.org/10.4049/jimmunol.176.12.7657
  86. Mouffoki, A., Adda Bedia, 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
  87. 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
  88. 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", J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  89. Panda, S.K. and Singh, B.N. (2013), "Thermal postbuckling behavior of laminated composite spherical shell panel using NFEM#", Mech. Bas. Des. Struct. Mach., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  90. Pisano, A.A., Sofi, A. and Fuschi, P. (2009), "Finite element solutions for nonhomogeneous nonlocal elastic problems", Mech. Res. Commun., 36, 755-761. https://doi.org/10.1016/j.mechrescom.2009.06.003
  91. Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the 3rd International conference on micro- and nanosystems (MNS3), San Diego, California, U.S.A.
  92. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., 4(1), 31-44. https://doi.org/10.12989/anr.2016.4.1.031
  93. Sharma, N., Mahapatra, T.R. and Panda, S.K. (2017), "Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory", Compos. Struct., 180, 116-129. https://doi.org/10.1016/j.compstruct.2017.08.012
  94. Sharma, N., Mahapatra, T.R., Panda, S.K. and Katariya, P. (2018), "Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel", J. Sandw. Struct. Mater., 1099636218784846.
  95. Shokravi, M. (2017a), "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
  96. Shokravi, M. (2017b), "Vibration analysis of silica nanoparticles-reinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  97. Shokravi, M. (2017c), "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
  98. Singh, V.K. and Panda, S.K. (2015), "Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers", Smart Struct. Syst., 16(5), 853-872. https://doi.org/10.12989/sss.2015.16.5.853
  99. Tounsi, A., Al-Basyouni, K.S. 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
  100. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  101. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124301. https://doi.org/10.1152/japplphysiol.00337.2005
  102. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  103. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  104. Yaghoobi, H. and Fereidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341.
  105. 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
  106. 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
  107. 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., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519
  108. Yu, Y.Y. (2012), Vibrations of Elastic Plates: Linear and Nonlinear Dynamical Modeling of Sandwiches, Laminated Composites, and Piezoelectric Layers, Springer Science & Business Media.
  109. Zamanian, M., Kolahchi, R. And Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with $SiO_2$ nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043
  110. 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
  111. 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
  112. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2
  113. Zidour, M., Hadji, L., Bouazza, M., Tounsi, A. and Bedia, E.A. (2015), "The mechanical properties of Zigzag carbon nanotube using the energy-equivalent model", J. Chem. Mater. Res., 3, 9-14.
  114. 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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