DOI QR코드

DOI QR Code

Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT

  • Boutaleb, Sabrina (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bakora, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Algarni, Ali (Statistics Department, Faculty of Science, King Abdulaziz University) ;
  • 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) ;
  • Tounsi, Abdeldjebbar (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)
  • 투고 : 2018.10.17
  • 심사 : 2019.04.26
  • 발행 : 2019.05.25

초록

In the present work the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosize FG plate. In HSDT a cubic function is employed in terms of thickness coordinate to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton's principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature and a good agreement is observed. Finally, the influence of the various parameters such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness to length ratio on the dynamic properties of the FG nanoplates is illustrated and discussed in detail.

키워드

참고문헌

  1. Aagesen, M. and Sorensen, C. (2008), "Nanoplates and their suitability for use as solar cells", Proceedings of Clean Technol., 109-112.
  2. Abdelaziz, H.H., Meziane, M.A.A, 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.
  3. 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
  4. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
  5. 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., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  6. Aifantis, E. (1999), "Strain gradient interpretation of size effects", Int. J. Fract., 95, 299-314. https://doi.org/10.1023/A:1018625006804
  7. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  8. Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55.
  9. 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
  10. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  11. Asghari, M. and Taati, E. (2013), "A size-dependent model for functionally graded micro-plates for mechanical analyses", J. Vib. Cont., 19, 1614-1632. https://doi.org/10.1177/1077546312442563
  12. Atmane, H.A., 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
  13. 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
  14. 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.
  15. 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.
  16. Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., Int. J., 21(6), 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347
  17. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Beg, O.A. (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
  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.
  19. 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., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  20. 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., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  21. 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, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  22. 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., Int. J., 62(6), 695-702.
  23. 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., Int. J., 25(3), 257-270.
  24. Benadouda, M., Ait Atmane, 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., Int. J., 13(3), 255-265.
  25. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., Int. J., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  26. 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.
  27. 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
  28. Bensaid, I. (2017), "A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., Int. J., 5(2), 113-126. https://doi.org/10.21474/IJAR01/3121
  29. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., Int. J., 6(3), 279-298.
  30. 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., Int. J., 19(6), 601-614.
  31. 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.
  32. 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., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  33. Bouazza, M., Lairedj, A., Benseddiq, N. and Khalki, S. (2016), "A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates", Mech. Res. Commun., 73, 117-126. https://doi.org/10.1016/j.mechrescom.2016.02.015
  34. Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects", Acta Mech., 229(5), 2251-2265. https://doi.org/10.1007/s00707-017-2097-8
  35. 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., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  36. 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., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  37. 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.
  38. 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., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  39. 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. [To be published]
  40. 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
  41. 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., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  42. 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.
  43. 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.
  44. 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
  45. 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
  46. 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. [To be published]
  47. 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
  48. 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
  49. 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
  50. Chen, Y., Lee, J.D. and Eskandarian, A. (2004), "Atomistic viewpoint of the applicability of microcontinuum theories", Int. J. Sol. Struct., 41, 2085-2097. https://doi.org/10.1016/j.ijsolstr.2003.11.030
  51. Dash, S., Sharma, N., Mahapatra, T.R., Panda, S.K. and Sahu, P. (2018), "Free vibration analysis of functionally graded sandwich flat panel", IOP Conf. Series: Materials Science and Engineering, 377, 012140. https://doi.org/10.1088/1757-899X/377/1/012140
  52. 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
  53. 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
  54. Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  55. Ebrahimi, F. and Rastgoo, A. (2008a), "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct., 17(1), 015044. https://doi.org/10.1088/0964-1726/17/1/015044
  56. Ebrahimi, F. and Rastgo, A. (2008b), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin-Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008
  57. Ebrahimi, F., Rastgoo, A. and Atai, A.A. (2009a), "A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech. -A/Solids, 28(5), 962-973. https://doi.org/10.1016/j.euromechsol.2008.12.008
  58. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009b), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Tech., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  59. Ebrahimi, F., Mahmoodi, F. and Barati, M.R. (2017), "Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory", Adv. Mater. Res., Int. J., 6(3), 279-301.
  60. 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.
  61. 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.
  62. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on Pasternak elastic foundation using higher order shear deformation plate theories", Smart Struct. Syst., Int. J., 21(1), 113-122.
  63. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218, 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  64. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013a), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039
  65. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013b), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030
  66. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., Int. J., 4(1), 51-64.
  67. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  68. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  69. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  70. 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.
  71. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018a), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  72. Faleh, N.M., Fenjan, R.M. and Ahmed, R.A. (2018b), "Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads", Eur. Phys. J. Plus, 133, 348. https://doi.org/10.1140/epjp/i2018-12152-5
  73. 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.
  74. Ghorbanpour Arani, A., Kolahchi, R. and Vossough, H. (2012), "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory", Physica B: Condensed Matter, 407(22), 4458-4465. https://doi.org/10.1016/j.physb.2012.07.046
  75. 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., Int. J., 25(6), 717-726.
  76. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  77. 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", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  78. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Phys. E, 40, 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021
  79. Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", J. Aerosp. Eng., 30(5), 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756
  80. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model, 34, 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  81. Hosseini-Hashemi, S., Bedroud, M. and Nazemnezhad, R. (2013a), "An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Compos. Struct., 103, 108-118. https://doi.org/10.1016/j.compstruct.2013.02.022
  82. Hosseini-Hashemi, S., Zare, M. and Nazemnezhad, R. (2013b), "An exact analytical approach for free vibration of Mindlin rectangular nanoplates via nonlocal elasticity", Compos. Struct., 100, 290-299. https://doi.org/10.1016/j.compstruct.2012.11.035
  83. 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., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  84. Huang, C., Yang, P. and Chang, M. (2012), "Threedimensional vibration analyses of functionally graded material rectangular plates with through internal cracks", Compos. Struct., 94, 2764-2776. https://doi.org/10.1016/j.compstruct.2012.04.003
  85. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  86. Janghorban, M. (2016), "Static analysis of functionally graded rectangular nanoplates based on nonlocal third order shear deformation theory", Int. J. Eng. Appl. Sci. (IJEAS), 8(2), 87-100.
  87. 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., Int. J., 65(5), 621-631.
  88. 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
  89. Kar, V.R. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Thermal Stress., 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623
  90. Kar, V.R. and Panda, S.K. (2016b), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronaut., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  91. 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.
  92. Karami, B., Janghorban, M. and Tounsi, A. (2018a), "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
  93. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
  94. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
  95. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput. [In press]
  96. 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
  97. 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., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487
  98. 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.
  99. Katariya, P.V. and Panda, S.K. (2018), "Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings", Eng. Comput. [In press]
  100. Katariya, P.V. and Panda, S.K. (2019), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: A Finite Element Approach", Arab. J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0
  101. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017a), "Prediction of nonlinear eigenfrequency of laminated curved sandwich structure using higher-order equivalent single-layer theory", J. Sandw. Struct. Mater. [In press]
  102. 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., Int. J., 20(5), 595-605.
  103. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017c), "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.
  104. Katariya, P.V., Das, A. and Panda, S.K. (2018a), "Buckling analysis of SMA bonded sandwich structure - using FEM", IOP Conf. Series: Materials Science and Engineering, 338, 012035. https://doi.org/10.1088/1757-899X/338/1/012035
  105. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2018b) "Bending and vibration analysis of skew sandwich plate", Aircraft Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087
  106. Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2019), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35(2), 467-485. https://doi.org/10.1007/s00366-018-0609-3
  107. Ke, L.L., Yang, J., Kitipornchai, S. and Bradford, M.A. (2012), "Bending, buckling and vibration of size-dependent functionally graded annular microplates", Compos. Struct., 94, 3250-3257. https://doi.org/10.1016/j.compstruct.2012.04.037
  108. Ke, L.L., Yang, J., Kitipornchai, S., Bradford, M.A. and Wang, Y.S. (2013), "Axisymmetric nonlinear free vibration of sizedependent functionally graded annular microplates", Compos. Part B: Eng., 53, 207-217. https://doi.org/10.1016/j.compositesb.2013.04.066
  109. 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., Int. J., 64(4), 391-402.
  110. 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 four-variable quasi 3D HSDT", Eng. Comput. [In press]
  111. Khorshidi, K., Asgari, T. and Fallah, A. (2015), "Free vibrations analysis of functionally graded rectangular nano-plates based on nonlocal exponential shear deformation theory", Mech. Adv. Compos. Struct., 2, 79-93.
  112. 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., Int. J., 63(4), 439-446.
  113. Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., Int. J., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  114. Koiter, W.T. (1969), "Couple-stresses in the theory of elasticity, I & II", J. Philosoph. Transact. Royal Soc. London B, 67, 17-44.
  115. Kumar, Y. and Lal, R. (2013), "Prediction of frequencies of free axisymmetric vibration of twodirectional functionally graded annular plates on Winkler foundation", Eur. J. Mech. A Solid, 42, 219-228. https://doi.org/10.1016/j.euromechsol.2013.06.001
  116. Lam, D.C.C., Yang, F., Chong, A.C.M. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  117. 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., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  118. Li, L, Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  119. Ma, M., Tu, J.P., Yuan, Y.F., Wang, X.L., Li, K.F., Mao, F. and Zeng, Z.Y. (2008), "Electrochemical performance of ZnO nanoplates as anode materials for Ni/Zn secondary batteries", J. Power Sources, 179, 395-400. https://doi.org/10.1016/j.jpowsour.2008.01.026
  120. 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, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  121. Malekzadeh, P. and Beni, A.A. (2010), "Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment", Compos. Struct., 92, 2758-2767. https://doi.org/10.1016/j.compstruct.2010.04.011
  122. Malekzadeh, P. and Heydarpour, Y. (2012), "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Compos. Struct., 94, 2971-2981. https://doi.org/10.1016/j.compstruct.2012.04.011
  123. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  124. Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038
  125. Mehar, K. and Panda, S.K. (2018), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578.
  126. 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
  127. Mehar, K., Panda, S.K. and Patle, B.K. (2018a), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809. https://doi.org/10.1002/pc.24409
  128. Mehar, K., Mahapatra, T.R, Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018b), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519
  129. 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
  130. 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.
  131. 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
  132. Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11, 139. https://doi.org/10.1088/0957-4484/11/3/301
  133. Mindlin, R. and Tiersten, H. (1962), "Effects of couple-stresses in linear elasticity", Arch. Rational Mech. Anal., 11, 415-448. https://doi.org/10.1007/BF00253946
  134. 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.
  135. 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., Int. J., 20(3), 369-383.
  136. Murmu, T. and Pradhan, S. (2009a), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Phys. E, 41, 1232-1239. https://doi.org/10.1016/j.physe.2009.02.004
  137. Murmu, T. and Pradhan, S. (2009b), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46, 854-859. https://doi.org/10.1016/j.commatsci.2009.04.019
  138. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93, 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028
  139. Nie, G. and Zhong, Z. (2007), "Semi-analytical solution for three-dimensional vibration of functionally graded circular plates", Comput. Method Appl. M, 196, 4901-4910. https://doi.org/10.1016/j.cma.2007.06.028
  140. Nix, W.D. and Gao, H. (1998), "Indentation size effects in crystalline materials: a law for strain gradient plasticity", J. Mech. Phys. Solids, 46, 411-425. https://doi.org/10.1016/S0022-5096(97)00086-0
  141. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  142. Pradhan, S. and Phadikar, J. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A, 373, 1062-1069. https://doi.org/10.1016/j.physleta.2009.01.030
  143. Pradyumna, S. and Bandyopadhyay, J. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finiteelement formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  144. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  145. Rafiee, M.A., Rafiee, J., Srivastava, I., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2010), "Fracture and fatigue in graphene nanocomposites", small, 6, 179-183. https://doi.org/10.1002/smll.200901480
  146. Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  147. Reddy, J. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59, 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008
  148. Reddy, J. and Pang, S. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103, 023511. https://doi.org/10.1063/1.2833431
  149. Sahoo, S.S., Panda, S.K. and Sen, D. (2016), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA Journal, 54(8), 2530-2544. https://doi.org/10.2514/1.J054908
  150. Sahoo, S.S., Panda, S.K. and Singh, V.K. (2017), "Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 231(5), 463-478. https://doi.org/10.1177/1464420715600191
  151. Sakhaee-Pour, A., Ahmadian, M. and Vafai, A. (2008a), "Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors", Solid State Commun., 145, 168-172. https://doi.org/10.1016/j.ssc.2007.10.032
  152. Sakhaee-Pour, A., Ahmadian, M. and Vafai, A. (2008b), "Potential application of single-layered graphene sheet as strain sensor", Solid State Commun., 147, 336-340. https://doi.org/10.1016/j.ssc.2008.04.016
  153. 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., Int. J., 25(4), 389-401.
  154. 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., Int. J., 64(6), 737-749.
  155. 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.
  156. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40.
  157. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wavepropagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29(1), 53-66.
  158. Shen, H.S. and Zhang, C.L. (2010), "Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model", Compos. Struct., 92, 1073-1084. https://doi.org/10.1016/j.compstruct.2009.10.002
  159. Singh, V.K. and Panda, S.K. (2017), "Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers", J. Vib. Control, 23(13), 2078-2093. https://doi.org/10.1177/1077546315609988
  160. Tang, Y. and Liu, Y. (2018), "Effect of van der Waals force on wave propagation in viscoelastic double-walled carbon nanotubes", Modern Phys. Lett. B, 32(24), 1850291. https://doi.org/10.1142/s0217984918502913
  161. 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.
  162. Toupin, R.A. (1962), "Elastic materials with couple-stresses", Arch. Rational Mech. Anal., 11, 385-414. https://doi.org/10.1007/BF00253945
  163. 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. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  164. Ungbhakorn, V. and Wattanasakulpong, N. (2013), "Thermo-elastic vibration analysis of third order shear deformable functionally graded plates with distributed patch mass under thermal environment", Appl. Acoust., 74, 1045-1059. https://doi.org/10.1016/j.apacoust.2013.03.010
  165. Vel, S.S. and Batra, R. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7
  166. Wang, L. (2009), "Dynamical behaviors of double walled carbon nanotubes conveying fluidaccounting for the role of small length scale", Comput. Mater. Sci., 45, 584-588. https://doi.org/10.1016/j.commatsci.2008.12.006
  167. Wu, C.P., Chen, Y.H., Hong, Z.L. and Lin, C.H. (2018), "Nonlinear vibration analysis of an embedded multi-walled carbon nanotube", Adv. Nano Res., Int. J., 6(2), 163-182.
  168. Yahia, S.A., 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  169. 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.
  170. Ye, C., Bando, Y., Shen, G. and Golberg, D. (2006), "Thickness-dependent photocatalytic performance of ZnO nanoplatelets", J. Phys. Chem. B, 110, 15146-15151. https://doi.org/10.1021/jp061874w
  171. 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.
  172. 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.
  173. 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
  174. 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., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  175. Zhao, X., Lee, Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319, 918-939. https://doi.org/10.1016/j.jsv.2008.06.025
  176. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  177. 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., Int. J., 64(2), 145-153.
  178. 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.

피인용 문헌

  1. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.699
  2. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  3. Stochastic Perturbation-Based Finite Element for Free Vibration of Functionally Graded Beams with an Uncertain Elastic Modulus vol.56, pp.4, 2020, https://doi.org/10.1007/s11029-020-09897-z
  4. A Levy solution for bending, buckling, and vibration of Mindlin micro plates with a modified couple stress theory vol.2, pp.12, 2019, https://doi.org/10.1007/s42452-020-03939-w
  5. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2019, https://doi.org/10.12989/amr.2020.9.4.265
  6. Time Harmonic interactions in the axisymmetric behaviour of transversely isotropic thermoelastic solid using New M-CST vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.521
  7. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.025
  8. Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates vol.10, pp.2, 2019, https://doi.org/10.12989/anr.2021.10.2.151
  9. Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell vol.10, pp.2, 2019, https://doi.org/10.12989/anr.2021.10.2.175
  10. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.271
  11. Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.281
  12. Exact third-order static and free vibration analyses of functionally graded porous curved beam vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.001
  13. The effects of ring and fraction laws: Vibration of rotating isotropic cylindrical shell vol.11, pp.1, 2021, https://doi.org/10.12989/anr.2021.11.1.019
  14. Mechanical analysis of bi-functionally graded sandwich nanobeams vol.11, pp.1, 2019, https://doi.org/10.12989/anr.2021.11.1.055
  15. A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation vol.26, 2021, https://doi.org/10.1016/j.csite.2021.101170
  16. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157