Steel and Composite Structures

  • 재36권6호
  • /
  • Pages.631-642
  • /
  • 2020
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Strain gradient based static stability analysis of composite crystalline shell structures having porosities

  • Fenjan, Raad M. (Al-Mustansiriah University, Engineering Collage) ;
  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage) ;
  • Ridha, Ahmed A. (Al-Mustansiriah University, Engineering Collage)
  • 투고 : 2019.10.15
  • 심사 : 2020.08.11
  • 발행 : 2020.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper studies nonlinear stability behavior of a nanocrystalline silicon curved nanoshell considering strain gradient size-dependency. Nanocrystallines are composite materials with an interface phase and randomly distributed nano-size grains and pores. Imperfectness of the curved nanoshell has been defined based on an initial deflection. The formulation of nanocrystalline nanoshell has been established by thin shell theory and an analytical approach has been used in order to solve the buckling problem. For accurately describing the size effects related to nano-grains or nano-pores, their surface energies have been included. Nonlinear stability curves of the nanoshell are affected by the size of nano-grain, curvature radius and nano-pore volume fraction. It is found that increasing the nano-pore volume fraction results in lower buckling loads.

키워드

과제정보

The authors would like to thank Mustansiriyah university (www.uomustansiriyah.edu.iq) Baghdad-Iraq for its support in the present work.

참고문헌

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  2. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  3. Ahmed, R.A., Fenjan, R.M and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  4. Al-Maliki, A.F., Faleh, N.M and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities. Struct. Monit. Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.
  5. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  6. 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. Design, 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x.
  7. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimensional Syst. Nanostruc., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  8. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  9. 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.
  10. Barati, M.R and Shahverdi, H. (2017a), "An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position", Mech. Adv. Mater. Struct., 24(10), 840-853. https://doi.org/10.1080/15376494.2016.1196788
  11. Barati, M.R. and Shahverdi, H. (2017b), "Hygro-thermal vibration analysis of graded double-refined-nanoplate systems using hybrid nonlocal stress-strain gradient theory", Compos. Struct., 176, 982-995. https://doi.org/10.1016/j.compstruct.2017.06.004.
  12. Barati, M.R. and Shahverdi, H. (2017c), "Vibration analysis of multi-phase nanocrystalline silicon nanoplates considering the size and surface energies of nanograins/nanovoids", Int. J. Eng. Sci., 119, 128-141. https://doi.org/10.1016/j.ijengsci.2017.06.002.
  13. Barati, M.R. and Shahverdi, H. (2017d), "Frequency analysis of porous nano-mechanical mass sensors made of multi-phase nanocrystalline silicon materials", Mater. Res. Express, 4(7).
  14. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., 5(4), 393-414. https://doi.org/10.12989/anr.2017.5.4.393.
  15. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  16. Bedia, W.A., 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.
  17. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.
  18. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  19. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  20. 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.
  21. Bouamoud, A., Boucham, B., Bourada, F., Houari, M.S.A. and Tounsi, A. (2019), "Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory", Steel Compos. Struct., 32(5), 611-632. https://doi.org/10.12989/scs.2019.32.5.611.
  22. 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., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  23. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  24. 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.
  25. 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., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  26. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  27. Boutaleb, S., Benrahou, K. H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191.
  28. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  29. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617.
  30. Draiche, K., Bousahla, A. A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  31. 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.
  32. Ebrahimi, F. and Barati, M.R. (2016), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9.
  33. Ebrahimi, F and Barati, M.R. (2017a), "Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects", Acta Mechanica, 228(3), 1197-1210. https://doi.org/10.1007/s00707-016-1755-6.
  34. Ebrahimi, F. and Barati, M.R. (2017b), "Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory", Compos. Struct., 166, 256-267. https://doi.org/10.1016/j.compstruct.2017.01.036.
  35. Ebrahimi, F. and Barati, M.R. (2018), "Stability analysis of porous multi-phase nanocrystalline nonlocal beams based on a general higher-order couple-stress beam model", Struct. Eng. Mech., 65(4), 465-476. https://doi.org/10.12989/sem.2018.65.4.465.
  36. Eltaher, M.A., Mahmoud, F.F., Assie, A.E. and Meletis, E.I. (2013), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774. https://doi.org/10.1016/j.amc.2013.09.002.
  37. Eringen, A.C. (1983). "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  38. Farajpour, A., Rastgoo, A. and Mohammadi, M. (2017), "Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment", Physica B: Condensed Matter, 509, 100-114. https://doi.org/10.1016/j.physb.2017.01.006
  39. Forsat, M. (2020), "Investigating nonlinear vibrations of higher-order hyper-elastic beams using the Hamiltonian method", Acta Mechanica, 231(1), 125-138. https://doi.org/10.1007/s00707-019-02533-5.
  40. Forsat, M., Badnava, S., Mirjavadi, S.S., Barati, M.R. and Hamouda, A.M.S. (2020), "Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory", Eur. Phys. J. Plus, 135(1), 81. https://doi.org/10.1140/epjp/s13360-019-00042-x.
  41. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater., 1099636219845841. https://doi.org/10.1177%2F1099636219845841.
  42. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  43. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  44. Ke, L.L., Wang, Y.S and Reddy, J.N. (2014), "Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions", Compos. Struct., 116, 626-636. https://doi.org/10.1016/j.compstruct.2014.05.048
  45. Ke, L.L., Wang, Y.S. and Wang, Z.D. (2012), "Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory", Compos. Struct., 94(6), 2038-2047. https://doi.org/10.1016/j.compstruct.2012.01.023
  46. 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. with Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1.
  47. Khosravi, F., Hosseini, S.A. and Tounsi, A. (2020), "Torsional dynamic response of viscoelastic SWCNT subjected to linear and harmonic torques with general boundary conditions via Eringen's nonlocal differential model", Euro. Phys. J. Plus, 135(2), 183. https://doi.org/10.1140/epjp/s13360-020-00207-z.
  48. Li, C. (2014), "A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries", Compos. Struct., 118, 607-621. https://doi.org/10.1016/j.compstruct.2014.08.008
  49. Li, C. (2014), "Torsional vibration of carbon nanotubes: comparison of two nonlocal models and a semi-continuum model", Int. J. Mech. Sci., 82, 25-31. https://doi.org/10.1016/j.ijmecsci.2014.02.023.
  50. Li, C., Guo, L., Shen, J.P., He, Y.P. and Ju, H. (2013), "Forced Vibration Analysis on Nanoscale Beams Accounting for Effective Nonlocal Size Effects", Adv. Vib. Eng., 12(6), 623-633.
  51. Li, L., Hu, Y and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028.
  52. Lim, C.W. (2010), "On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection", Appl. Math. Mech., 31(1), 37-54. https://doi.org/10.1007/s10483-010-0105-7.
  53. Lim, C.W., Zhang, G and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  54. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177%2F1099636217727577. https://doi.org/10.1177/1099636217727577
  55. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  56. Mehralian, F., Beni, Y.T and Ansari, R. (2016), "Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell", Compos. Struct., 152, 45-61. https://doi.org/10.1016/j.compstruct.2016.05.024.
  57. Mehralian, F., Beni, Y.T and Zeverdejani, M.K. (2017), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Physica B: Condensed Matter, 514, 61-69. https://doi.org/10.1016/j.physb.2017.03.030.
  58. 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%2F1099636217698443. https://doi.org/10.1177/1099636217698443
  59. Merazi, M., Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305.
  60. Meyers, M.A., Mishra, A and Benson, D.J. (2006), "Mechanical properties of nanocrystalline materials", Progress in Mater. Sci., 51(4), 427-556. https://doi.org/10.1016/j.pmatsci.2005.08.003
  61. Mirjavadi, S.S., Forsat, M. and Badnava, S. (2019a), "Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models", Biomech. Model. Mechanobiology, 1-13. https://doi.org/10.1007/s10237-019-01265-8.
  62. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Afshari, B.M., Hamouda, A.M.S. and Rabby, S. (2019d), "Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency", Eur. Phys. J. Plus, 134(5), 214. https://doi.org/10.1140/epjp/i2019-12540-3.
  63. Mirjavadi, S.S., Forsat, M., Barati, M.R., Abdella, G.M., Hamouda, A.M.S., Afshari, B.M. and Rabby, S. (2019c), "Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents", Microsyst. Technologies, 25(9), 3477-3488. https://doi.org/10.1007/s00542-018-4241-3.
  64. Mirjavadi, S.S., Forsat, M., Hamouda, A.M.S. and Barati, M.R. (2019e), "Dynamic response of functionally graded graphene nanoplatelet reinforced shells with porosity distributions under transverse dynamic loads", Mater. Res. Express, 6(7), 075045. https://doi.org/10.1088/2053-1591/ab1552.
  65. Mirjavadi, S.S., Forsat, M., Nikookar, M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", Eur. Phys. J. Plus, 134(10), 508. https://doi.org/10.1140/epjp/i2019-12806-8.
  66. 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.
  67. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  68. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  69. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  70. Saidi, H., Tounsi, A and Bousahla, A.A. (2016), "A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations", Geomech. Eng., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289.
  71. 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., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  72. Shaat, M. and Abdelkefi, A. (2015), "Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications", Int. J. Mech. Sci., 101-102, 280-291. https://doi.org/10.1016/j.ijmecsci.2015.08.002.
  73. Shen, J.P., Wang, P.Y., Li, C. and Wang, Y.Y. (2019), "New observations on transverse dynamics of microtubules based on nonlocal strain gradient theory", Compos. Struct., 111036.
  74. Soltani, K., Bessaim, A., Houari, M.S.A., Kaci, A., Benguediab, M., Tounsi, A. and Alhodaly, M.S. (2019), "A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations", Steel Compos. Struct., 30(1), 13-29. https://doi.org/10.12989/scs.2019.30.1.013.
  75. Sun, J., Lim, C.W., Zhou, Z., Xu, X and Sun, W. (2016), "Rigorous buckling analysis of size-dependent functionally graded cylindrical nanoshells", J. Appl. Phys., 119(21), 214303. https://doi.org/10.1063/1.4952984
  76. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011.
  77. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.
  78. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  79. Wang, G.F., Feng, X.Q., Yu, S.W. and Nan, C.W. (2003), "Interface effects on effective elastic moduli of nanocrystalline materials", Mater. Sci. Eng.: A, 363(1), 1-8. https://doi.org/10.1016/S0921-5093(03)00253-3.
  80. 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.
  81. Zaera, R., Fernandez-Saez, J and Loya, J.A. (2013), "Axisymmetric free vibration of closed thin spherical nano-shell", Compos. Struct., 104, 154-161. https://doi.org/10.1016/j.compstruct.2013.04.022.
  82. 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: Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  83. Zaoui, F.Z., Tounsi, A., Ouinas, D. and Olay, J.A.V. (2020), "A refined HSDT for bending and dynamic analysis of FGM plates. Struct. Eng. Mech., 74(1), 105-119. https://doi.org/10.12989/sem.2020.74.1.105.
  84. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  85. Zeighampour, H. and Beni, Y.T. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47. https://doi.org/10.1016/j.ijengsci.2014.01.004.
  86. Zenkour, A.M. and Abouelregal, A.E. (2014), "Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model", Acta Mechanica, 225(12), 3409-3421. https://doi.org/10.1007/s00707-014-1146-9.
  87. Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015), "An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation", Appl. Math. Model., 39(13), 3814-3845. https://doi.org/10.1016/j.apm.2014.12.001.
  88. Zhou, J.Q., Wang, L and Ye, Z.X. (2013), "Micromechanics model for nanovoid growth in nanocrystalline materials", Appl. Mech. Mater., 364, 754-759. https://doi.org/10.4028/www.scientific.net/AMM.364.754.

피인용 문헌

  1. On the free vibration response of laminated composite plates via FEM vol.39, pp.2, 2020, https://doi.org/10.12989/scs.2021.39.2.149
  2. Finite element simulation for investigation on thermal post-buckling of geometrically imperfect GOP-reinforced beam vol.12, pp.2, 2021, https://doi.org/10.12989/acc.2021.12.2.135
  3. Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method vol.28, pp.3, 2021, https://doi.org/10.12989/cac.2021.28.3.233
  4. Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment vol.40, pp.6, 2021, https://doi.org/10.12989/scs.2021.40.6.893