Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials

  • Hamad, Luay Badr (Al-Mustansiriah University, Engineering Collage) ;
  • Khalaf, Basima Salman (Al-Mustansiriah University, Engineering Collage) ;
  • Faleh, Nadhim M. (Al-Mustansiriah University, Engineering Collage)
  • Received : 2019.07.28
  • Accepted : 2019.10.20
  • Published : 2019.09.25
⟨ Previous Next ⟩

Abstract

This paper researches static and dynamic bending behaviors of a crystalline nano-size shell having pores and grains in the framework of strain gradient elasticity. Thus, the nanoshell is made of a multi-phase porous material for which all material properties on dependent on the size of grains. Also, in order to take into account small size effects much accurately, the surface energies related to grains and pores have been considered. In order to take into account all aforementioned factors, a micro-mechanical procedure has been applied for describing material properties of the nanoshell. A numerical trend is implemented to solve the governing equations and derive static and dynamic deflections. It will be proved that the static and dynamic deflections of the crystalline nanoshell rely on pore size, grain size, pore percentage, load location and strain gradient coefficient.

Keywords

Acknowledgement

Supported by : Mustansiriyah university

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

References

  1. 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., Int. J., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175
  2. 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. Monitor. Maint., Int. J., 6(2), 147-159. https:// doi.org/10.12989/smm.2019.6.2.147
  3. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  4. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., Int. J., 5(4), 393-414. https://doi.org/10.12989/anr.2017.5.4.393
  5. 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., Int. J., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  6. 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
  7. Barati, M.R. and Shahverdi, H. (2017b), "Hygro-thermal vibration analysis of graded double-refinednanoplate systems using hybrid nonlocal stress-strain gradient theory", Compos. Struct., 176, 982-995. https://doi.org/10.1016/j.compstruct.2017.06.004
  8. 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
  9. 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), 075019. https://doi.org/10.1088/2053-1591/aa7ac2
  10. 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. https://doi.org/10.12989/sss.2017.19.6.601
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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., Int. J., 65(4), 465-476. https://doi.org/10.12989/sem.2018.65.4.465
  16. 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. Computat., 224, 760-774. https://doi.org/10.1016/j.amc.2013.09.002
  17. 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
  18. 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
  19. 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
  20. 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
  21. Li, C. (2014a), "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
  22. Li, C. (2014b), "Torsional vibration of carbon nanotubes: comparison of two nonlocal models and a semicontinuum model", Int. J. Mech. Sci., 82, 25-31. https://doi.org/10.1016/j.ijmecsci.2014.02.023
  23. 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.
  24. 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-dimens. Syst. Nanostruct., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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., Int. J., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  30. Meyers, M.A., Mishra, A. and Benson, D.J. (2006), "Mechanical properties of nanocrystalline materials", Progress Mater. Sci., 51(4), 427-556. https://doi.org/10.1016/j.pmatsci.2005.08.003
  31. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397
  32. 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., Int. J., 11(2), 289-307. https://doi.org/10.12989/gae.2016.11.2.289
  33. 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., 225, 111036. https://doi.org/10.1016/j.compstruct.2019.111036
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. Zenkour, A.M. and Abouelregal, A.E. (2014), "Vibration of FG nanobeams induced by sinusoidal pulseheating via a nonlocal thermoelastic model", Acta Mechanica, 225(12), 3409-3421. https://doi.org/10.1007/s00707-014-1146-9
  40. 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

Cited by

  1. Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations vol.25, pp.4, 2019, https://doi.org/10.12989/cac.2020.25.4.311
  2. Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory vol.26, pp.5, 2020, https://doi.org/10.12989/cac.2020.26.5.439