Advances in nano research

  • 제9권1호
  • /
  • Pages.33-45
  • /
  • 2020
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On post-buckling characteristics of functionally graded smart magneto-electro-elastic nanoscale shells

  • Asrari, Reza (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University) ;
  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Kheirikhah, Mohammad Mahdi (Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University)
  • 투고 : 2018.12.11
  • 심사 : 2020.06.26
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

Geometrically nonlinear buckling of functionally graded magneto-electro-elastic (FG-MEE) nanoshells with the use of classical shell theory and nonlocal strain gradient theory (NSGT) has been analyzed in present research. Mathematical formulation based on NSGT gives two scale coefficients for simultaneous description of structural stiffness reduction and increment. Functional gradation of material properties is described based on power-law formulation. The nanoshell is under a multi-physical field related to applied voltage, magnetic potential, and mechanical load. Exerting a strong electric voltage, magnetic potential or mechanical load may lead to buckling of nanoshell. Taking into account geometric nonlinearity effects after buckling, the behavior of nanoshell in post-buckling regime can be analyzed. Nonlinear governing equations are reduced to ordinary equations utilizing Galerkin's approach and post-buckling curves are obtained based on an analytical procedure. It will be shown that post-buckling curves are dependent on nonlocal/strain gradient parameters, electric voltage magnitude and sign, magnetic potential magnitude and sign and material gradation exponent.

키워드

참고문헌

  1. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B: Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057
  2. Barati, M.R. and Zenkour, A.M. (2018), "Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions", J. Vib. Control, 24(10), 1910-1926. https://doi.org/10.1177%2F1077546316672788 https://doi.org/10.1177/1077546316672788
  3. Barretta, R., Feo, L., Luciano, R., de Sciarra, F.M. and Penna, R. (2016), "Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation", Compos. Part B: Eng., 100, 208-219. https://doi.org/10.1016/j.compositesb.2016.05.052
  4. Bich, D.H., Nguyen, N.X. and Van Tung, H. (2013), "Postbuckling of functionally graded cylindrical shells based on improved Donnell equations", Vietnam J. Mech., 35(1), 1-15. https://doi.org/10.15625/0866-7136/35/1/2894
  5. Ebrahimi, F. and Barati, M.R. (2016), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  6. Ebrahimi, F. and Barati, M.R. (2018), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magnetoelectrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177%2F1077546316646239 https://doi.org/10.1177/1077546316646239
  7. Ebrahimi, F. and Dabbagh, A. (2017), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293. https://doi.org/10.1016/j.compstruct.2016.11.058
  8. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  9. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Mathe. Model., 40(5-6), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026
  10. 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
  11. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  12. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039
  13. Heydarpour, Y. and Malekzadeh, P. (2019), "Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads", J. Brazil. Soc. Mech. Sci. Eng., 41(4), 184. https://doi.org/10.1007/s40430-019-1675-1
  14. Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E: Low-dimens. Syst. Nanostruct., 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002
  15. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart Mater. Struct., 23(12), 125036. https://doi.org/10.1088/0964-1726/23/12/125036
  16. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  17. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011
  18. 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
  19. Lu, L., Guo, X. and Zhao, J. (2017), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006
  20. Ma, L.H., Ke, L.L., Reddy, J.N., Yang, J., Kitipornchai, S. and Wang, Y.S. (2018), "Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory", Compos. Struct., 199, 10-23. https://doi.org/10.1016/j.compstruct.2018.05.061
  21. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017), "Calibration of nonlocal strain gradient shell model for buckling analysis of nanotubes using molecular dynamics simulations", Physica B: Condensed Matter, 521, 102-111. https://doi.org/10.1016/j.physb.2017.06.058
  22. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68(4), 608-618. https://doi.org/10.1115/1.1380385
  23. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., Int. J., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239
  24. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magneto-electro-elastic laminated plates", J. Sound Vib., 292(3-5), 626-644. https://doi.org/10.1016/j.jsv.2005.08.004
  25. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063
  26. Simsek, M. (2019), "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041
  27. Waksmanski, N. and Pan, E. (2017), "An analytical threedimensional solution for free vibration of a magneto-electroelastic plate considering the nonlocal effect", J. Intel. Mater. Syst. Struct., 28(11), 1501-1513. https://doi.org/10.1177%2F1045389X16672734 https://doi.org/10.1177/1045389X16672734
  28. Zeighampour, H., Beni, Y.T. and Dehkordi, M.B. (2018), "Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory", Thin-Wall. Struct., 122, 378-386. https://doi.org/10.1016/j.tws.2017.10.037