Advances in nano research

  • 제7권4호
  • /
  • Pages.265-275
  • /
  • 2019
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Non-classical plate model for single-layered graphene sheet for axial buckling

  • Safaei, Babak (Department of Mechanical Engineering, Tsinghua University) ;
  • Khoda, Farzad Hamed (Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University) ;
  • Fattahi, A.M. (Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University)
  • 투고 : 2019.01.21
  • 심사 : 2019.05.02
  • 발행 : 2019.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

키워드

참고문헌

  1. Alizadeh, M. and Fattahi, A.M. (2019), "Non-classical plate model for FGMs", Eng. Comput., 35(1), 215-228. https://doi.org/10.1007/s00366-018-0594-6
  2. Azizi, S., Safaei, B., Fattahi, A.M. and Tekere, M. (2015), "Nonlinear vibrational analysis of nanobeams embedded in an elastic medium including surface stress effects", Adv. Mater. Sci. Eng., 2015, 1-7. http://dx.doi.org/10.1155/2015/318539
  3. Behfar, K. and Naghdabadi, R. (2005), "Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium", Compos. Sci. Technol., 65(7), 1159-1164. https://doi.org/10.1016/j.compscitech.2004.11.011
  4. 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. https://doi.org/10.12989/anr.2018.6.2.147
  5. Daouadji, T.H. and Adim, B. (2017), "Mechanical behaviour of FGM sandwich plates using a quasi-3D higher order shear and normal deformation theory", Struct. Eng. Mech., Int. J., 61(1), 49-63. https://doi.org/10.12989/sem.2018.67.2.143
  6. Ebrahimi, F. and Barati, M.R. (2018), "Surface and flexoelectricity effects on size-dependent thermal stability analysis of smart piezoelectric nanoplates", Struct. Eng. Mech., Int. J., 67(2), 143-153. https://doi.org/10.12989/sem.2017.61.1.049
  7. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  8. Fattahi, A.M. and Safaei, B. (2017), "Buckling analysis of CNT-reinforced beams with arbitrary boundary conditions", Microsyst. Technol., 23(10), 5079-5091. https://doi.org/10.1007/s00542-017-3345-5
  9. Fattahi, A.M. and Sahmani, S. (2017), "Size dependency in the axial postbuckling behavior of nanopanels made of functionally graded material considering surface elasticity", Arab. J. Sci. Eng., 42, 4617-4633. https://doi.org/10.1007/s13369-017-2600-5
  10. Filiz, S. and Aydogdu, M. (2010), "Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity", Compos. Mater. Sci., 49(3), 619-627. https://doi.org/10.1016/j.commatsci.2010.06.003
  11. Hao, M.J., Guo, X.M. and Wang, Q. (2010), "Small-scale effect on torsional buckling of multi-walled carbon nanotubes", Eur. J. Mech. A/Solids, 29(1), 49-55. https://doi.org/10.1016/j.euromechsol.2009.05.008
  12. Jalali, M.H., Zargar, O. and Baghani, M. (2018), "Size-dependent vibration analysis of FG microbeams in thermal environment based on modified couple stress theory", IJST-T Mech. Eng., 1-11. https://doi.org/10.1007/s40997-018-0193-6
  13. Kiani, K. (2010), "A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect", Int. J. Mech. Sci., 52(10), 1343-1356. https://doi.org/10.1016/j.ijmecsci.2010.06.010
  14. Kitipornchai, S., He, X.Q. and Liew, K.M. (2005), "Continuum model for the vibration of multilayered graphene sheets", Phys. Rev. B, 72(7), 075443. https://doi.org/10.1103/PhysRevB.72.075443
  15. Liew, K.M., He, X.Q. and Kitipornchai, S. (2006), "Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix", Acta Mater., 54(16), 4229-4236. https://doi.org/10.1016/j.actamat.2006.05.016
  16. Mohammadsalehi, M., Zargar, O. and Baghani, M. (2017), "Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory", Meccanica, 52(4-5), 1063-1077. https://doi.org/10.1007/s11012-016-0432-0
  17. Moheimani, R. and Ahmadian, M.T. (2012), "On Free Vibration of Functionally Graded Euler-Bernoulli Beam Models Based on the Non-Local Theory", ASME 2012 International Mechanical Engineering Congress and Exposition, 12, Vibration Acoustics and Wave Propagation, Houston, TX, USA, November.
  18. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., Int. J., 22(2), 277-299. https://doi.org/10.12989/scs.2016.22.2.277
  19. Moradi-Dastjerdi, R. and Malek-Mohammadi, H. (2017), "Biaxial buckling analysis of functionally graded nanocomposite sandwich plates reinforced by aggregated carbon nanotube using improved high-order theory", J. Sandw. Struct. Mater., 19, 736-769. https://doi.org/10.1177/1099636216643425
  20. Moradi-Dastjerdi, R., Malek-Mohammadi, H. and Momeni-Khabisi, H. (2017), "Free vibration analysis of nanocomposite sandwich plates reinforced with CNT aggregates", ZAMM - J. Appl. Math. Mech./Zeitschrift Fur Angew Math Und Mech, 97, 1418-1435. https://doi.org/10.1002/zamm.201600209
  21. Pasharavesh, A., Vaghasloo, Y.A., Ahmadian, M.T. and Moheimani, R. (2011), "Nonlinear vibration analysis of nano to micron scale beams under electric force using nonlocal theory", ASME Conference Proceedings, DETC2011-47615, 145-151, Washington, DC, USA, August.
  22. Pasternak, P.L. (1954), "On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants", Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui Arkhitekture, Moscow, Russia.
  23. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  24. Pradhan, S.C. and Murmu, T. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A, 373(11), 1062-1069. https://doi.org/10.1016/j.physleta.2009.01.030
  25. Pradhan, S.C. and Murmu, T. (2010), "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E, 42(5), 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053
  26. Qin, Z., Pang, X., Safaei, B. and Chu, F. (2019), "Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions", Compos. Struct., 220, 847-860. https://doi.org/10.1016/j.compstruct.2019.04.046
  27. Safaei, B. and Fattahi, A.M. (2017), "Free vibrational response of single-layered graphene sheets embedded in an elastic matrix using different nonlocal plate models", Mechanika, 23(5), 678-687. https://doi.org/10.5755/j01.mech.23.5.14883
  28. Safaei, B., Naseradinmousavi, P. and Rahmani, A. (2016), "Development of an accurate molecular mechanics model for buckling behavior of multi-walled carbon nanotubes under axial compression", J. Mol. Graph. Modell., 65, 43-60. https://doi.org/10.1016/j.jmgm.2016.02.001
  29. Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2019), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B Eng., 161, 44-54. https://doi.org/10.1016/j.compositesb.2018.10.049
  30. Sahmani, S. and Fattahi, A.M. (2017a), "An anisotropic calibrated nonlocal plate model for biaxial instability analysis of 3D metallic carbon nanosheets using molecular dynamics simulations", Mater. Res. Express, 4(6), 1-14.
  31. Sahmani, S. and Fattahi, A.M. (2017b), "Calibration of developed nonlocal anisotropic shear deformable plate model for uniaxial instability of 3D metallic carbon nanosheets using MD simulations", Comput. Method Appl. Mech. Eng., 322, 187-207. https://doi.org/10.1016/j.cma.2017.04.015
  32. Shahriari, B., Zargar, O., Baghani, M. and Baniassadi, M. (2018), "Free vibration analysis of rotating functionally graded annular disc of variable thickness using generalized differential quadrature method", Scientia Iranica, 25(2), 728-740. https://doi.org/10.24200/SCI.2017.4325
  33. Shen, H.S. (2010), "Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model", J. Theor. Biol., 264(2), 386-394. https://doi.org/10.1016/j.jtbi.2010.02.014
  34. Shen, L., Shen, H.S. and Zhang, C.L. (2010), "Nonlocal plate Model for Nonlinear Vibration of Single Layer Graphene Sheets in Thermal Enviroments", Compos. Mater. Sci., 48(3), 680-685. https://doi.org/10.1016/j.commatsci.2010.03.006
  35. Winkler, E. (1867), "Theory of Elasticity and Strength", H. Dominicus, Prague, Czech Republic.
  36. Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E, 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035
  37. Zenkour, A.M. (2018), "Nonlocal elasticity and shear deformation effects on thermal buckling of a CNT embedded in a viscoelastic medium", Eur. Phys. J. Plus, 133, 193. https://doi.org/10.1140/epjp/i2018-12014-2

피인용 문헌

  1. Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model vol.34, pp.5, 2019, https://doi.org/10.12989/scs.2020.34.5.643
  2. Flow of casson nanofluid along permeable exponentially stretching cylinder: Variation of mass concentration profile vol.38, pp.1, 2019, https://doi.org/10.12989/scs.2021.38.1.033
  3. Confinement effectiveness of Timoshenko and Euler Bernoulli theories on buckling of microfilaments vol.11, pp.1, 2021, https://doi.org/10.12989/acc.2021.11.1.081
  4. Experimental studies on elastic properties of high density polyethylene-multi walled carbon nanotube nanocomposites vol.38, pp.2, 2019, https://doi.org/10.12989/scs.2021.38.2.177
  5. Monitoring and control of multiple fraction laws with ring based composite structure vol.10, pp.2, 2021, https://doi.org/10.12989/anr.2021.10.2.129
  6. Flow of MHD Powell-Eyring nanofluid: Heat absorption and Cattaneo-Christov heat flux model vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.221
  7. Effect of suction on flow of dusty fluid along exponentially stretching cylinder vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.263
  8. 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
  9. Calcium carbonate nanoparticles effects on cement plast properties vol.27, pp.8, 2021, https://doi.org/10.1007/s00542-020-05136-6
  10. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2019, https://doi.org/10.12989/scs.2021.40.3.355
  11. An innovative system for novel vibration of rotating FG shell with combination of fraction laws vol.12, pp.2, 2019, https://doi.org/10.12989/acc.2021.12.2.157
  12. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.115
  13. Propagation of waves with nonlocal effects for vibration response of armchair double-walled CNTs vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.183
  14. An investigation of mechanical properties of kidney tissues by using mechanical bidomain model vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.193
  15. Damped harmonic vibrations of axisymmetric graphene‐enhanced cylinders in thermal environment vol.42, pp.11, 2019, https://doi.org/10.1002/pc.26258