Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Buckling of a single-layered graphene sheet embedded in visco-Pasternak's medium via nonlocal first-order theory

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.03.17
  • Accepted : 2016.11.07
  • Published : 2016.12.25
⟨ Previous Next ⟩

Abstract

The buckling response of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak's medium is presented. The nonlocal first-order shear deformation elasticity theory is used for this purpose. The visco-Pasternak's medium is considered by adding the damping effect to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus. The SLGS be subjected to distributive compressive in-plane edge forces per unit length. The governing equilibrium equations are obtained and solved for getting the critical buckling loads of simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak's foundation, damping coefficient, and mode numbers on the buckling analysis of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

Keywords

References

  1. Akgoz, B. and Civalek, O. (2011), "Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams", Int. J. Eng. Sci., 49, 1268-1280. https://doi.org/10.1016/j.ijengsci.2010.12.009
  2. Akgoz, B. and Civalek, O. (2012), "Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory", Mater. Des., 42, 164-171. https://doi.org/10.1016/j.matdes.2012.06.002
  3. Akgoz, B. and Civalek, O. (2013a), "A size-dependent shear deformation beam model based on the strain gradient elasticity theory", Int. J. Eng. Sci., 70, 1-14. https://doi.org/10.1016/j.ijengsci.2013.04.004
  4. Akgoz, B. and Civalek, O. (2013b), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mech., 224, 2185-2201. https://doi.org/10.1007/s00707-013-0883-5
  5. Akgo, B. and Civalek, O. (2013c), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020
  6. Anjomshoa, A., Shahidi, A.R., Hassani B. and Jomehzadeh, E. (2014), "Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory", Appl. Math. Model., 38, 5934-5955. https://doi.org/10.1016/j.apm.2014.03.036
  7. Ansari, R. and Sahmani, S. (2013), "Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations", Appl. Math. Model., 37, 7338-7351. https://doi.org/10.1016/j.apm.2013.03.004
  8. Basua, S. and Bhattacharyya, P. (2012), "Recent developments on graphene and graphene oxide based solid state gas sensors", Sens. Actuat. B, 173, 1-21.
  9. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity, solutions of screw dislocation, surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  10. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Verlag, New York.
  11. Eringen, A.C. (2006), "Nonlocal continuum mechanics based on distributions", Int. J. Eng. Sci., 44, 141-147. https://doi.org/10.1016/j.ijengsci.2005.11.002
  12. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  13. Farajpour, A., Solghar, A.A. and Shahidi, A. (2013a), "Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression", Phys. E, 47, 197-206. https://doi.org/10.1016/j.physe.2012.10.028
  14. Farajpour, A., Dehghany, M. and Shahidi, A.R. (2013b), "Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment", Compos B, 50, 333-343. https://doi.org/10.1016/j.compositesb.2013.02.026
  15. Ghorbanpour Arani, A., Amir, S., Dashti, P. and Yousefi, M. (2014), "Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect", Comput. Mater. Sci., 86, 144-154. https://doi.org/10.1016/j.commatsci.2014.01.047
  16. Golmakani, M.E. and Rezatalab, J. (2015), "Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory", Compos. Struct., 119, 238-250. https://doi.org/10.1016/j.compstruct.2014.08.037
  17. Hosseini-Hashemi, S., Kermajani, M. and Nazemnezhad, R. (2015), "An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory", Europ. J. Mech. A/Solids, 51, 29-43. https://doi.org/10.1016/j.euromechsol.2014.11.005
  18. Karlicic, D., Cajic, M., Kozic, P. and Pavlovic, I. (2015), "Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium", Compos. Struct., 131, 672-681. https://doi.org/10.1016/j.compstruct.2015.05.058
  19. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory", J. Sound Vib., 331, 94-106. https://doi.org/10.1016/j.jsv.2011.08.020
  20. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solid., 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  21. Li, F., Li, J., Feng, Y., Yang, L. and Du, Z. (2011), "Electrochemical behavior of graphene doped carbon paste electrode and its application for sensitive determination of ascorbic acid", Sens. Actuat. B, 157, 110-114. https://doi.org/10.1016/j.snb.2011.03.033
  22. Lim, C.W., Li, C. and Yu, J.L. (2010), "Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach", Acta Mech. Sinica, 26, 755-765. https://doi.org/10.1007/s10409-010-0374-z
  23. Mohammadi, M., Farajpour, A., Moradi, A. and Ghayour, M. (2014), "Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment", Compos. B, 56, 629-637. https://doi.org/10.1016/j.compositesb.2013.08.060
  24. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A.A. (2004), "Electric field effect in atomically thin carbon films", Science, 306, 666-669. https://doi.org/10.1126/science.1102896
  25. Pantelic, R.S., Meyer, J.C., Kaiser, U. and Stahlberg, H. (2012), "The application of graphene as a sample support in transmission electron microscopy", Solid State Commun., 152, 1375-1382. https://doi.org/10.1016/j.ssc.2012.04.038
  26. Pradhan, S.C. and Murmu, T. (2009), "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Comput. Mater. Sci., 47, 268-274. https://doi.org/10.1016/j.commatsci.2009.08.001
  27. 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", Phys. E, 42, 1293-1301. https://doi.org/10.1016/j.physe.2009.10.053
  28. Radic, N., Jeremić, D., Trifkovic, S. and Milutinovic, M. (2014), "Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory", Compos. B, 61, 162-171. https://doi.org/10.1016/j.compositesb.2014.01.042
  29. Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solid., 59, 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008
  30. Sakhaee-Pour, A. (2009), "Elastic buckling of single-layered graphene sheet", Comput. Mater. Sci., 45, 266-270. https://doi.org/10.1016/j.commatsci.2008.09.024
  31. Sakhaee-Pour, A., Ahmadian, M.T. and Vafai, A. (2008), "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
  32. Samaei, A.T., Abbasion, S. and Mirsayar, M.M. (2011), "Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory", Mech. Res. Commun., 38, 481-485. https://doi.org/10.1016/j.mechrescom.2011.06.003
  33. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, 2nd Edition, McGraw-Hill, New York.
  34. Wang, J., Li, Z., Fan, G., Pan, H., Chen, Z. and Zhang, D. (2012), "Reinforcement with graphene nanosheets in aluminum matrix composites", Scripta Mater., 66, 594-597. https://doi.org/10.1016/j.scriptamat.2012.01.012
  35. Xu, Y.M., Shen, H.S. and Zhang, C.L. (2013), "Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments", Compos. Struct., 98, 294-302. https://doi.org/10.1016/j.compstruct.2012.10.041
  36. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solid. Struct., 39, 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  37. Zenkour, A.M. (2001), "Buckling and free vibration of elastic plates using simple and mixed shear deformation theories", Acta Mech., 146, 183-197. https://doi.org/10.1007/BF01246732
  38. Zenkour, A.M. (2016a), "Nonlocal transient thermal analysis of a single-layered graphene sheet embedded in viscoelastic medium", Phys. E, 79, 87-97. https://doi.org/10.1016/j.physe.2015.12.003
  39. Zenkour, A.M. (2016b), "Vibration analysis of a single-layered graphene sheet embedded in visco-Pasternak's medium using nonlocal elasticity theory", J. Vibroeng., 18, 2319-2330. https://doi.org/10.21595/jve.2016.16585
  40. Zhang, Y., Zhang, L.W., Liew, K.M. and Yu, J.L. (2016) "Buckling analysis of graphene sheets embedded in an elastic medium based on the kp-Ritz method and non-local elasticity theory", Eng. Anal. Bound. Elem. 70, 31-39. https://doi.org/10.1016/j.enganabound.2016.05.009

Cited by

  1. Thermo-electro-magneto-mechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates vol.84, 2017, https://doi.org/10.1016/j.mechrescom.2017.06.002
  2. Vibration analysis of carbon nanotubes with multiple cracks in thermal environment vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.057
  3. Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials vol.7, pp.1, 2016, https://doi.org/10.12989/anr.2019.7.1.051
  4. Modeling of low-dimensional pristine and vacancy incorporated graphene nanoribbons using tight binding model and their electronic structures vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.209
  5. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  6. Size-dependent vibration analysis of laminated composite plates vol.7, pp.5, 2016, https://doi.org/10.12989/anr.2019.7.5.337
  7. Frequency response analysis of curved embedded magneto-electro-viscoelastic functionally graded nanobeams vol.7, pp.6, 2019, https://doi.org/10.12989/anr.2019.7.6.391
  8. Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.405
  9. Nonlocal strain gradient effects on forced vibrations of porous FG cylindrical nanoshells vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.149
  10. Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model vol.34, pp.5, 2016, https://doi.org/10.12989/scs.2020.34.5.643
  11. Investigation of microstructure and surface effects on vibrational characteristics of nanobeams based on nonlocal couple stress theory vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.191
  12. A Nonlocal Strain Gradient Theory for Porous Functionally Graded Curved Nanobeams under Different Boundary Conditions vol.23, pp.6, 2016, https://doi.org/10.1134/s1029959920060168
  13. Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory vol.37, pp.6, 2016, https://doi.org/10.12989/scs.2020.37.6.695
  14. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2016, https://doi.org/10.12989/anr.2021.11.2.115