Structural Engineering and Mechanics

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Buckling analysis of graphene oxide powder-reinforced nanocomposite beams subjected to non-uniform magnetic field

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Nouraei, Mostafa (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Dabbagh, Ali (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Civalek, Omer (Akdeniz University, Engineering Faculty, Civil Engineering Dept., Division of Mechanics)
  • Received : 2019.02.28
  • Accepted : 2019.04.05
  • Published : 2019.08.25
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Abstract

Present article deals with the static stability analysis of compositionally graded nanocomposite beams reinforced with graphene oxide powder (GOP) is undertaken once the beam is subjected to an induced force caused by nonuniform magnetic field. The homogenized material properties of the constituent material are approximated through Halpin-Tsai micromechanical scheme. Three distribution types of GOPs are considered, namely uniform, X and O. Also, a higher-order refined beam model is incorporated with the dynamic form of the virtual work's principle to derive the partial differential motion equations of the problem. The governing equations are solved via Galerkin's method. The introduced mathematical model is numerically validated presenting a comparison between the results of present work with responses obtained from previous articles. New results for the buckling load of GOP reinforced nanocomposites are presented regarding for different values of magnetic field intensity. Besides, other investigations are performed to show the impacts of other variants, such as slenderness ratio, boundary condition, distribution type and so on, on the critical stability limit of beams made from nanocomposites.

Keywords

References

  1. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48, 195-205. https://doi.org/10.12989/sem.2013.48.2.195.
  2. Arani, A.G., Maghamikia, S., Mohammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods", J. Mech. Sci. Technol., 25, 809-820. https://doi.org/10.1007/s12206-011-0127-3.
  3. Balandin, A.A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F. and Lau, C.N. (2008), "Superior thermal conductivity of single-layer graphene", Nano Lett., 8, 902-907. https://doi.org/10.1021/nl0731872.
  4. Barati, M.R. and Zenkour, A.M. (2017), "Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection", Compos. Struct., 181, 194-202. https://doi.org/10.1016/j.compstruct.2017.08.082.
  5. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19, 115-126. https://doi.org/10.12989/sss.2017.19.2.115.
  6. 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, 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  7. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24, 820-829. https://doi.org/10.1080/15376494.2016.1196786.
  8. Ebrahimi, F. and Haghi, P. (2018), "A nonlocal strain gradient theory for scale-dependent wave dispersion analysis of rotating nanobeams considering physical field effects", Coupled Syst. Mech., 7, 373-393. https://doi.org/10.12989/CSM.2018.7.4.373
  9. Ebrahimi, F. and Rostami, P. (2018), "Wave propagation analysis of carbon nanotube reinforced composite beams", Europ. Phys. J. Plus, 133, 285. https://doi.org/10.1140/epjp/i2018-12069-y.
  10. Ebrahimi, F. and Barati, M.R. (2016a), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", J. Smart Nano Mater., 7(3), 1-25. https://doi.org/10.1080/19475411.2016.1223203.
  11. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, https://doi.org/10.1177/1077546316646239.
  12. Ebrahimi, F. and Barati, M.R. (2016c), "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. (2016d), "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), https://doi.org/10.1088/0964-1726/25/10/105014.
  14. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intelligent Mater. Syst. Struct., https://doi.org/10.1177/1045389X16672569.
  15. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  16. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, https://doi.org/10.1016/j.compstruct.2016.11.058.
  17. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Thermal Stresses, 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684.
  18. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Europe Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16160-1.
  19. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arabian J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4.
  20. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", European Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y.
  21. Ebrahimi, F. and Barati, M.R. (2016h), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18. https://doi.org/10.1007/s00339-016-0001-3.
  22. Ebrahimi, F. and Barati, M.R. (2016i), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2.
  23. Ebrahimi, F. and Barati, M.R. (2016j), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001.
  24. Ebrahimi, F. and Barati, M.R. (2016k), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, https://doi.org/10.1016/j.compstruct.2016.09.092.
  25. Ebrahimi, F. and Barati, M.R. (2016l), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazilian Soc. Mech. Sci. Eng., 39(3), 1-16.
  26. Ebrahimi, F. and Barati, M.R. (2016m), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", European Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  27. Ebrahimi, F. and Barati, M.R. (2016n), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11. https://doi.org/10.1017/jmech.2016.46.
  28. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)", Compos. Part B Eng., 110, 132-140. https://doi.org/10.1016/j.compositesb.2016.11.024.
  29. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  30. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  31. Gomez-Navarro, C., Burghard, M. and Kern, K. (2008), "Elastic properties of chemically derived single graphene sheets", Nano Lett., 8, 2045-2049. https://doi.org/10.1021/nl801384y.
  32. Hamza-Cherif, R., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, S. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", Adv. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1.
  33. Kant, T. and Babu, C. (2000), "Thermal buckling analysis of skew fibre-reinforced composite and sandwich plates using shear deformable finite element models", Compos. Struct., 49(1), 77-85. https://doi.org/10.1016/S0263-8223(99)00127-0.
  34. Lei, Z., Liew, K. and Yu, J. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006.
  35. Liew, K., Lei, Z., Yu, J. and Zhang, L. (2014), "Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Methods Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001.
  36. Liu, G., Chen, X. and Reddy, J. (2002), "Buckling of symmetrically laminated composite plates using the elementfree Galerkin method", J. Struct. Stability Dynam., 2(3), 281-294. https://doi.org/10.1142/S0219455402000634.
  37. Mikoushkin, V., Shnitov, V., Nikonov, S.Y., Dideykin, A., Vul, A. Y., Sakseev, D., Vyalikh, D. and Vilkov, O.Y. (2011), "Controlling graphite oxide bandgap width by reduction in hydrogen", Tech. Phys. Lett., 37, 942. https://doi.org/10.1134/S1063785011100257.
  38. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52, 5-25. https://doi.org/10.1016/j.polymer.2010.11.042.
  39. Shan, L. and Qiao, P. (2005), "Flexural-torsional buckling of fiber-reinforced plastic composite open channel beams", Compos. Struct., 68(2), 211-224. https://doi.org/10.1016/j.compstruct.2004.03.015.
  40. Shariyat, M. (2010), "A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads", J. Mech. Sci., 52(3), 495-514. https://doi.org/10.1016/j.ijmecsci.2009.11.010.
  41. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018a), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", European Phys. J. Plus, 133, 368. https://doi.org/10.1140/epjp/i2018-12196-5.
  42. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  43. She, G.L., Yuan, F.G. and Ren, Y.R. (2018b), "On wave propagation of porous nanotubes", J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002.
  44. She, G.L., Yuan, F.G., Ren, Y.R. and Xiao, W.S. (2017b), "On buckling and postbuckling behavior of nanotubes", J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005.
  45. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.
  46. Shen, H.S., Xiang, Y. and Lin, F. (2017a), "Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments", Compos. Struct., 170, 80-90. https://doi.org/10.1016/j.compstruct.2017.03.001.
  47. Shen, H.S., Xiang, Y. and Lin, F. (2017b), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments", Comput. Methods Appl. Mech. Eng., 319, 175-193. https://doi.org/10.1016/j.cma.2017.02.029.
  48. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Design, 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.
  49. Shojaee, S., Valizadeh, N., Izadpanah, E., Bui, T. and Vu, T.V. (2012), "Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method", Compos. Struct., 94(5), 1677-1693. https://doi.org/10.1016/j.compstruct.2012.01.012.
  50. Sobhani, A., Saeedifar, M., Najafabadi, M.A., Fotouhi, M. and Zarouchas, D. (2018), "The study of buckling and post-buckling behavior of laminated composites consisting multiple delaminations using acoustic emission", Thin-Walled Struct., 127, 145-156. https://doi.org/10.1016/j.tws.2018.02.011.
  51. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B Eng., 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043.
  52. Suk, J.W., Piner, R.D., An, J. and Ruoff, R.S. (2010), "Mechanical properties of monolayer graphene oxide", ACS nano, 4, 6557-6564. https://doi.org/10.1021/nn101781v.
  53. Tornabene, F., Fantuzzi, N., Viola, E. and Carrera, E. (2014), "Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method", Compos. Struct., 107, 675-697. https://doi.org/10.1016/j.compstruct.2013.08.038.
  54. Urthaler, Y. and Reddy, J. (2008), "A mixed finite element for the nonlinear bending analysis of laminated composite plates based on FSDT", Mech. Adv. Mater. Struct., 15(5), 335-354. https://doi.org/10.1080/15376490802045671.
  55. Wang, Q., Shi, D., Liang, Q. and Pang, F. (2017), "Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints", Appl. Math. Model., 46, 227-262. https://doi.org/10.1016/j.apm.2017.01.070.
  56. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50, 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  57. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028.
  58. Wu, H., Yang, J. and Kitipornchai, S. (2016), "Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections", Composites Part B Eng., 90, 86-96. https://doi.org/10.1016/j.compositesb.2015.12.007.
  59. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048.
  60. Yas, M. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", J. Pressure Vessels Piping, 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  61. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M. S. A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015.
  62. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmo ud, S. (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.
  63. Zhang, L., Lei, Z. and Liew, K. (2015), "Vibration characteristic of moderately thick functionally graded carbon nanotube reinforced composite skew plates", Compos. Struct., 122, 172-183. https://doi.org/10.1016/j.compstruct.2014.11.070.
  64. Zhang, Z., Li, Y., Wu, H., Zhang, H., Wu, H., Jiang, S. and Chai, G. (2018), "Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the firstorder shear deformation theory", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1444216.
  65. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, 799-808. https://doi.org/10.1016/j.compstruct.2017.08.044.
  66. Zhen, W. and Wanji, C. (2006), "Free vibration of laminated composite and sandwich plates using global-local higher-order theory", J. Sound Vib., 298(1-2), 333-349. https://doi.org/10.1016/j.jsv.2006.05.022.
  67. Zhu, P., Lei, Z. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010.

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