Structural Engineering and Mechanics

  • 제66권3호
  • /
  • Pages.369-377
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  • 2018
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  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A unified formulation for modeling of inhomogeneous nonlocal beams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, Amirkabir University of Technology)
  • 투고 : 2017.06.09
  • 심사 : 2018.02.14
  • 발행 : 2018.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, buckling and free vibration of functionally graded (FG) nanobeams resting on elastic foundation are investigated by developing various higher order beam theories which capture shear deformation influences through the thickness of the beam without the need for shear correction factors. The elastic foundation is modeled as linear Winkler springs as well as Pasternak shear layer. The material properties of FG nanobeam are supposed to change gradually along the thickness through the Mori-Tanaka model. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. From Hamilton's principle, the nonlocal governing equations of motion are derived and then solved applying analytical solution. To verify the validity of the developed theories, the results of the present work are compared with those available in literature. The effects of shear deformation, elastic foundation, gradient index, nonlocal parameter and slenderness ratio on the buckling and free vibration behavior of FG nanobeams are studied.

키워드

참고문헌

  1. Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
  2. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
  3. Atmane, H.A., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 1-14.
  4. Aydogdu, M. (2009), "A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration", Phys. E: Low-Dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  5. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  6. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  7. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  8. Ebrahimi, F. and Barati, M.R. (2016a), "Thermal buckling analysis of size-dependent FG nanobeams based on the third-order shear deformation beam theory", Acta Mech. Sol. Sinic., 29(5), 547-554. https://doi.org/10.1016/S0894-9166(16)30272-5
  9. Ebrahimi, F. and Barati, M.R. (2016b), "Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory", J. Therm. Stress., 39(12), 1560-1571. https://doi.org/10.1080/01495739.2016.1219243
  10. Ebrahimi, F. and Barati, M.R. (2016c), "Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler-Pasternak foundation", Appl. Phys. A, 122(11), 952. https://doi.org/10.1007/s00339-016-0466-0
  11. Ebrahimi, F. and Barati, M.R. (2016d), "Analytical solution for nonlocal buckling characteristics of higher-order inhomogeneous nanosize beams embedded in elastic medium", Adv. Nano Res., 4(3), 229-249. https://doi.org/10.12989/anr.2016.4.3.229
  12. Ebrahimi, F. and Barati, M.R. (2017a), "Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field", J. Therm. Stress., 40(5), 548-563. https://doi.org/10.1080/01495739.2016.1254076
  13. Ebrahimi, F. and Barati, M.R. (2017b), "Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory", Struct. Eng. Mech., 61(6), 721-736. https://doi.org/10.12989/sem.2017.61.6.721
  14. Ebrahimi, F. and Barati, M.R. (2017c), "Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory", J. Mech. Eng. Sci., 231(23), 4457-4469. https://doi.org/10.1177/0954406216668912
  15. Ebrahimi, F. and Barati, M.R. (2017d), "Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory", Smart Mater. Struct., 26(6), 065018. https://doi.org/10.1088/1361-665X/aa6eec
  16. Ebrahimi, F. and Barati, M.R. (2017e), "Longitudinal varying elastic foundation effects on vibration behavior of axially graded nanobeams via nonlocal strain gradient elasticity theory", Mech. Adv. Mater. Struct., Just Accepted.
  17. Ebrahimi, F. and Barati, M.R. (2018), "Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygrothermal effects employing nonlocal strain gradient theory", Compos. Struct., 185, 241-253. https://doi.org/10.1016/j.compstruct.2017.10.021
  18. Ebrahimi, F. and Dabbagh, A. (2017a), "On wave dispersion characteristics of double-layered graphene sheets in thermal environments", J. Electromagnet. Wave. Appl., 1-20.
  19. Ebrahimi, F. and Dabbagh, A. (2017b), "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
  20. Ebrahimi, F. and Dabbagh, A. (2017c), "Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory", J. Electromagnet. Wave. Appl., 1-32.
  21. Ebrahimi, F. and Dabbagh, A. (2017d), "Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory", Eur. Phys. J. Plus, 132(11), 449. https://doi.org/10.1140/epjp/i2017-11694-2
  22. Ebrahimi, F. and Dabbagh, A. (2017e), "Nonlocal strain gradient based wave dispersion behavior of smart rotating magnetoelectro-elastic nanoplates", Mater. Res. Expr., 4(2), 025003. https://doi.org/10.1088/2053-1591/aa55b5
  23. Ebrahimi, F. and Dabbagh, A. (2018), "Wave propagation analysis of magnetostrictive sandwich composite nanoplates via nonlocal strain gradient theory", J. Mech. Eng. Sci., 0954406217748687. https://doi.org/10.1177/0954406217748687
  24. Ebrahimi, F. and Daman, M. (2017), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., 64(1), 121-133.
  25. Ebrahimi, F. and Haghi, P. (2017), "Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory", Acta Mech. Sol. Sinic., 30(6), 647-657. https://doi.org/10.1016/j.camss.2017.09.007
  26. Ebrahimi, F. and Heidari, E. (2017), "Surface effects on nonlinear vibration of embedded functionally graded nanoplates via higher order shear deformation plate theory", Mech. Adv. Mater. Struct., 1-29.
  27. Ebrahimi, F. and Karimiasl, M. (2017), "Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams", Mech. Adv. Mater. Struct., Just Accepted.
  28. Ebrahimi, F. and Salari, E. (2015), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B: Eng., 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  29. 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
  30. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2017), "Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects", Wave. Rand. Compl. Med., 1-21.
  31. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  32. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  33. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  34. 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
  35. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  36. Hosseini, S.A.H. and Rahmani, O. (2016), "Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory", Meccan., 1-17.
  37. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  38. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Sol. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  39. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 39.
  40. Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., 46(3), 417-431. https://doi.org/10.12989/sem.2013.46.3.417
  41. Kulkarni, K., Singh, B.N. and Maiti, D.K. (2015), "Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory", Compos. Struct.
  42. Larbi, L.O., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Bas. Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  43. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  44. Mahi, A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  45. Mahi, A., Bedia, E.A., Tounsi, A. and Mechab, I. (2010), "An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions", Compos. Struct., 92(8), 1877-1887. https://doi.org/10.1016/j.compstruct.2010.01.010
  46. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B: Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  47. Nguyen, T.K., Nguyen, T.T.P., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. Part B: Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032
  48. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061
  49. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119(3), 1019-1032. https://doi.org/10.1007/s00339-015-9061-z
  50. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  51. Rahmani, O., Refaeinejad, V. and Hosseini, S.A.H. (2017), "Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams", Steel Compos. Struct., 23(3), 339-350. https://doi.org/10.12989/scs.2017.23.3.339
  52. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  53. Sedighi, H.M., Daneshmand, F. and Abadyan, M. (2016), "Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators", J. Appl. Math. Mech., 96(3), 385-400.
  54. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  55. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  56. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3-4), 195-220. https://doi.org/10.1007/BF01176650
  57. Taghizadeh, M., Ovesy, H.R. and Ghannadpour, S.A.M. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., 54(4), 755-769. https://doi.org/10.12989/sem.2015.54.4.755
  58. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  59. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  60. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  61. Vo, T.P., Thai, H.T., Nguyen, T.K. and Inam, F. (2014), "Static and vibration analysis of functionally graded beams using refined shear deformation theory", Meccan., 49(1), 155-168. https://doi.org/10.1007/s11012-013-9780-1
  62. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006
  63. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693

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