Structural Engineering and Mechanics

  • 제65권4호
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  • Pages.465-476
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  • 2018
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Stability analysis of porous multi-phase nanocrystalline nonlocal beams based on a general higher-order couple-stress beam model

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2017.07.27
  • 심사 : 2017.12.26
  • 발행 : 2018.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

This article investigates buckling behavior of a multi-phase nanocrystalline nanobeam resting on Winkler-Pasternak foundation in the framework of nonlocal couple stress elasticity and a higher order refined beam model. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, and couple stress effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical approach. The buckling loads are compared with those of nonlocal couple stress-based beams. It is showed that buckling loads of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, shear deformation, surface effect, nonlocality and boundary conditions.

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참고문헌

  1. Ansari, R., Mohammadi, V., Shojaei, M. F., Gholami, R. and Rouhi, H. (2014), "Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory", Eur. J. Mech.-A/Sol., 45, 143-152. https://doi.org/10.1016/j.euromechsol.2013.11.002
  2. Ansari, R., Mohammadi, V., Shojaei, M.F., Gholami, R. and Sahmani, S. (2014), "Postbuckling analysis of Timoshenko nanobeams including surface stress effect", J. Eng. Sci., 75, 1-10. https://doi.org/10.1016/j.ijengsci.2013.10.002
  3. Ansari, R., Oskouie, M.F. and Gholami, R. (2016), "Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory", Phys. E: Low-Dimens. Syst. Nanostruct., 75, 266-271. https://doi.org/10.1016/j.physe.2015.09.022
  4. Attia, M.A. and Mahmoud, F.F. (2016), "Modeling and analysis of nanobeams based on nonlocal-couple stress elasticity and surface energy theories", J. Mech. Sci., 105, 126-134. https://doi.org/10.1016/j.ijmecsci.2015.11.002
  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. Ebrahimi, F. and Barati, M.R. (2016a), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  7. Ebrahimi, F. and Barati, M.R. (2016b), "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
  8. Ebrahimi, F. and Barati, M.R. (2016c), "Dynamic modeling of a thermos-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  9. Ebrahimi, F. and Barati, M.R. (2016d), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 1077546316646239.
  10. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  11. Ebrahimi, F. and Barati, M.R. (2016f), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  12. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  13. Ebrahimi, F. and Barati, M.R. (2016h), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., Just Accepted.
  14. 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
  15. Ebrahimi, F. and Boreiry, M. (2015), "Investigating various surface effects on nonlocal vibrational behavior of nanobeams", Appl. Phys. A, 121(3), 1305-1316. https://doi.org/10.1007/s00339-015-9512-6
  16. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016b), "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
  17. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  18. Ebrahimi, F., Shaghaghi, G.R. and Boreiry, M. (2016a), "An investigation into the influence of thermal loading and surface effects on mechanical characteristics of nanotubes", Struct. Eng. Mech., 57(1), 179-200. https://doi.org/10.12989/sem.2016.57.1.179
  19. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Modell., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  20. Eltaher, M.A., Mahmoud, F.F., Assie, A.E. and Meletis, E.I. (2013), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774.
  21. Eringen, A.C. (1972), "Nonlocal polar elastic continua", J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  22. 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
  23. Gheshlaghi, B. and Hasheminejad, S.M. (2011), "Surface effects on nonlinear free vibration of nanobeams", Compos. Part B: Eng., 42(4), 934-937. https://doi.org/10.1016/j.compositesb.2010.12.026
  24. Gleiter, H. (2000), "Nanostructured materials: basic concepts and microstructure", Acta Mater., 48(1), 1-29. https://doi.org/10.1016/S1359-6454(99)00285-2
  25. Guo, J.G. and Zhao, Y.P. (2007), "The size-dependent bending elastic properties of nanobeams with surface effects", Nanotechnol., 18(29), 295701. https://doi.org/10.1088/0957-4484/18/29/295701
  26. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Rat. Mech. Analy., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  27. Huang, Y., Hu, K.X., Wei, X. and Chandra, A. (1994), "A generalized self-consistent mechanics method for composite materials with multiphase inclusions", J. Mech. Phys. Sol., 42(3), 491-504. https://doi.org/10.1016/0022-5096(94)90028-0
  28. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", J. Eng. Sci., 50(1), 256-267. https://doi.org/10.1016/j.ijengsci.2010.12.008
  29. Kim, H.S. and Bush, M.B. (1999), "The effects of grain size and porosity on the elastic modulus of nanocrystalline materials", Nanostruct. Mater., 11(3), 361-367. https://doi.org/10.1016/S0965-9773(99)00052-5
  30. Li, L. and Hu, Y. (2017), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", J. Mech. Sci., 120, 159-170. https://doi.org/10.1016/j.ijmecsci.2016.11.025
  31. Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Phys. E: Low-Dimens. Syst. Nanostruct., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028
  32. Murmu, T. and Adhikari, S. (2012), "Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems", Eur. J. Mech.-A/Sol., 34, 52-62. https://doi.org/10.1016/j.euromechsol.2011.11.010
  33. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  34. Sahmani, S., Bahrami, M. and Ansari, R. (2014), "Surface energy effects on the free vibration characteristics of postbuckled third-order shear deformable nanobeams", Compos. Struct., 116, 552-561. https://doi.org/10.1016/j.compstruct.2014.05.035
  35. Shaat, M. (2015), "Effects of grain size and microstructure rigid rotations on the bending behavior of nanocrystalline material beams", J. Mech. Sci., 94, 27-35.
  36. Shaat, M. and Abdelkefi, A. (2015), "Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications", J. Mech. Sci., 101, 280-291.
  37. Shaat, M. and Abdelkefi, A. (2015), "Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force", J. Eng. Sci., 90, 58-75. https://doi.org/10.1016/j.ijengsci.2015.02.002
  38. Shaat, M. and Abdelkefi, A. (2016), "Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs", Microsyst. Technol., 22(2), 305-318. https://doi.org/10.1007/s00542-015-2421-y
  39. Shaat, M., Khorshidi, M.A., Abdelkefi, A. and Shariati, M. (2016), "Modeling and vibration characteristics of cracked nano-beams made of nanocrystalline materials", J. Mech. Sci., 115, 574-585.
  40. Simsek, M. (2014), "Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory", Compos. Part B: Eng., 56, 621-628. https://doi.org/10.1016/j.compositesb.2013.08.082
  41. Tounsi, A., Semmah, A. and Bousahla, A.A. (2013), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech., 3(3), 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  42. Wang, G.F. and Feng, X.Q. (2009), "Timoshenko beam model for buckling and vibration of nanowires with surface effects", J. Phys. D: Appl. Phys., 42(15), 155411. https://doi.org/10.1088/0022-3727/42/15/155411
  43. Wang, G.F., Feng, X.Q., Yu, S.W. and Nan, C.W. (2003), "Interface effects on effective elastic moduli of nanocrystalline materials", Mater. Sci. Eng.: A, 363(1), 1-8. https://doi.org/10.1016/S0921-5093(03)00253-3
  44. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress-based strain gradient theory for elasticity", J. Sol. Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  45. Zenkour, A.M., Abouelregal, A.E., Alnefaie, K.A., Abu-Hamdeh, N.H., Aljinaidi, A.A. and Aifantis, E.C. (2015), "State space approach for the vibration of nanobeams based on the nonlocal thermoelasticity theory without energy dissipation", J. Mech. Sci. Technol., 29(7), 2921-2931. https://doi.org/10.1007/s12206-015-0623-y

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