Advances in nano research

  • 제4권4호
  • /
  • Pages.251-264
  • /
  • 2016
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams

  • Kheroubi, Boumediene (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Benzair, Abdelnour (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Tounsi, Abdelouahed (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Semmah, Abdelwahed (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique)
  • 투고 : 2016.02.25
  • 심사 : 2016.10.28
  • 발행 : 2016.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a simple and refined nonlocal hyperbolic higher-order beam theory is proposed for bending and vibration response of nanoscale beams. The present formulation incorporates the nonlocal scale parameter which can capture the small scale effect, and it considers both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness without employing shear correction factor. The highlight of this formulation is that, in addition to modeling the displacement field with only two unknowns, the thickness stretching effect (${\varepsilon}_z{\neq}0$) is also included in the present model. By utilizing the Hamilton's principle and the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale beam are reformulated. Verification studies demonstrate that the developed theory is not only more accurate than the refined nonlocal beam theory, but also comparable with the higher-order shear deformation theories which contain more number of unknowns. The theoretical formulation proposed herein may serve as a reference for nonlocal theories as applied to the static and dynamic responses of complex-nanobeam-system such as complex carbon nanotube system.

키워드

과제정보

연구 과제 주관 기관 : Algerian National Thematic Agency of Research in Science and Technology (ATRST), university of Sidi Bel Abbes (UDL SBA) in Algeria

참고문헌

  1. Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326, 277-289. https://doi.org/10.1016/j.jsv.2009.04.044
  2. Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  3. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  4. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  5. Amara, K., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34, 3933-3942. https://doi.org/10.1016/j.apm.2010.03.029
  6. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  7. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  8. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  9. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020
  10. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  11. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (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
  12. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  13. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  14. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  15. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  16. Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193
  17. Duan, W.H. and Wang, C.M. (2007), "Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory", Nanotechnology, 18, 385704. https://doi.org/10.1088/0957-4484/18/38/385704
  18. Ebrahimi, F. and Barati, M.R. (2016), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  19. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51-64. https://doi.org/10.12989/anr.2016.4.1.051
  20. Eringen AC. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  21. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  22. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  23. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  24. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  25. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  26. Lu, P., Zhang, P.Q., Lee, H.P., Wang, C.M. and Reddy, J.N. (2007), "Non-local elastic plate theories", Proc. Royal Soc. A: Math. Phys. Eng. Sci., 463, 3225-3240. https://doi.org/10.1098/rspa.2007.1903
  27. Murmu, T. and Pradhan, S.C. (2009a), "Buckling of biaxially compressed orthotropic plates at small scales", Mech. Res. Commun., 36, 933-938. https://doi.org/10.1016/j.mechrescom.2009.08.006
  28. Murmu, T. and Pradhan, S.C. (2009b), "Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model", Physica E: Low-dimens. Syst. Nanostruct., 41, 1628-1633. https://doi.org/10.1016/j.physe.2009.05.013
  29. Murmu, T. and Pradhan, S.C. (2009c), "Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity", J. Appl. Phys., 106, 104301. https://doi.org/10.1063/1.3233914
  30. Murmu, T. and Pradhan, S.C. (2009d), "Vibration analysis of nano-single-layered grapheme sheets embedded in elastic medium based on nonlocal elasticity theory", J. Appl. Phys., 105, 064319. https://doi.org/10.1063/1.3091292
  31. Pradhan, S.C. (2009), "Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", Phys. Lett. A, 373, 4182-4188. https://doi.org/10.1016/j.physleta.2009.09.021
  32. Pradhan, S.C. and Kumar, A. (2011), "Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method", Compos. Struct., 93, 774-779. https://doi.org/10.1016/j.compstruct.2010.08.004
  33. 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
  34. Pradhan, S.C. and Phadikar, J.K. (2009a), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A, 373, 1062-1069. https://doi.org/10.1016/j.physleta.2009.01.030
  35. Pradhan, S.C. and Phadikar, J.K. (2009b), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325, 206-223. https://doi.org/10.1016/j.jsv.2009.03.007
  36. Pradhan, S.C. and Phadikar, J.K. (2010), "Scale effect and buckling analysis of multilayered graphene sheets based on nonlocal continuum mechanics", J. Comput. Theor. Nanosci., 7, 1948-1954. https://doi.org/10.1166/jctn.2010.1565
  37. Pradhan, S.C. and Sahu, B. (2010), "Vibration of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory", J. Comput. Theor. Nanosci., 7, 1042-1050. https://doi.org/10.1166/jctn.2010.1451
  38. Reddy, J.N. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48, 1507-1518. https://doi.org/10.1016/j.ijengsci.2010.09.020
  39. Reddy, J.N. and Pang, S.D. (2008). "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103, 023511-1-023511-16. https://doi.org/10.1063/1.2833431
  40. Semmah, A., Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2015), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Full. Nanotube. Carbon Nanostruct., 23, 518-522. https://doi.org/10.1080/1536383X.2012.749457
  41. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013c), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  42. Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013a), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12, 1350025. https://doi.org/10.1142/S0219581X13500257
  43. 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
  44. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013d), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  45. Tounsi, A., Semmah, A. and Bousahla, A.A. (2013b), "Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory", ASCE J. Nanomech. Micromech., 3, 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  46. Wang, C.Y., Murmu, T. and Adhikari, S. (2011), "Mechanisms of nonlocal effect on the vibration of nanoplates", Appl. Phys. Lett., 98, 153101. https://doi.org/10.1063/1.3579249
  47. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124301. https://doi.org/10.1063/1.2141648
  48. 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
  49. Zenkour, A.M. (2013), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Model., 37, 9041-9051. https://doi.org/10.1016/j.apm.2013.04.022
  50. Zidi, M., Tounsi, A., Houari M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.771
  2. A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.269
  3. Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method vol.76, pp.3, 2016, https://doi.org/10.12989/sem.2020.76.3.413
  4. In-plane varying bending force effects on wave dispersion characteristics of single-layered graphene sheets vol.10, pp.2, 2021, https://doi.org/10.12989/anr.2021.10.2.101
  5. Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory vol.10, pp.3, 2016, https://doi.org/10.12989/anr.2021.10.3.281