Coupled systems mechanics

  • 제4권1호
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  • Pages.99-114
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  • 2015
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Static bending and free vibration of FGM beam using an exponential shear deformation theory

  • Hadji, L. (Universite Ibn Khaldoun) ;
  • Khelifa, Z. (Universite Ibn Khaldoun) ;
  • Daouadji, T.H. (Universite Ibn Khaldoun) ;
  • Bedia, E.A. (Laboratoire des Materiaux and Hydrologie, Universite de Sidi Bel Abbes)
  • 투고 : 2014.11.24
  • 심사 : 2015.03.03
  • 발행 : 2015.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

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참고문헌

  1. 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. Sandwich Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. 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
  3. Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Thermal Stresses, 35, 677-694. https://doi.org/10.1080/01495739.2012.688665
  4. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory" Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  5. 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", Composites: Part B - Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  6. Benachour, A.., Daouadji Tahar, H., Ait Atmane, H.., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Composites Part B -Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  7. Benatta, M.A, Tounsi, A., Mechab, I. and Bachir Bouiadjra, M., (2009), "Mathematical solution for bending of short hybrid composite beams with variable fibers spacing", Appl. Math. Comput., 212(2), 337-348. https://doi.org/10.1016/j.amc.2009.02.030
  8. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Composites Part B-Eng., 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020
  9. Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Physics, 41, 225404. https://doi.org/10.1088/0022-3727/41/22/225404
  10. 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
  11. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandwich Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888
  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. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandwich Struct. Mater., 14, 5-33. https://doi.org/10.1177/1099636211426386
  14. Bouremana, M, Houari, M.S.A, Tounsi, A, Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., 15(5), 467-479. https://doi.org/10.12989/scs.2013.15.5.467
  15. Bousahla, A.A., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A., (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computational Methods, (In press).
  16. Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  17. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  18. Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., 13(1), 91-107. https://doi.org/10.12989/scs.2012.13.1.091
  19. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  20. Hadji, L., Daouadji, T.H.,Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  21. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. -ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  22. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E, 40(8), 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021
  23. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  24. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Computational Methods, (In press).
  25. 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), 399-423. https://doi.org/10.12989/scs.2013.15.4.399
  26. Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., 17(1), 21-46. https://doi.org/10.12989/scs.2014.17.1.021
  27. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  28. Li, X.F., Wang, B.L. and Han, J.C. (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212. https://doi.org/10.1007/s00419-010-0435-6
  29. Marur, P.R. (1999), Fracture behaviour of functionally graded materials, Ph.D. Dissertation, Auburn University, Auburn, AL, USA.
  30. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6
  31. Ould Larbi, L., 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. Based Des. Struc., 41, 421-433. https://doi.org/10.1080/15397734.2013.763713
  32. Sallai, B.O., Tounsi, A., Mechab, I., Bachir, B.M, Meradjah, M. and Adda, B.E.A. (2009), "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams", Comput. Mater. Sci., 44(4), 1344-1350. https://doi.org/10.1016/j.commatsci.2008.09.001
  33. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  34. Simsek, M. (2010a), "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
  35. Simsek, M. (2010b), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  36. 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
  37. Tounsi, A, Heireche, H, Berrabah, HM, Benzair, A, Boumia, L. (2008), "Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field", J. Appl. Phys., 104(10), 104301. https://doi.org/10.1063/1.3018330
  38. Tounsi, A., Hassaine Daouadji, T., Benyoucef, S. and Addabedia, E.A. (2009), "Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations", Int. J. Adhes. Adhes., 29(4), 343-351. https://doi.org/10.1016/j.ijadhadh.2008.06.008
  39. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013a), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerospace Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  40. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "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
  41. Tounsi, A., Semmah, A. and Bousahla, A.A. (2013c), "Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech. -ASCE, 3(3), 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  42. Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R. and Amziane, S. (2013d), "Mathematical modeling and optimization of functionally graded structures", Math. Probl. Eng., 213, 1-2.
  43. Zhong, Z. and Yu, T. (2007), "Analytical solution of a cantilever functionally graded beam", Compos. Sci. Technol., 67(3-4), 481-488. https://doi.org/10.1016/j.compscitech.2006.08.023
  44. 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", Aerospace Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

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