Steel and Composite Structures

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A new first shear deformation beam theory based on neutral surface position for functionally graded beams

  • Received : 2013.01.13
  • Accepted : 2013.07.31
  • Published : 2013.11.25
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Abstract

In this paper, a new first-order shear deformation beam theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded beams. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded beam which its material properties vary in the thickness direction is determined. Based on the present new first-order shear deformation beam theory and the neutral surface concept together with Hamilton's principle, the motion equations are derived. To examine accuracy of the present formulation, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending and free vibration responses of functionally graded beam are discussed.

Keywords

References

  1. Alshorbagy, A.E., Eltaher, M. and Mahmoud, F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  2. Asghari, M. (2010), "On the size-dependent behavior of functionally graded micro-beams", Mater. Design, 31(5), 2324-2329. https://doi.org/10.1016/j.matdes.2009.12.006
  3. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039
  4. 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
  5. Kaci, A., Bakhti, K. and Tounsi, A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., Int. J., 12(6), 491-504. https://doi.org/10.12989/scs.2012.12.6.491
  6. 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
  7. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  8. 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. Struct. Mach. [In press]
  9. 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
  10. 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
  11. Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Adda Bedia, E.A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19(8), 641-652. https://doi.org/10.1080/15376494.2011.581409
  12. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  13. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, (2nd Edition), John Wiley & Sons Inc.
  14. Sallai, B.O., Tounsi, A., Mechab, I., Bachir Bouiadjra, M., Meradjah, M. and Adda Bedia, 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
  15. Sanjay Anandrao, K., Gupta, R.K., Ramchandran, P., Venkateswara Rao, G. (2012), "Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams", Struct. Eng. Mech., Int. J., 44(3), 339-361. https://doi.org/10.12989/sem.2012.44.3.339
  16. Simsek, M. (2009), "Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method", Int. J. Eng. Appl. Sci., 1(3), 1-11.
  17. 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
  18. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  19. Simsek, M. and Yurtçu, H.H. (2012), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal timoshenko beam theory," Compos. Struct., 97, 378-386.
  20. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  21. Soldatos, K. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3-4), 195-220. https://doi.org/10.1007/BF01176650
  22. Suresh, S. and Mortensen, A. (1998), "Fundamentals of Functionally Graded Materials", IOM Communications Ltd., London.
  23. 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
  24. Yahoobi, H. and Feraidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341. https://doi.org/10.3923/jas.2010.337.342
  25. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83(1), 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006
  26. Yesilce, Y. (2010), "Effect of axial force on the free vibration of Reddy-Bickford multi-span beam carrying multiple spring-mass systems", J. Vib. Control, 16(1), 11-32. https://doi.org/10.1177/1077546309102673
  27. Yesilce, Y. and Catal, S. (2009), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method", Struct. Eng. Mech., Int. J., 31(4), 453-476. https://doi.org/10.12989/sem.2009.31.4.453
  28. Yesilce, Y. and Catal, S. (2011), "Solution of free vibration equations of semi-rigid connected Reddy-Bickford beams resting on elastic soil using the differential transform method", Arch. Appl. Mech., 81(2), 199-213. https://doi.org/10.1007/s00419-010-0405-z
  29. Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44(2), 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016

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