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Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory

  • Received : 2016.09.08
  • Accepted : 2016.12.21
  • Published : 2016.12.25
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Abstract

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

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References

  1. Abdelhak, Z., Hadji, L., Hassaine Daouadji, T. and Adda bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind. Struct., 22(3), 291-305. https://doi.org/10.12989/was.2016.22.3.291
  2. Abrate, S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B, 39(1),151-158. https://doi.org/10.1016/j.compositesb.2007.02.026
  3. Adim, B., Hassaine Daouadji, T. and Rabahi, A. (2016), "A simple higher order shear deformation theory for mechanical behavior of laminated composite plates", Int. J. Adv. Struct. Eng., IJAS, 8(2), 103-117. https://doi.org/10.1007/s40091-016-0109-x
  4. Ait Atmane, H., Tounsi, A., Mechab, I. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mat., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x
  5. 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
  6. Baghdadi, H., Tounsi, A., Zidour, M. and Benzair, A. (2015), "Thermal effect on vibration characteristics of armchair and zigzag single-walled carbon nanotubes using nonlocal parabolic beam theory", Fullerenes, Nanotube. Carbon Nanostruct., 23(3), 266-272. https://doi.org/10.1080/1536383X.2013.787605
  7. Benferhat, R., Hassaine Daouadji, T. and Said Mansour, M. (2016), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(5), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429
  8. Bensattalah, T., Zidour, M., Tounsi, A. and Bedia, E.A.A. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon anotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 1-14. https://doi.org/10.1007/s11029-016-9553-8
  9. Bhimaraddi, A. and Stevens, L. (1984), "A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates", J. Appl. Mech., ASME, 51(1), 195-198. https://doi.org/10.1115/1.3167569
  10. Bellifa, H., Benrahou, K.H.L., Hadji, Houari, M.S.A. and Tounsi, A. (2015), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275.
  11. 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
  12. Boumia, L., Zidour, M., Benzair, A. and Tounsi, A. (2014), "A Timoshenko beam model for vibration analysis of chiral single-walled carbon nanotubes", Physica E: Low-dimensional Syst. Nanostruct., 59, 186-191. https://doi.org/10.1016/j.physe.2014.01.020
  13. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda Bedia, El A. (2015), "Postbuckling analysis of functionally graded beams using hyperbolic shear deformation theory", Rev. Inform. Eng. Appl., 2(1), 1- 14. https://doi.org/10.1186/s40535-014-0004-0
  14. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda Bedia, El A. (2015), "Postbuckling analysis of nanobeams using trigonometric Shear deformation theory", Appl. Sci. Report., 10(2), 112-121.
  15. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda Bedia, El A. (2014), "Hygrothermal effects on the postbuckling response of composite beams", Am. J. Mater. Res., 1(2), 35-43.
  16. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Comp. Part B: Eng., 42(2), 23-133.
  17. Carrera, E. and Ciuffreda, A. (2005), "A unified formulation to assess theories of multilayered plates for various bending problems", Compos. Struct., 69(3), 271-293. https://doi.org/10.1016/j.compstruct.2004.07.003
  18. Carrera, E., Brischetto, S. and Nali, P. (2011), Plates and shells for smart structures: classical and advanced theories for modeling and analysis, New York, USA, John Wiley & Sons.
  19. Gafour, F., Zidour, M., Tounsi, A., Heireche, H. and Semmah, A. (2015), "Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory", Physica E: Low-dimensional Syst. Nanostruct., 48, 118-123.
  20. Feldman, E. and Aboudi, J. (1997), "Buckling analysis of functionally graded plates subjected to uniaxial loading", Compos. Struct., 38(1-4), 29-36. https://doi.org/10.1016/S0263-8223(97)00038-X
  21. 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
  22. Hassaine Daouadji, T. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631
  23. Hassaine Daouadji, T. and Adda bedia, E.A. (2013), "Analytical solution for bending analysis of functionally graded plates", Scientia Iranica, Trans. B: Mech. Eng., 20(3), 516-523.
  24. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), "A high-order theory of plate deformation-part 2: laminated plates", J. Appl. Mech., ASME, 44(4), 669-674. https://doi.org/10.1115/1.3424155
  25. Mahi, A., Adda Bedia, E. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plate", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  26. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87(4), 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002
  27. 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
  28. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., ASME, 18, 31-38.
  29. Moradi, S. and Mansouri, M.H. (2012), "Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature", Steel Compos Struct., 12, 129-147. https://doi.org/10.12989/scs.2012.12.2.129
  30. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  31. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C. and Jorge, R.M.N. (2013), "Free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089
  32. Nelson, R.B., Lorch, D.R. (1974), "A refined theory for laminated orthotropic plates", J. Appl. Mech., ASME, 41(1), 177-184. https://doi.org/10.1115/1.3423219
  33. Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method", Compos. Part B: Eng., 35(6), 685-697. https://doi.org/10.1016/j.compositesb.2004.02.004
  34. Rashidi, M.M., Shooshtari, A. and Anwar, Beg O. (2012), "Homotopy perturbation study of nonlinear vibration of Von Karman rectangular plates", Comput. Struct., 106-107, 46-55. https://doi.org/10.1016/j.compstruc.2012.04.004
  35. Reissner, E. (1945), "Reflection on the theory of elastic plates", J. Appl. Mech., ASME, 38(11), 1453-1464.
  36. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., ASME, 51(4), 745-752. https://doi.org/10.1115/1.3167719
  37. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Num. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  38. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct., 1(1), 1-21. https://doi.org/10.3850/S201042861100002X
  39. Mantari, J.L. and Guedes Soares, C. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019
  40. Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030
  41. Tlidji, Y., Hassaine Daouadji, T., Hadji, L. and Adda bedia E.A. (2014), "Elasticity solution for bending response of functionally graded sandwich plates under thermo mechanical loading", J. Therm. Stress, 37(7), 852-869. https://doi.org/10.1080/01495739.2014.912917
  42. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  43. Zenkour, A. (2007), "Trigonometric Benchmark. Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Arch. Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y
  44. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  45. Zidour, M., Benrahou, K.H., Tounsi, A., Bedia, E.A.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0

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