Wind and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bending analysis of FGM plates using a sinusoidal shear deformation theory

  • Hadji, Lazreg (Departement de Genie Civil, Universite Ibn Khaldoun) ;
  • Zouatnia, Nafissa (Laboratoire de Structures, Geotechnique et Risques, Universite Hassiba Benbouali de Chlef) ;
  • Kassoul, Amar (Laboratoire de Structures, Geotechnique et Risques, Universite Hassiba Benbouali de Chlef)
  • Received : 2016.07.03
  • Accepted : 2016.10.06
  • Published : 2016.12.25
⟨ Previous Next ⟩

Abstract

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.

Keywords

References

  1. 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
  2. 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
  3. 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
  4. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  5. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  6. Bakora, A. and Tounsi, A. (2015)," Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  7. 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
  8. 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
  9. 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, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  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. 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
  12. Bouderba, B., Houari, M.S.A. and Tounsi, A., Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  13. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  14. 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
  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. 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
  17. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and 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. Comput. Method, 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  18. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., DOI: http://dx.doi.org/10.1016/j.ijmecsci.2016.01.025.
  19. 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
  20. Fukui, Y., Yamanaka, N. and Enokida, Y. (1997), "Bending Strength of an AI-AI3Ni Functionally Graded Material", Compos. : Part B, 28, 37-43. https://doi.org/10.1016/S1359-8368(96)00018-2
  21. 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", J. Eng. Mech.- ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  22. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties", Steel Compos. Struct., 15(5), 481-505. https://doi.org/10.12989/scs.2013.15.5.481
  23. Koizumi, M. (1997), "FGM activites in Japan", Compos.: Part B, 28(1), 1-4.
  24. 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
  25. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  26. Mantari, J.L. and Guedes Soares, C. (2012), "Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory" , Compos. Struct., 94, 1991-2000. https://doi.org/10.1016/j.compstruct.2012.01.005
  27. 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), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  28. Prakash, T., Singha, M.K. and Ganapathi, M. (2009), "Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates", Comput. Mech., 43, 341-350. https://doi.org/10.1007/s00466-008-0309-8
  29. Sina, S.A. Navazi H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Design, 30, 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  30. Tai, H.T. and Kim, S.E. (2013a), "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
  31. Tai, H.T. and Kim, S.E. (2013b), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025
  32. Tai, 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, 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  33. Tai, H.T., Nguyen, T.K. and Vo, T.P. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech. A Solids, 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  34. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209 -220. https://doi.org/10.1016/j.ast.2011.11.009
  35. Xiang, H.J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Compos. : Part B, 39, 292-303. https://doi.org/10.1016/j.compositesb.2007.01.005
  36. 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
  37. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  38. Zhang, D.G. (2013), "Modeling and analysis of FGM rectangular plates based on physical neutral surface and high order shear deformation theory", Int. J. Mech. Sci., 68, 92-104. https://doi.org/10.1016/j.ijmecsci.2013.01.002
  39. 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

Cited by

  1. Analysis of functionally graded plates using a sinusoidal shear deformation theory vol.19, pp.4, 2017, https://doi.org/10.12989/sss.2017.19.4.441
  2. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  3. A refined hyperbolic shear deformation theory for bending of functionally graded beams based on neutral surface position vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.683
  4. Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations vol.66, pp.6, 2016, https://doi.org/10.12989/sem.2018.66.6.729
  5. Elastic analysis of arbitrary shape plates using Meshless local Petrov-Galerkin method vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.235