Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An analytical approach for buckling of functionally graded plates

  • Received : 2016.10.08
  • Accepted : 2016.11.02
  • Published : 2016.09.25
⟨ Previous Next ⟩

Abstract

In this paper, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, 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 mechanical properties of functionally graded material are assumed to vary according to a power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates are obtained. Comparison studies are performed to verify the validity of present results. The effects of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are investigated and discussed.

Keywords

References

  1. Abdelhak Z., Hadji, L., Hassaine Daouadji, T. and Adda, bedia (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. Adim, B., Tahar H.D. and Rabahi A., (2016), "A simple higher order shear deformation theory for mechanical behavior of laminated composite plates", IJAS, Int. J. Adv. Struct. Eng., 8(2), 103-117. https://doi.org/10.1007/s40091-016-0109-x
  3. Ait Amar Meziane, M., Tounsi, A. and Abdelaziz, H. (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
  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. Ahmed, B., Hassen Ait, A., Abdelouahed, T. 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
  6. 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
  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", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  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. Benferhat, R., Hassaine Daouadji, T. and Mohamed Said, 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
  10. Bennoun, M. 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. Bouazza, M., Abdelouahed, T., Adda-Bedia, E.A. and Megueni, A. (2010), "Thermoelastic stability analysis of functionally graded plates: An analytical approach", Comput. Mater. Sci., 49(4), 865-870. https://doi.org/10.1016/j.commatsci.2010.06.038
  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., 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
  14. Bouderba, B., Houari, M.S.A., Tounsi, A. and 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
  15. 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
  16. 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. Computat. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  17. Chikh, A., Houari, H. and Tounsi, A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617
  18. Cheng, Z.Q. and Batra, R.C. (2000), "Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories", Arch. Mech., 52(1), 143-158.
  19. Eslami, M.R. and Samsam Shariat, B.A. (2006), "Thermal buckling of imperfect functionally graded plates", Int. J. Solid. Struct., 43(14), 4082-4096. https://doi.org/10.1016/j.ijsolstr.2005.04.005
  20. 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
  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. 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
  23. Hirai, T. and Chen, L. (1999), "Recent and prospective development of functionally graded materials in Japan", Mater. Sci. Forum, 308, 308-311.
  24. Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", ZAMM, 82(4), 277-283. https://doi.org/10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y
  25. Koizumi, M. (1993), "The concept of FGM", Ceramic Trans., Funct. Gradient Mater., 34, 3-10.
  26. Laoufi, I., Ameur, M. and Zidi, M. (2016), "Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory", Steel Compos. Struct., 20(4), 889-911. https://doi.org/10.12989/scs.2016.20.4.889
  27. 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
  28. Matsunaga, H. (2009), "Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory", Compos. Struct., 90(1), 76-86. https://doi.org/10.1016/j.compstruct.2009.02.004
  29. Najafizadeh, M. and Heydari, H. (2008), "An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression", Int. J. Mech. Sci., 50(3), 603-612. https://doi.org/10.1016/j.ijmecsci.2007.07.010
  30. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. 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
  31. Salima, A., Abdelkader, F. and Hayat, S. (2016), "An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations", Wind Struct., 22(3), 329-348. https://doi.org/10.12989/was.2016.22.3.329
  32. Sobhy, M. and Zenkour, A.M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012
  33. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  34. Shimpi, R. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622
  35. Tanigawa, Y. (1995), "Some basic thermoelastic problems for nonhomogeneous structural materials", Appl. Math. Mech., 48(6), 287-300.
  36. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  37. 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
  38. Zenkour, A.M. and Mashat, D.S. (2010), "Thermal buckling analysis of ceramic-metal functionally graded plates", Nat. Sci., 2(9), 968-978.
  39. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Be, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001
  40. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005

Cited by

  1. Aluminum and E-glass epoxy plates behavior subjected to shock loading vol.6, pp.2, 2017, https://doi.org/10.12989/amr.2017.6.2.155
  2. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  3. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  4. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  5. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  6. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633
  7. Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate vol.9, pp.5, 2016, https://doi.org/10.12989/csm.2020.9.5.473
  8. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2016, https://doi.org/10.12989/amr.2020.9.4.265
  9. Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation vol.9, pp.6, 2016, https://doi.org/10.12989/csm.2020.9.6.499
  10. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  11. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2016, https://doi.org/10.12989/csm.2021.10.1.061
  12. Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations vol.77, pp.6, 2016, https://doi.org/10.12989/sem.2021.77.6.797