DOI QR코드

DOI QR Code

Nonlinear cylindrical bending analysis of E-FGM plates with variable thickness

  • Kaci, Abdelhakim (Department of Civil Engineering and Hydraulics, University of Saida) ;
  • Belakhdar, Khalil (Department of Civil Engineering and Hydraulics, University of Saida) ;
  • Tounsi, Abdelouahed (Laboratory of Materials and Hydrology, University of Sidi Bel Abbes) ;
  • Bedia, El Abbes Adda (Laboratory of Materials and Hydrology, University of Sidi Bel Abbes)
  • 투고 : 2012.11.05
  • 심사 : 2013.11.11
  • 발행 : 2014.04.25

초록

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

키워드

참고문헌

  1. Atmane, H., Tounsi, A., Ziane, N. and Mechab, I. (2011), "Mathematical solution for free vibration of sigmoidfunctionally graded beams with varying cross-section", Steel Comp. Struct., Int. J., 11(6), 489-504. https://doi.org/10.12989/scs.2011.11.6.489
  2. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Comp. Struct., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  3. Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299(4-5), 720-738. https://doi.org/10.1016/j.jsv.2006.06.068
  4. Fertis, D.G. and Mijatov, M.M. (1989), "Equivalent systems for variable thickness plates", ASCE J. Eng. Mech., 115(10), 2287-300. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:10(2287)
  5. GhannadPour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75(1-4), 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004
  6. Hirano, T., Yamada, T., Teraki, J., Niino, M. and Kumakawa, A. (1988), "A study on functionally gradient material design system for a thrust chamber", Proceedings of the 16th International Symposium on Space Technology and Science, Sapporo, Japan, May.
  7. Hiroyuki, M. (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
  8. Kaci, A., Tounsi, A., Bakhti, K. and Bedia, E.A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Comp. Struct., Int. J., 12(6), 491-504. https://doi.org/10.12989/scs.2012.12.6.491
  9. Kashtalyan, M. (2004), "Three-dimensional elasticity solution for bending of functionally graded rectangular plates", Europ. J. Mech. A/Solids, 23(5), 853-864. https://doi.org/10.1016/j.euromechsol.2004.04.002
  10. Markworth, A.J., Ramesh, K.S. and Parks, W.P. (1995), "Modeling studies applied to functionally graded materials", J. Mater. Sci., 30(9), 2183-2193. https://doi.org/10.1007/BF01184560
  11. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  12. Mizuguchi, F. and Ohnabe, H. (1996), "Large deflections of heated functionally graded simply supported rectangular plates with varying rigidity in thickness direction", Proceedings of the 11th Technical Conference of the American Society for Composites, USA, pp. 957-966.
  13. Navazi, H.M., Haddadpour, H. and Rasekh, M. (2006), "An analytical solution for nonlinear cylindrical bending of functionally graded plates", Thin Wall. Struct., 44(11), 1129-1137. https://doi.org/10.1016/j.tws.2006.10.013
  14. Niino, M. and Maeda, S. (1990), "Recent development status of functionally gradient materials", ISIJ Int., 30(9), 699-703. https://doi.org/10.2355/isijinternational.30.699
  15. Pradhan, S.C. and Sarkar, A. (2009), "Analyses of tapered FGM beams with nonlocal theory", Struct. Eng. Mech., Int. J., 32(6), 811-833. https://doi.org/10.12989/sem.2009.32.6.811
  16. Praveen, G.N., Chin, C.D. and Reddy, J.N. (1999), "Thermoelastic analysis of functionally graded ceramic-metal cylinder", J. Eng. Mech. ASCE, 125(11), 1259-1267. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:11(1259)
  17. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  18. 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
  19. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally grade circular and annular plates" Euro. J. Mech. A/Solids, 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4
  20. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, (2nd Ed.), CRC Press, Boca Raton, FL, USA.
  21. 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", Comp. Mater. Sci., 44(4), 1344-1350.
  22. Sun, C.T. and Chin, H. (1988), "Analysis of asymmetric composite laminates", AIAA J., 26(6), 714-718. https://doi.org/10.2514/3.9957
  23. Sun, C.T. and Chin, H. (1991), "Cylindrical bending of unsymmetric composite laminates", AIAA J., 30(5), 1438-1440.
  24. Tanigawa, Y., Akai, T., Kawamura, R. and Oka, N. (1996), "Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature dependent material properties", J. Therm. Stresses, 19(1), 77-102. https://doi.org/10.1080/01495739608946161
  25. Xu, Y.P. and Zhou, D. (2008), "Three-dimensional elasticity solution for simply supported rectangular plates with variable thickness", J. Strain Anal. Eng. Des., 43(3), 165-176. https://doi.org/10.1243/03093247JSA353
  26. Yas, B., Aragh, S. and Heshmati, M. (2011), "Three-dimensional free vibration analysis of functionally graded fiber reinforced cylindrical panels using differential quadrature method", Struct. Eng. Mech., Int. J., 37(5), 529-542. https://doi.org/10.12989/sem.2011.37.5.529
  27. Yepeng, X. and Ding, Z. (2009), "Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness", Compos. Struct., 91(1), 56-65. https://doi.org/10.1016/j.compstruct.2009.04.031
  28. Zenkour, A.M. (2007), "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
  29. Zhong, Z. and Shang, E.T. (2003), "Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate", Int. J. Solids Struct., 40(20), 5335-5352. https://doi.org/10.1016/S0020-7683(03)00288-9

피인용 문헌

  1. Hygrothermal analysis of laminated composites using C0 FE model based on higher order zigzag theory vol.23, pp.1, 2014, https://doi.org/10.12989/scs.2017.23.1.041
  2. Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element vol.28, pp.3, 2014, https://doi.org/10.12989/scs.2018.28.3.389
  3. Nonlinear thermoelastic analysis of FGM thick plates vol.8, pp.5, 2014, https://doi.org/10.12989/csm.2019.8.5.439
  4. Three-dimensional modelling of functionally graded beams using Saint-Venant's beam theory vol.72, pp.2, 2014, https://doi.org/10.12989/sem.2019.72.2.257