Structural Engineering and Mechanics

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Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium

  • Received : 2015.03.11
  • Accepted : 2015.07.31
  • Published : 2015.09.10
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Abstract

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

Keywords

References

  1. Ameur, M., Tounsi, A., Mechab, I. and El Bedia, A.A., (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15, 1405-1414. https://doi.org/10.1007/s12205-011-1361-z
  2. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda Bedia, E.A., (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46, 425-434. https://doi.org/10.1007/s11029-010-9159-5
  3. Della Croce, L. and Venini, P. (2004), "Finite elements for functionally graded Reissner-Mindlin plates", Comput. Meth. Appl. Mech. Eng., 193, 705-725. https://doi.org/10.1016/j.cma.2003.09.014
  4. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  5. Fares, M.E., Elmarghany, M.K. and Atta, D. (2009), "An efficient and simple refined theory for bending and vibration of functionally graded plates", Compos. Struct., 91, 296-305. https://doi.org/10.1016/j.compstruct.2009.05.008
  6. Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82, 277-283.
  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, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  8. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  9. Merdaci, S., Tounsi, A., Houari, M., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81, 1507-1522. https://doi.org/10.1007/s00419-010-0497-5
  10. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib. 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  11. Reddy J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  12. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34, 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  13. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2011), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Tech., 24, 563-572.
  14. Xiao, J.R., Batra, R.C., Gilhooley, D.F., Gillespie, J.W. and McCarthy, M.A. (2007), "Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions", Comput. Meth. Appl. Mech. Eng., 196, 979-987. https://doi.org/10.1016/j.cma.2006.08.002
  15. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solid. Struct., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  16. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93, 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022

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