Steel and Composite Structures

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Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT

  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Rostami, Rasoul (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arefi, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2015.04.22
  • Accepted : 2015.11.12
  • Published : 2016.02.29
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Abstract

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Arefi, M. (2015a), "Nonlinear electromechanical stability of a functionally graded circular plate integrated with functionally graded piezoelectric layers", Latin Am. J. Solids Struct., 12(9), 1653-1665. https://doi.org/10.1590/1679-78251449
  2. Arefi, M. (2015b), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195
  3. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  4. Arefi, M. and Rahimi, G.H. (2011), "Nonlinear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart Struct. Syst., Int. J., 8(5), 433-446. https://doi.org/10.12989/sss.2011.8.5.433
  5. Askari Farsangi, M.A. and Saidi, A.R. (2013), "Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers", Smart. Mater. Struct., 21(9), 1-15.
  6. Bodaghi, M. and Saidi, A.R. (2011), "Buckling behavior of standing laminated Mindlin plates subjected to body force and vertical loading", Compos. Struct., 93(2), 538-547. https://doi.org/10.1016/j.compstruct.2010.08.026
  7. Bodaghi, M. and Saidi, A.R. (2012), "Buckling analysis of functionally graded Mindlin plates subjected to linearly varying in-plane loading using power series method of Frobenius", Int. J. Eng. Transactions: A, 25(1), 89-106.
  8. Brunelle, E.J. (1971), "Buckling of transversely isotropic Mindlin plates", AIAA J., 9(6), 1018-1022. https://doi.org/10.2514/3.6326
  9. Brunelle, E.J. and Robertson, S.R. (1974), "Initially stressed Mindlin plates", AIAA J., 12(8), 1036-1045. https://doi.org/10.2514/3.49407
  10. Chen, W.C. and Liu, W.H. (1993), "Thermal buckling of antisymmetric angle-ply laminated plates-an analytical Levy-type solution", Therm. Stress., 16(4), 401-419. https://doi.org/10.1080/01495739308946237
  11. Dozio, L. (2013), "Natural frequencies of sandwich plates with FGM core via variable-kinematic 2-D Ritz models", Compos. Struct., 96, 561-568. https://doi.org/10.1016/j.compstruct.2012.08.016
  12. Ghorbanpour Arani, A., Hashemian, M., Loghman, A., Mohammadimeihr, M. (2011), "Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Technical Phys., 52 (5), 815-824. https://doi.org/10.1134/S0021894411050178
  13. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  14. Hasani Baferani, A., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020
  15. Hosseini Hashemi, Sh., Es'haghi, M. and Karimi, M. (2010), "Closed-form solution for free vibration of piezoelectric coupled annular plates using Levinson plate theory", J. Sound Vib., 329(9), 1390-1408. https://doi.org/10.1016/j.jsv.2009.10.043
  16. Jabbari, M., Farzaneh Joubaneh, E. and Mojahedin, A. (2014), "Thermal buckling analysis of porous circularplate with piezoelectric actuators based onfirst order shear deformation theory", Int. J. Mech. Sciences, 83, 57-64. https://doi.org/10.1016/j.ijmecsci.2014.03.024
  17. Kang, J.H. and Leissa, A.W. (2005), "Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges", Int. J. Solids Struct., 42(14), 4220-4238. https://doi.org/10.1016/j.ijsolstr.2004.12.011
  18. Kashtalyan, M. and Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos. Struct., 87(1), 36-43. https://doi.org/10.1016/j.compstruct.2007.12.003
  19. Kim, J. and Reddy, J.N. (2013), "Analytical solutions for bending, vibration, and buckling of FGM platesusing a couple stress-based third-order theory", Compos. Struct., 103, 86-8. https://doi.org/10.1016/j.compstruct.2013.03.007
  20. Ma, L.S. and Wang, T.J. (2004), "Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory", Int. J. Solids Struct., 41(1), 85-101. https://doi.org/10.1016/j.ijsolstr.2003.09.008
  21. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., Trans. ASME, 18, 31-38.
  22. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2010), "Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundation using nonlocal theory", 24(6), 1289-1299. https://doi.org/10.1007/s12206-010-0331-6
  23. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B: Eng., 87, 132-148. DOI: 10.1016/j.compositesb.2015.10.007
  24. Najafizadeh, M.M. and Heydari, H.R. (2004), "Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory", Eur. J. Mech. A/Solid, 23(6), 1085-1100. https://doi.org/10.1016/j.euromechsol.2004.08.004
  25. Najafizadeh, M.M. and Heydari, H.R. (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
  26. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Static, 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", J. Compos. Part B, 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089
  27. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  28. Nosier, A. and Reddy, J.N. (1992), "On vibration and buckling of symmetric laminated plates according to shear deformation theories", Acta. Mech., 94(3), 145-169. https://doi.org/10.1007/BF01176648
  29. Oktem, A.S. and Chaudhuri, R.A. (2007), "Levy type analysis of cross-ply plates based on higher-order theory", Compos. Struct., 78(2), 243-253. https://doi.org/10.1016/j.compstruct.2005.09.012
  30. Palardy, R.F. and Palazotto, A.N. (1990), "Buckling and vibration of composite plates using the levy method", Compos. Struct., 14(1), 61-86. https://doi.org/10.1016/0263-8223(90)90059-N
  31. Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wily and Sons.
  32. Reddy, J.N. (1990), "A review of refined theories of laminated composite plates", Shock. Vib. Digest., 22(7), 3-17. https://doi.org/10.1177/058310249002200703
  33. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using fourvariable refined plate theory", Thin-Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010
  34. Samsam Shariat, B.A. and Eslami, M.R. (2007), "Buckling of thick functionally graded plates under mechanical and thermal loads", Compos. Struct., 78(3), 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001
  35. Shen, H.S. and Li, S.R. (2008), "Postbuckling of sandwich plates with FGM face sheets and temperaturedependent properties", Compos. Struct. Part B, 39(2), 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004
  36. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates restingon elastic foundations under various boundary conditions", Compos. Struct., 99, 76-7. https://doi.org/10.1016/j.compstruct.2012.11.018
  37. Sobhy, M. and Zenkour, A.M. (2015), "Thermodynamical bending of FGM sandwich plates resting on Pasternak's elastic foundations", Adv. Appl. Math. Mech., 7(1), 116-134. https://doi.org/10.4208/aamm.2013.m143
  38. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (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
  39. Whitney, J.M. (1987), Structural Analysis of Laminated Anisotropic Plates, Thechnomic, Lancaster, PA, USA.
  40. Yang, B., Chen, W.Q. and Ding, H.J. (2014), "3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holes", Acta. Mechanica., 226(5), 1571-1590. https://doi.org/10.1007/s00707-014-1270-6
  41. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  42. Zenkour, A.M. and Sobhy, 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
  43. Zenkour, A.M. and Sobhy, M. (2012), "Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates", J. Mecha., 28(3), 439-452. https://doi.org/10.1017/jmech.2012.53

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