Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bending response of functionally graded piezoelectric plates using a two-variable shear deformation theory

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University) ;
  • Hafed, Zahra S. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2019.02.06
  • Accepted : 2019.06.21
  • Published : 2020.03.25
⟨ Previous Next ⟩

Abstract

This paper proposes a bending analysis for a functionally graded piezoelectric (FGP) plate through utilizing a two-variable shear deformation plate theory under simply-supported edge conditions. The number of unknown functions used in this theory is only four. The electric potential distribution is assumed to be a combination of a cosine function along the cartesian coordinate. Applying the analytical solutions of FGP plate by using Navier's approach and the principle of virtual work, the equilibrium equations are derived. The paper also discusses thoroughly the impact of applied electric voltage, plate's aspect ratio, thickness ratio and inhomogeneity parameter. Results are compared with the analytical solution obtained by classical plate theory, first-order-shear deformation theory, higher-order shear deformation plate theories and quasi-three-dimensional sinusoidal shear deformation plate theory.

Keywords

References

  1. Arefi, M. and Zenkour, A.M. (2016a), "A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magnet-thermo-electric environment", J. Sandw. Struct. Mater., 18, 624-651. https://doi.org/10.1177%2F1099636216652581. https://doi.org/10.1177/1099636216652581
  2. Arefi, M. and Zenkour, A.M. (2016b), "Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets", Smart. Mater. Struct., 25, 115040. https://doi.org/10.1088/0964-1726/25/11/115040.
  3. Arefi, M. and Zenkour, A.M. (2017a), "Nonlocal electro-thermo mechanical analysis of a sandwich nanoplate containing a Kelvin-Voigt viscoelastic nanoplate and two piezoelectric layers", Acta. Mech., 228, 475-493. https://doi.org/10.1007/s00707-016-1716-0.
  4. Arefi, M. and Zenkour, A.M. (2017b), "Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face sheets", Compos. Struct., 159, 479-90. https://doi.org/10.1016/j.compstruct.2016.09.088.
  5. Arefi, M. and Zenkour, A.M. (2017c), "Thermo-electro-mechanical bending behavior of sandwich nanoplate integrated with piezoelectric face-sheets based on trigonometric plate theory", Compos. Struct., 162, 108-22. https://doi.org/10.1016/j.compstruct.2016.11.071.
  6. Baltacioglu, A.K., Akgoz, B. and Civalek, O. (2010), "Nonlinear static response of laminated composite plates by discrete singular convolution method", Compos. Struct., 93, 153-161. https://doi.org/10.1016/j.compstruct.2010.06.005.
  7. Benbakhti A., Bouiadjra, M.B., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates", Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975.
  8. Bouazza, M., Zenkour, A.M. and Benseddiq, N. (2018), "Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects", Acta Mech., 229(5), 2251-2265. https://doi.org/10.1007/s00707-017-2097-8.
  9. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46(1), 194-203. https://doi.org/10.2514/1.32490.
  10. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. B Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  11. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis", Int. J. Solid Struct., 43, 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  12. Demir, C., Mercan, K. and Civalek, O. (2016), "Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel", Compos. B Eng., 94, 1-10. https://doi.org/10.1016/j.compositesb.2016.03.031.
  13. Ebrahimi, F. and Rastgoo, A. (2008), "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct., 17(1), 15044. https://doi.org/10.1088/0964-1726/17/1/015044.
  14. Fereidoon, A., Asghardokht, S.M. and Mohyeddin, A. (2011), "Bending analysis of thin functionally graded plates using generalized differential quadrature method", Arch. Appl. Mech., 81, 1523-1539. https://doi.org/10.1007/s00419-010-0499-3.
  15. Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C. and Polit, O. (2011), "Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Compos. B Eng., 42(5), 1276-1284. https://doi.org/10.1016/j.compositesb.2011.01.031.
  16. Ghasemabadian, M.A. and Kadkhodayan, M. (2016), "Investigation of buckling behavior of functionally graded piezoelectric (FGP) rectangular plates under open and closed circuit conditions", Struct. Eng. Mech., 60(2), 271-299. http://doi.org/10.12989/sem.2016.60.2.271.
  17. Giannakopoulos, A.E. and Suresh, S. (1999), "Theory of indentation of piezoelectric materials", Acta Mater., 47, 2153-2164. https://doi.org/10.1016/S1359-6454(99)00076-2.
  18. Gurses, M., Civalek, O., Korkmaz, A. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory", Int. J. Numer. Meth. Eng., 79, 290-313. https://doi.org/10.1002/nme.2553.
  19. Jandaghian, A.A. and Rahmani, O. (2017), "Size-dependent free vibration analysis of functionally graded piezoelectric plate subjected to thermo-electro-mechanical loading", J. Intell. Mater. Syst. Struct., 28, 3039-3053. https://doi.org/10.1177%2F1045389X17704920. https://doi.org/10.1177/1045389x17704920
  20. Jha, D.K., Kant, T. and Singh, R.K. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001.
  21. Liew, K.M., He, X.Q., Tan, M.J. and Lim, H.K. (2004), "Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method", Int. J. Mech. Sci., 46, 411-31. https://doi.org/10.1016/j.ijmecsci.2004.03.011.
  22. Mantari, J.L. and Guedes Soares, C. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019.
  23. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012a), "A new higher order shear deformation theory for sandwich and composite laminated plates", Compos. B Eng., 43(3), 1489-1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
  24. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012b), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids Struct., 49(1), 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008.
  25. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012c), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94(2), 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007.
  26. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87, 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002.
  27. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  28. 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. (2012a), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  29. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012b), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. B Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  30. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.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", Compos. B Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  31. 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(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056.
  32. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-52. https://doi.org/10.1115/1.3167719.
  33. 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%3C663::AID-NME787%3E3.0.CO;2-8.
  34. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct., 1(1), 1-21. http://dx.doi.org/10.3850/S201042861100002X.
  35. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys., 23, 184-191. https://doi.org/10.1002/sapm1944231184.
  36. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
  37. 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(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  38. Tu, T.M., Quoc, T.H. and Long, N.V. (2017), "Bending analysis of functionally graded plates using new eight-unknown higher order shear deformation theory", Struct. Eng. Mech., 62(3), 311-324. https://doi.org/10.12989/sem.2017.62.3.311.
  39. Zenkour, A.M. (2004), "Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory", Acta Mech., 171(3-4), 171-187. https://doi.org/10.1007/s00707-004-0145-7.
  40. Zenkour, A.M. (2005a), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solids Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  41. Zenkour, A.M. (2005b), "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. (2005c), "On vibration of functionally graded plates according to a refined trigonometric plate theory", Int. J. Struct. Stab. Dyn., 5(2), 279-297. https://doi.org/10.1142/S0219455405001581.
  43. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009.
  44. 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.
  45. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11-12), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026.
  46. Zenkour, A.M. (2013a), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Model., 37(20-21), 9041-9051. https://doi.org/10.1016/j.apm.2013.04.022.
  47. Zenkour, A.M. (2013b), "Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory", J. Sandw. Struct. Mater., 15(6), 629-656. https://doi.org/10.1177%2F1099636213498886. https://doi.org/10.1177/1099636213498886
  48. Zenkour, A.M. (2013c), "Bending of FGM plates by a simplified four-unknown shear and normal deformations theory", Int. J. Appl. Mech., 5(2) 1350020, 1-15. https://doi.org/10.1142/S1758825113500208.
  49. Zenkour, A.M. (2015), "Thermal bending of layered composite plates resting on elastic foundations using four-unknown shear and normal deformations theory", Compos. Struct., 122, 260-270. https://doi.org/10.1016/j.compstruct.2014.11.064.
  50. Zenkour, A.M. and Aljadani, M.H. (2018), "Mechanical buckling of functionally graded plates using a refined higher-order shear and normal deformation plate theory", Adv. Aircraft Spacecraft Sci., 5(6), 615-632. https://doi.org/10.12989/aas.2018.5.6.615.

Cited by

  1. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.115