Structural Engineering and Mechanics

  • 제62권6호
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  • Pages.675-693
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Stability analysis of transversely isotropic laminated Mindlin plates with piezoelectric layers using a Levy-type solution

  • Ghasemabadian, M.A. (Department of Mechanical Engineering, Ferdowsi University of Mashhad) ;
  • Saidi, A.R. (Department of Mechanical Engineering, Shahid Bahonar University of Kerman)
  • 투고 : 2016.02.14
  • 심사 : 2016.11.23
  • 발행 : 2017.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

키워드

참고문헌

  1. Abdollahi, M., Saidi, A. and Mohammadi, M. (2015), "Buckling analysis of thick functionally graded piezoelectric plates based on the higher-order shear and normal deformable theory", Acta Mechanica 226(8), 1-14. https://doi.org/10.1007/s00707-014-1156-7
  2. Akhras, G. and Li, W. (2010), "Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method", Compos. Struct., 92(1), 31-38. https://doi.org/10.1016/j.compstruct.2009.06.010
  3. Arefi, M. (2016), "Buckling analysis of the functionally graded sandwich rectangular plates integrated with piezoelectric layers under bi-axial loads", J. Sandwich Struct. Mater., doi: 10.1177/1099636216642393.
  4. Askari Farsangi, M.A. and Saidi, A. (2012), "Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers", Smart Mater. Struct., 21(9), 1-15.
  5. Askari Farsangi, M.A., Saidi, A. and Batra, R. (2013), "Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates", J. Sound Vib., 332(22), 5981-5998. https://doi.org/10.1016/j.jsv.2013.05.010
  6. Batra, R. and Geng, T. (2001a), "Enhancement of the dynamic buckling load for a plate by using piezoceramic actuators", Smart Mater. Struct., 10(5), 925-933. https://doi.org/10.1088/0964-1726/10/5/309
  7. Bodaghi, M. and Saidi, A. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016
  8. Bodaghi, M. and Saidi, A. (2011a), "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
  9. Bodaghi, M. and Saidi, A. (2011b), "Thermoelastic buckling behavior of thick functionally graded rectangular plates", Arch. Appl. Mech., 81(11), 1555-1572. https://doi.org/10.1007/s00419-010-0501-0
  10. Chandrashekhara, K. and Bhatia, K. (1993), "Active buckling control of smart composite plates-finite-element analysis", Smart Mater. Struct., 2(1), 31-38. https://doi.org/10.1088/0964-1726/2/1/005
  11. Chen, X.L., Zhao, Z.Y. and Liew, K.M. (2008), "Stability of piezoelectric FGM rectangular plates subjected to non-uniformly distributed load, heat and voltage", Adv. Eng. Softw., 39(2), 121-131. https://doi.org/10.1016/j.advengsoft.2006.12.004
  12. Cheng, J., Han, H. and Taheri, F. (2008), "An adaptive enhancement of dynamic buckling of a laminated composite beam under axial impact by surface bonded piezoelectric patches", Comput. Method. Appl. Mech. Eng., 197(33), 2680-2691. https://doi.org/10.1016/j.cma.2007.12.023
  13. De Faria, A. (2004), "On buckling enhancement of laminated beams with piezoelectric actuators via stress stiffening", Compos. Struct., 65(2), 187-192. https://doi.org/10.1016/j.compstruct.2003.10.015
  14. De Faria, A.R. and De Almeida, S.F.M. (1999), "Enhancement of pre-buckling behavior of composite beams with geometric imperfections using piezoelectric actuators", Compos. Part B: Eng., 30(1), 43-50. https://doi.org/10.1016/S1359-8368(98)00047-X
  15. Faria, A.R.D. and Donadon, M.V. (2010), "The use of piezoelectric stress stiffening to enhance buckling of laminated plates", Latin Am. J. Solid. Struct., 7(2), 167-183. https://doi.org/10.1590/S1679-78252010000200004
  16. Giannopoulos, G., Santafe, F., Monreal, J. and Vantomme, J. (2007), "Thermal, electrical, mechanical coupled mechanics for initial buckling analysis of smart plates and beams using discrete layer kinematics", Int. J. Solid. Struct., 44(14), 4707-4722. https://doi.org/10.1016/j.ijsolstr.2006.11.048
  17. Jadhav, P.A. and Bajoria, K.M. (2012), "Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading", Smart Mater. Struct., 21(10), 1-10.
  18. Jerome, R. and Ganesan, N. (2010), "New generalized plane strain FE formulation for the buckling analysis of piezocomposite beam", Finite Element. Anal. Des., 46(10), 896-904. https://doi.org/10.1016/j.finel.2010.06.003
  19. Jomehzadeh, E. and Saidi, A. (2009), "Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function", Thin-Wall. Struct., 47(1), 82-88. https://doi.org/10.1016/j.tws.2008.05.004
  20. Kapuria, S. and Achary, G. (2004), "Exact 3-D piezoelasticity solution for buckling of hybrid cross-ply plates using transfer matrices", Acta Mechanica, 170(1-2), 25-45. https://doi.org/10.1007/s00707-004-0108-z
  21. Kapuria, S. and Achary, G. (2006), "Nonlinear coupled zigzag theory for buckling of hybrid piezoelectric plates", Compos. Struct., 74(3), 253-264. https://doi.org/10.1016/j.compstruct.2005.04.010
  22. Kapuria, S. and Alam, N. (2004a), "Exact two-dimensional piezoelasticity solution for buckling of hybrid beams and cross-ply panels using transfer matrices", Compos. Struct., 64(1), 1-11. https://doi.org/10.1016/S0263-8223(03)00140-5
  23. Kapuria, S. and Alam, N. (2004b), "Zigzag theory for buckling of hybrid piezoelectric beams under electromechanical loads", Int. J. Mech. Sci., 46(1), 1-25. https://doi.org/10.1016/j.ijmecsci.2004.03.003
  24. Kim, G.W. and Lee, K.Y. (2008), "Influence of weak interfaces on buckling of orthotropic piezoelectric rectangular laminates", Compos. Struct., 82(2), 290-294. https://doi.org/10.1016/j.compstruct.2007.01.006
  25. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016), "Buckling analysis of CNT reinforced functionally graded laminated composite plates", Compos. Struct., 152, 62-73. https://doi.org/10.1016/j.compstruct.2016.05.047
  26. Liew, K.M., Yang, J. and Kitipornchai, S. (2003), "Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading", Int. J. Solid. Struct., 40(15), 3869-3892. https://doi.org/10.1016/S0020-7683(03)00096-9
  27. Mirzavand, B. and Eslami, M. (2011), "A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties", Acta Mechanica, 218(1-2), 87-101. https://doi.org/10.1007/s00707-010-0402-x
  28. Mohammadi, M., Saidi, A. and Jomehzadeh, E. (2010), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Proc. Inst. Mech. Engineers, Part C: J. Mech. Eng. Sci., 224(9), 1831-1841. https://doi.org/10.1243/09544062JMES1804
  29. Oh, I., Han, J. and Lee, I. (2000), "Postbuckling and vibration characteristics of piezolaminated composite plate subject to thermo-piezoelectric loads", J. Sound Vib., 233(1), 19-40. https://doi.org/10.1006/jsvi.1999.2788
  30. Rahmat Talabi, M.R. and Saidi, A. (2013), "An explicit exact analytical approach for free vibration of circular/annular functionally graded plates bonded to piezoelectric actuator/sensor layers based on Reddy's plate theory", Appl. Math. Model., 37(14), 7664-7684. https://doi.org/10.1016/j.apm.2013.03.021
  31. Saidi, A. and Jomehzadeh, E. (2009), "On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported", Proc. Inst. Mech. Engineers, Part C: J. Mech. Eng. Sci., 223(9), 2009-2016. https://doi.org/10.1243/09544062JMES1431
  32. Shariyat, M. (2009a), "Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties", Compos. Struct., 88(2), 228-239. https://doi.org/10.1016/j.compstruct.2008.03.044
  33. Shariyat, M. (2009b), "Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions", Compos. Struct., 88(2), 240-252. https://doi.org/10.1016/j.compstruct.2008.04.003
  34. Shen, H.S. (2001a), "Postbuckling of shear deformable laminated plates with piezoelectric actuators under complex loading conditions", Int. J. Solid. Struct., 38(44), 7703-7721. https://doi.org/10.1016/S0020-7683(01)00120-2
  35. Shen, H.S. (2001b), "Thermal postbuckling of shear-deformable laminated plates with piezoelectric actuators", Compos. Sci. Technol., 61(13), 1931-1943. https://doi.org/10.1016/S0266-3538(01)00099-9
  36. Shen, H.S. (2005), "Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings", Int. J. Solid. Struct., 42(23), 6101-6121. https://doi.org/10.1016/j.ijsolstr.2005.03.042
  37. Shen, H.S. (2009), "A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators", Compos. Struct., 91(3), 375-384. https://doi.org/10.1016/j.compstruct.2009.06.005
  38. Thai, H., Nguyen, T., 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/Solid., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  39. Thang, P.T. (2016), "Analytical solution for thermal buckling analysis of rectangular plates with functionally graded coatings", Aero. Sci. Technol., 55, 465-473. https://doi.org/10.1016/j.ast.2016.06.021
  40. Varelis, D. and Saravanos, D.A. (2002), "Nonlinear coupled mechanics and initial buckling of composite plates with piezoelectric actuators and sensors", Smart Mater. Struct., 11(3), 330-336. https://doi.org/10.1088/0964-1726/11/3/302
  41. Varelis, D. and Saravanos, D.A. (2004), "Coupled buckling and postbuckling analysis of active laminated piezoelectric composite plates", Int. J. Solid. Struct., 41(5), 1519-1538. https://doi.org/10.1016/j.ijsolstr.2003.09.034
  42. Wang, Q. (2002), "On buckling of column structures with a pair of piezoelectric layers", Eng. Struct., 24(2), 199-205. https://doi.org/10.1016/S0141-0296(01)00088-8
  43. Wang, Q. (2010), "Active buckling control of beams using piezoelectric actuators and strain gauge sensors", Smart Mater. Struct., 19(6), 065022. https://doi.org/10.1088/0964-1726/19/6/065022
  44. Wang, Q. and Quek, S. (2002), "Enhancing flutter and buckling capacity of column by piezoelectric layers", Int. J. Solid. Struct., 39(16), 4167-4180. https://doi.org/10.1016/S0020-7683(02)00334-7
  45. Wang, Q., Quek, S., Sun, C. and Liu, X. (2001), "Analysis of piezoelectric coupled circular plate", Smart Mater. Struct., 10(2), 229-239. https://doi.org/10.1088/0964-1726/10/2/308
  46. Wu, N., Wang, Q. and Quek, S. (2010), "Free vibration analysis of piezoelectric coupled circular plate with open circuit", J. Sound Vib., 329(8), 1126-1136. https://doi.org/10.1016/j.jsv.2009.10.040
  47. Yaghoobi, H. and Rajabi, I. (2013), "Buckling analysis of three-layered rectangular plate with piezoelectric layers", J. Theo. Appl. Mech., 51, 813-826.

피인용 문헌

  1. Response of angle-ply laminated cylindrical shells with surface-bonded piezoelectric layers vol.76, pp.5, 2017, https://doi.org/10.12989/sem.2020.76.5.599