DOI QR코드

DOI QR Code

Semi-analytical solution for buckling of SMA thin plates with linearly distributed loads

  • Received : 2018.12.06
  • Accepted : 2019.03.16
  • Published : 2019.06.25

Abstract

Buckling analysis of shape memory alloy (SMA) rectangular plates subjected to uniform and linearly distributed inplane loads is the main objective in the present paper. Brinson's model is developed to express the constitutive characteristics of SMA plate. Using the classical plate theory and variational approach, stability equations are derived. In addition to external inplane mechanical loads, the plate is subjected to the pre-stresses caused by the recovery stresses that are generated during martensitic phase transformation. Ritz method is used for solving the governing stability equations. Finally, the effects of conditions on the edges, thickness, aspect ratio, temperature and pre-strains on the critical buckling loads of SMA plate are investigated in details.

Keywords

References

  1. Abolghasemi, S., Eipakchi, H. and Shariati, M. (2015), "Analytical solution for buckling of rectangular plates subjected to non-uniform in-plane loading based on first order shear deformation theory", Modares Mech. Eng., 14.
  2. Akesson, B. (2007), Plate Buckling in Bridges and Other Structures, CRC Press, U.S.A.
  3. Asadi, H., Akbarzadeh, A., Chen, Z. and Aghdam, M. (2015), "Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys", Smart Mater. Struct., 24. 045022. https://doi.org/10.1088/0964-1726/24/4/045022
  4. Auricchio, F. and Sacco, E. (1997), "A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite", J. Non-Linear Mech., 32(6), 1101-1114, https://doi.org/10.1016/S0020-7462(96)00130-8.
  5. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions" Struct. Eng. Mech., 66. https://doi.org/10.12989/sem.2018.66.6.761.
  6. Brinson, L.C. (1993), "One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with nonconstant material functions and redefined martensite internal variable", J. Int. Mater. Syst. Struct., 4, 229-242. https://doi.org/10.1177/1045389X9300400213.
  7. Burton, D., Gao, X. and Brinson, L. (2006), "Finite element simulation of a self-healing shape memory alloy composite", Mech. Mater., 38, 525-537. https://doi.org/10.1016/j.mechmat.2005.05.021.
  8. Chang, K.H., Shim, H.J. and Kang, J.H. (2004), "Free vibrations and buckling of rectangular plates with linearly varying in-plane loading", J. Korean Assoc. Spatial Struct., 4, 99-111.
  9. Chen, T.L. (1967), "Design of composite-material plates for maximum uniaxial compressive buckling load", Proceedings of the Oklahoma Academy of Science, 104-107.
  10. Chen, Y., Lee, Y., Li, Q. and Guo, Y. (2009), "Concise formula for the critical buckling stresses of an elastic plate under biaxial compression and shear", J. Construct. Steel Res., 65, 1507-1510. https://doi.org/10.1016/j.jcsr.2009.02.006.
  11. Ibrahim, H.H., Tawfik, M. and Negm, H.M. (2011), "Thermal buckling and nonlinear flutter behavior of shape memory alloy hybrid composite plates", J. Vib. Control, 17, 321-333. https://doi.org/10.1177/1077546309353368.
  12. Javaheri, R. and Eslami, M. (2002), "Buckling of Functionally Graded Plates under In plane Compressive Loading", Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik, 82, 277-283. https://doi.org/10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y
  13. Javaheri, R. and Eslami, M. (2002), "Thermal buckling of functionally graded plates", AIAA J., 40, 162-184. https://doi.org/10.2514/2.1626.
  14. Kapania, R.K. and Raciti, S. (1989), "Recent advances in analysis of laminated beams and plates, Part I: Shear effects and buckling", AIAA J., 27, 923-935. https://doi.org/10.2514/3.10202.
  15. Kumar, S. and Singh, B. (2009), "Thermal buckling analysis of SMA fiber-reinforced composite plates using layerwise model", J. Aerosp. Eng., 22, 342-353. https://doi.org/10.1061/(ASCE)0893-1321(2009)22:4(342)
  16. Kuo, S.Y., Shiau, L.C. and Chen, K.H. (2009), "Buckling analysis of shape memory alloy reinforced composite laminates", Compos. Struct., 90, 188-195. https://doi.org/10.1016/j.compstruct.2009.03.007.
  17. Lanhe, W. (2004), "Thermal buckling of a simply supported moderately thick rectangular FGM plate" Compos. Struct., 64, 211-218. https://doi.org/10.1016/j.compstruct.2003.08.004.
  18. Lee, H.J. and Lee, J.J. (2000), "A numerical analysis of the buckling and postbuckling behavior of laminated composite shells with embedded shape memory alloy wire actuators", Smart Mater. Struct., 9, 780-790. https://doi.org/10.1088/0964-1726/9/6/307
  19. Leissa, A.W. (1987), "A review of laminated composite plate buckling", Appl. Mech. Rev. 40, 575-591. http://doi.org/10.1115/1.3149534. https://doi.org/10.1115/1.3149534.
  20. Mahabadi, R.K., Shakeri, M. and Pazhooh, M.D. (2016), "Free vibration of laminated composite plate with shape memory alloy fibers", Latin American J. Solids Struct., 13, 314-330. http://dx.doi.org/10.1590/1679-78252162.
  21. Megson, T.H.G. (2012), Aircraft Struct. Eng. Students, Butterworth-Heinemann, Oxford, United Kingdom.
  22. Musa, I.A. (2016), "Buckling of plates including effect of shear deformations: A hyperelastic formulation", Struct. Eng. Mech., 57.
  23. Ostachowicz, W., Krawczuk, M. and Zak, A. (2000), "Dynamics and buckling of a multilayer composite plate with embedded SMA wires", Compos. Struct., 48, 163-167. https://doi.org/10.1016/S0263-8223(99)00090-2.
  24. Park, J.S., Kim, J.H. and Moon, S.H. (2004), "Vibration of thermally post-buckled composite plates embedded with shape memory alloy fibers", Compos. Struct., 63, 179-188. https://doi.org/10.1016/S0263-8223(03)00146-6.
  25. Reddy, J. and Khdeir, A. (1989), "Buckling and vibration of laminated composite plates using various plate theories" AIAA J., 27, 1808-1817. https://doi.org/10.2514/3.10338.
  26. Reddy, J.N. (2017), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, U.S.A.
  27. Roh, J.H., Oh, I.K., Yang, S.M., Han, J.H. and Lee, I. (2004), "Thermal post-buckling analysis of shape memory alloy hybrid composite shell panels", Smart Mater. Struct., 13, 1337. https://doi.org/10.1088/0964-1726/13/6/006
  28. Shiau, L.C., Kuo, S.Y. and Chen, C.Y. (2010), "Thermal buckling behavior of composite laminated plates", Compos. Struct., 92, 508-514. https://doi.org/10.1016/j.compstruct.2009.08.035.
  29. Taylor, G. (1933), "The buckling load for a rectangular plate with four clamped edges", ZAMM Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik, 13, 147-152. https://doi.org/10.1002/zamm.19330130222
  30. Thompson, S. and Loughlan, J. (1997), "Adaptive post-buckling response of carbon fibre composite plates employing SMA actuators", Compos. Struct., 38, 667-678. https://doi.org/10.1016/S0263-8223(97)00104-9.
  31. Tupal, U., Nazarimofrad E. and Sadat Kholerdi S.E. (2018), "Shear buckling analysis of cross-ply laminated plates resting on Pasternak foundation", Struct. Eng. Mech., 68.
  32. Turvey, G.J. and Marshall, I.H. (2012), Buckling and Postbuckling of Composite Plates, Springer Science & Business Media, Germany.
  33. Ventsel, E. and Krauthammer, T. (2001), Thin Plates and Shells: Theory: Analysis, and Applications, CRC Press, USA.
  34. Wang, X., Bert, C. and Striz, A. (1993), "Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates", Comput. Struct., 48, 473-479. https://doi.org/10.1016/0045-7949(93)90324-7.
  35. Zhu, P., Stebner, A.P. and Brinson, L.C. (2014), "Plastic and transformation interactions of pores in shape memory alloy plates", Smart Mater. Struct., 23, 104008. https://doi.org/10.1088/0964-1726/23/10/104008