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An analytical solution for buckling of moderately thick functionally graded sector and annular sector plates

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Abstract

In this article, an analytical solution for buckling of moderately thick functionally graded (FG) sectorial plates is presented. It is assumed that the material properties of the FG plate vary through the thickness of the plate as a power function. The stability equations are derived according to the Mindlin plate theory. By introducing four new functions, the stability equations are decoupled. The decoupled stability equations are solved analytically for both sector and annular sector plates with two simply supported radial edges. Satisfying the edges conditions along the circular edges of the plate, an eigenvalue problem for finding the critical buckling load is obtained. Solving the eigenvalue problem, the numerical results for the critical buckling load and mode shapes are obtained for both sector and annular sector plates. Finally, the effects of boundary conditions, volume fraction, inner to outer radius ratio (annularity) and plate thickness are studied. The results for critical buckling load of functionally graded sectorial plates are reported for the first time and can be used as benchmark.

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References

  1. Birman V., Byrd W.L.: Modeling and analysis of functionally graded materials and structures. Appl. Mech. Rev. 60, 195–216 (2007)

    Article  Google Scholar 

  2. Sahraee S., Saidi A.R.: Free vibration and buckling analysis of functionally graded deep beam- columns on two-parameter elastic foundations using the differential quadrature method. IMech E Part C 223, 1273–1284 (2009)

    Article  Google Scholar 

  3. Sahraee S., Saidi A.R.: Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory. Eur. J. Mech. A/Solids 28, 974–984 (2009)

    Article  MATH  Google Scholar 

  4. Saidi A.R., Rasouli A., Sahraee S.: Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory. Compos. Struct. 89, 110–119 (2009)

    Article  Google Scholar 

  5. Aghdam M.M., Mohammadi M., Erfanian V.: Bending analysis of thin annular sector plates using extended Kantorovich method. Thin-Walled Struct. 45, 983–990 (2007)

    Article  Google Scholar 

  6. Sahraee S.: Bending analysis of functionally graded sectorial plates using Levinson plate theory. Compos. Struct. 88, 548–557 (2009)

    Article  Google Scholar 

  7. Jomehzadeh E., Saidi A.R., Atashipour S.R.: An analytical approach for stress analysis of functionally graded annular sector plates. Mater. Design 30, 3679–3685 (2009)

    Article  Google Scholar 

  8. Nie G.J., Zhong Z.: Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges. Compos. Struct. 84, 167–176 (2008)

    Article  Google Scholar 

  9. Jomehzadeh E., Saidi A.R.: Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function. Thin-Walled Struct. 47, 82–88 (2009)

    Article  Google Scholar 

  10. Liew K.M., Xiang Y., Kitipornchai S.: Analytical buckling solutions for Mindlin plates involving free edges. Int. J. Mech. Sci. 38, 1127–1138 (1996)

    Article  MATH  Google Scholar 

  11. Najafizadeh M.M., Eslami M.R.: Buckling analysis of circular plates of functionally graded materials under uniform radial compression. Int. J. Mech. Sci. 44, 2479–2493 (2002)

    Article  MATH  Google Scholar 

  12. Chen X.L., Liew K.M.: Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads. Smart Mater. Struct. 13, 1430–1437 (2004)

    Article  Google Scholar 

  13. Yang J., Liew K.M., Kitipornchai S.: Second-order statistics of the elastic buckling of functionally graded rectangular plates. Compos. Sci. Technol. 65, 1165–1175 (2005)

    Article  Google Scholar 

  14. Abrate S.: Free vibration, buckling and static deflections of functionally graded plates. Compos. Sci. Technol. 66, 2383–2394 (2006)

    Article  Google Scholar 

  15. Hosseini-Hashemi S., Khorshidi K., Amabili M.: Exact solution for linear buckling of rectangular Mindlin plates. J. Sound Vib. 315, 318–342 (2008)

    Article  Google Scholar 

  16. Mohammadi M., Saidi A.R., Jomehzadeh E.: Levy solution for buckling analysis of functionally graded rectangular plates. Appl. Compos. Mater. 17, 81–93 (2010)

    Article  Google Scholar 

  17. Rubin C.: Stability of polar orthotropic sector plates. J. Appl. Mech. 45, 448–450 (1978)

    Article  Google Scholar 

  18. Harik IE: Stability of annular sector plates with clamped radial edges. J. Appl. Mech. 52, 971–972 (1985)

    Article  Google Scholar 

  19. Srinivasan R.S., Thiruvenkatacharit V.: Stability of annular sector plates with variable thickness. AIAA J. 22, 315–317 (1984)

    Article  MATH  Google Scholar 

  20. Liu W.H., Chen W.C.: Note on the stability of annular sector plates with elastically restrained edges. Int. J. Mech. Sci. 31, 611–622 (1989)

    Article  MATH  Google Scholar 

  21. Altman W., Neto E.L.: Stability of annular sectors and plates subjected to follower loads based on a mixed finite element formulation. Comput. Struct. 31, 833–840 (1989)

    Article  MATH  Google Scholar 

  22. Zhou Y.H., Zheng X., Harik E.: A semi numerical method for buckling of sector plates. Comput. Struct. 57, 847–854 (1995)

    Article  MATH  Google Scholar 

  23. Wang C.M., Xiang Y.: Deducing buckling loads of sectorial Mindlin plates from Kirchhoff plates. J. Eng. Mech. 125, 596–598 (1999)

    Article  Google Scholar 

  24. Sharma A., Sharda H.B.: Stability and vibration of Mindlin sector plates: an analytical approach. AIAA J. 43, 1109–1115 (2005)

    Article  Google Scholar 

  25. Sharma A., Sharda H.B., Nath Y.: Stability and vibration of thick laminated composite sector plates. J Sound Vib. 287, 1–23 (2005)

    Article  Google Scholar 

  26. Brush D.O., Almroth B.O.: Buckling of Bars, Plates, and Shells. McGraw-Hill, New-York (1975)

    MATH  Google Scholar 

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  1. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    A. Naderi & A. R. Saidi

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  1. A. Naderi
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Correspondence to A. R. Saidi.

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Naderi, A., Saidi, A.R. An analytical solution for buckling of moderately thick functionally graded sector and annular sector plates. Arch Appl Mech 81, 809–828 (2011). https://doi.org/10.1007/s00419-010-0451-6

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