Skip to main content
Log in

Buckling response of moderately thick fluid-infiltrated porous annular sector plates

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In the present article, the buckling of a fluid-infiltrated porous plate is investigated using Mindlin plate theory and an analytical procedure. A cosine rule for the pore distribution across the plate thickness is assumed with a coefficient defining porosity level. The governing stability equations are rewritten in terms of four auxiliary functions and decoupled with the aid of some mathematical manipulations. The decoupled partial differential equations are solved analytically by assuming simply supported radial edges for the plate. The critical buckling loads are calculated by considering fluid-saturated and fluid free conditions for the interconnected network of pores for different sector angles, thickness–radius ratios, coefficients of plate porosity, aspect ratios, and boundary conditions. It is found that the pore fluid compressibility affects the buckling load significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Banhart, J.: Manufacture, characterisation and application of cellular metals and metal foams. Prog. Mater. Sci. 46, 559–632 (2001)

    Article  Google Scholar 

  2. Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. low-fequency range. J. Acoust. Soc. Am. 28, 168 (1956)

    Article  Google Scholar 

  3. Cheung, M.S., Chan, M.Y.T.: Static and dynamic analysis of thin and thick sectorial plates by the finite strip method. Comput. Struct. 14, 79–88 (1981)

    Article  Google Scholar 

  4. Kim, C.S., Dickinson, S.M.: The flexural vibration of line supported rectangular plate systems. J. Sound Vibr. 114, 129–142 (1987)

    Article  Google Scholar 

  5. 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 

  6. McGee, O.G., Huang, C.S., Leissa, A.W.: Comprehensive exact solutions for free vibrations of thick annular sectorial plates with simply supported radial edges. Int. J. Mech. Sci. 37, 537–566 (1995)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Saidi, A.R., Hasani Baferani, A.: Thermal buckling of moderately thick functionally graded annular sector plates. Compos. Struct. 92, 1744–1752 (2010)

    Article  Google Scholar 

  11. Atashipour, S.R., Saidi, A.R., Jomehzadeh, E.: On the boundary layer phenomenon in bending of thick annular sector plates using third-order shear deformation theory. Acta Mech. 211, 89–99 (2010)

    Article  MATH  Google Scholar 

  12. Naderi, A., Saidi, A.R.: Buckling analysis of functionally graded annular sector plates resting on elastic foundations. Proc. Inst. Mech. Eng. C J. Mech. 225, 312 (2011)

    Article  Google Scholar 

  13. Naderi, A., Saidi, A.R.: Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation. Compos. Struct. 93, 629–638 (2011)

    Article  MATH  Google Scholar 

  14. Hejripour, F., Saidi, A.R.: Nonlinear free vibration analysis of annular sector plates using differential quadrature method. Proc. Inst. Mech. Eng. CJ. Mech. 219, 309–335 (2011)

    Google Scholar 

  15. Saidi, A.R., Hasani Baferani, A., Jomehzadeh, E.: Benchmark solution for free vibration of functionally graded moderately thick annular sector plates. Acta Mech. 92, 1744–1752 (2011)

    MATH  Google Scholar 

  16. Hasani Baferani, A., Saidi, A.R., Jomehzadeh, E.: Exact analytical solution for free vibration of functionally graded thin annular sector plates resting on elastic foundation. J. Vib. Control 18, 246–267 (2012)

    Article  MATH  Google Scholar 

  17. Asemi, K., Salehi, M., Akhlaghi, M.: Three Dimensional graded finite element elastically shear buckling analysis of FGM annular sector plate. Aerosp. Sci. Technol. 43, 1–13 (2015)

    Article  Google Scholar 

  18. Biot, M.A.: Theory of buckling of a porous slab and its thermoelastic analogy. J. Appl. Mech. 31, 194–198 (1964)

    Article  MathSciNet  Google Scholar 

  19. Theodorakopoulos, D.D., Beskos, D.E.: Flexural vibration of poroelastic plates. Acta Mech. 103, 191–203 (1994)

    Article  MATH  Google Scholar 

  20. Aygun, H., Attenborough, K., Cummings, A.: Predicted effects of fluid loading on the vibration of elastic porous plates. Acta Acust. United Acust. 93, 284–289 (2003)

    Google Scholar 

  21. Leclaire, P., Horoshenkov, K.V., Cummings, A.: Transverse vibrations of a thin rectangular porous plate saturated by a fluid. J. Sound Vibr. 247, 1–18 (2001)

    Article  Google Scholar 

  22. Magnucka-Blandzi, E.: Axi-symmetrical deflection and buckling of circular porous-cellular plate. Thin Wall. Struct. 46, 333–337 (2008)

    Article  Google Scholar 

  23. Magnucka-Blandzi, E.: Dynamic stability of a metal foam cellular plate. J. Theor. Appl. Mech. 47, 421–433 (2009)

    Google Scholar 

  24. Jabbari, M., Farzaneh Joubaneh, E., Mojahedin, A.: Thermal buckling analysis of porous circular plate with piezoelectric actuators based on first order shear deformation theory. Int. J. Mech. Sci. 83, 57–64 (2014)

    Article  Google Scholar 

  25. Rezaei, A.S., Saidi, A.R.: Exact solution for free vibration of thick rectangular plates made of porous materials. Comput. Struct. 134, 1051–1060 (2015)

    Article  Google Scholar 

  26. Mojahedin, A., Jabbari, M., Khorshidvand, A.R., Eslami, M.R.: Buckling analysis of functionally graded circular porous materials based on higher order shear deformation theory. Thin Wall. Struct. 99, 83–90 (2016)

    Article  Google Scholar 

  27. Rezaei, A.S., Saidi, A.R.: Application of carrera unified formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates. Compos. Part B Eng. 91, 361–370 (2016)

    Article  Google Scholar 

  28. Rezaei, A.S., Saidi, A.R.: On the effect of coupled solid-fluid deformation on natural frequencies of fluid saturated porous plates. Eur. J. Mech. A Solid 63, 99–109 (2017)

    Article  MathSciNet  Google Scholar 

  29. Rice, J.R., Cleary, M.P.: Some basic stress-diffusion solutions for fluid saturated elastic porous media with compressible constituents. Rev. Geophys. 14, 227–241 (1976)

    Article  Google Scholar 

  30. Detournay, E., Cheng, A.H.D.: Fundamentals of Poroelasticity. Pergamon Press, Oxford (1993)

    Book  Google Scholar 

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

    Google Scholar 

  32. Samsam Shariat, B.A., Eslami, M.R.: Buckling of thick functionally graded plates under mechanical and thermal loads. Compos. Struct. 78, 433–439 (2007)

    Article  Google Scholar 

  33. You-He, Z., Xiaojing, Z., Harik, I.E.: A seminumerical method for buckling of sector plates. Comput. Struct. 57, 847–854 (1995)

    Article  MATH  Google Scholar 

  34. Saidi, A.R., Jomehzadeh, E.: On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported. Proc. Inst. Mech. Eng. CJ Mech. 223, 2009–2016 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  36. Sharma, A., Sharda, H.B.: Stability and vibration of mindlin sector plates: an analytical approach. AIAA J. 43, 1109–1116 (2005)

    Article  Google Scholar 

  37. Hasani Baferani, A., Saidi, A.R.: Accurate critical buckling load/temperature of thick annular sector plates. J. Eng. Mech. 138, 614–630 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. S. Rezaei.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rezaei, A.S., Saidi, A.R. Buckling response of moderately thick fluid-infiltrated porous annular sector plates. Acta Mech 228, 3929–3945 (2017). https://doi.org/10.1007/s00707-017-1908-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-017-1908-2

Navigation