Skip to main content
SpringerLink
Log in

A boundary layer theory for the buckling of thin cylindrical shells under external pressure

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref. [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amazigo, J.C., Asymptotic analysis of the buckling of externally pressurized cylinders with random imperfections,Quar. Appl. Math.,31 (1974), 429–442.

    MATH  Google Scholar 

  2. Amazigo, J.C. and W.B. Fraser, Buckling under external pressure of cylindrical shells with dimple shaped initial imperfections,Int. J. Solids Structures,7 (1971), 883–900.

    Article  MATH  Google Scholar 

  3. Batdorf, S.B., A simplified method of elastic-stability analysis for thin cylindrical shells, NACA Report, No. 874 (1947).

  4. Batista, R.C. and J.G.A. Croll, Simple buckling theory for pressurized cylinders,Proc. ASCE,108, EM5 (1982), 927–944.

    Google Scholar 

  5. Bijlaard, P.P., Buckling stress of thin cylindrical clamped shells subject to hydrostatic pressure,J. Aero. Sci.,21 (1954), 851–853.

    Google Scholar 

  6. Budiansky, B. and J.C. Amazigo, Initial post-buckling behavior of cylindrical shells under external pressure,J. Math. Phys.,47, 3 (1968), 223–235.

    MATH  Google Scholar 

  7. Donnell, L.H., Effect of imperfections on buckling of thin cylinders under external pressure,J. Appl. Mech.,23 (1956), 569–575.

    MATH  MathSciNet  Google Scholar 

  8. Donnell, L.H., Effect of imperfections on buckling of thin cylinders with fixed edges under external pressure,Proc. 3rd U.S. Nat. Conger. Appl. Mech. (1958), 305–311.

  9. Kempner, J., K.A.V. Pandalai, S.A. Patel and J. Crouzet-Pascal, Postbuckling behavior of circular cylindrical shells under hydrostatic pressure,J. Aero. Sci.,24 (1957), 253–264.

    MATH  MathSciNet  Google Scholar 

  10. Kirstein, A.F. and E. Wenk, Jr., Observations of snap-through action in thin cylindrical shells under external pressure,Proc. SESA,14, 1 (1956), 205–214.

    Google Scholar 

  11. von Mises, R., Der Kritische Aussendruck zylindrischer Rohre,Zeit. V.D.I.,58 (1914), 750–755.

    Google Scholar 

  12. von Mises, R., Der Kritische Aussendruck für allseits belastete zylindrische Rohre,Fest. zum 70 Geburstag von Prof. Dr. A. Stodola, Zurich (1929), 418–430.

  13. Nash, W.A., Buckling of thin cylindrical shells subject to hydrostatic pressure,J. Aero. Sci.,21 (1954), 354–355.

    MATH  Google Scholar 

  14. Shen, H.S. and T.Y. Chen, A boundary layer theory for the buckling of thin cylindrical shells under axial compression,The Advances of Applied Mathematics and Mechanics in China,2, (1988).

  15. Sturm, R.G., A. study of the collapsing pressure of thin-walled cylinders,Eng. Exp. Sta. Bull., Univ. Illinois, 329 (1941).

  16. Tennyson, R.C. The effect of shape imperfections and stiffening on the buckling of circular cylinders,Buckling of Structures, ed. by B. Budiansky, IUTAM Symp. (1974), 251–273, Springer-Verlag, Berlin Heidelberg, New York (1976).

    Google Scholar 

  17. Weingarten, V.I. and P. Seide, Elastic stability of thin-walled cylindrical and conical shells under combined external pressure and axial compression,AIAA J.,3, 5 (1965), 913–920.

    Google Scholar 

  18. Windenburg, D.F. and C. Trilling, Collapse by instability of thin cylindrical shells under external pressure,Trans. ASME,56 (1934), 819–825.

    Google Scholar 

  19. Yamaki, N., Influence of prebuckling deformations on the buckling of circular cylindrical shells under external pressure,AIAA J.,7, 4 (1969), 753–755.

    Article  MATH  Google Scholar 

  20. Yamaki, N. and K. Otomo, Experiments on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure,Exp. Mech.,13, 7 (1973), 299–304.

    Article  Google Scholar 

  21. Yamaki, N. and J. Tani, Postbuckling behavior of circular cylindrical shells under hydrostatic pressure,ZAMM,54, 11 (1974), 709–714.

    MATH  Google Scholar 

  22. Yamaki, N.,Elastic Stability of Circular Cylindrical Shells, Elsevier Science Publishers, B.V. (1984).

Download references

Author information

Authors and Affiliations

  1. Shanghai Jiaotong University, Shanghai

    Shen Hui-shen & Chen Tie-yun

Authors
  1. Shen Hui-shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Tie-yun
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Chien Wei-zang

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hui-shen, S., Tie-yun, C. A boundary layer theory for the buckling of thin cylindrical shells under external pressure. Appl Math Mech 9, 557–571 (1988). https://doi.org/10.1007/BF02465411

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02465411

Keywords

Search

Navigation