Skip to main content
SpringerLink
Log in

Large deflection analysis of conical head pressure vessels

  • Published:
Forschung im Ingenieurwesen A Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The present work investigates the nonlinear behaviour at and near the junction of cylindrical and conical shells under internal or external pressure. The results are useful for studying conical head pressure vessels and components of missiles, spacecrafts, underwater vessels, nuclear reactors, etc.Reissner's basic concept for the large deformation of axisymmetric shells, with proper modification and specialization, are used in the derivation of the governing equations for the present problem. The nonlinear differential equations are then solved by the multisegment method of integration developed byKalnins andLestingi. Results of this analysis indicate that the linear theory is very inadequate and conservative in its prediction of stresses and deformations in the region of the junction of the cylindrical and conical parts. In this analysis the tip of the conical part, where present, is assumed to be replaced by a very small spherical cap meeting tangentially with the conical part, in order to avoid singularity and to render the solution more realistic.

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. Watts, G.W. andH.A. Lang: The stresses in a pressure vessel with a flat head closure. Trans. ASME Vol. 74 (1952) pp. 1083/91.

    Google Scholar 

  2. Watts, G.W., andH.A. Lang: The stresses in a pressure vessel with a conical head. Trans. ASME Vol. 74 (1952) pp. 315/26.

    Google Scholar 

  3. Watts, G.W., andH.A. Lang: The stresses in a pressure vessel with a hemispherical head. Trans. ASME Vol. 75 (1953) pp. 83/89.

    Google Scholar 

  4. Krans, H., G.G. Bilodeau andB.F. Langer: Stresses in thin-walled pressure vessels with ellipsoidal heads. J. Engng. for Industry Vol. 83, Ser. B (1961) No. 1, pp. 29/42.

    Google Scholar 

  5. Galletly, G.D., andJ.R. Radok: On the accuracy of some shell solutions. Trans., ASME, Ser. E. Vol. 21 (1959).

  6. Galletly, G.D.: Bending of 2∶1 and 3∶1 open-crown ellipsoidal shells. Welding Research Council Bulletin No. 54, 1959.

  7. Ball, R.E.: A geometrically nonlinear analysis of arbitrary bended shells of revolution. NASA CR-909, 1968.

  8. Uddin, Md.W.: Large deflection analysis of composite shells of revolution. Carleton University, Ottawa 1969.

    Google Scholar 

  9. Kalnins, A., andJ.E. Lestingi: On nonlinear analysis of elastic shells of revolution. J. Appl. Mech., Vol. 34, Ser. E (1967) No. 1, pp. 59/64.

    Google Scholar 

  10. Thurston, G.A.: Newtons method applied to problems in nonlinear mechanics. J. Appl. Mech. (1965) pp. 383/88.

  11. Famili, I., andR.R. Archer: Finite asymmetric deformation of shallow spherical shells. AIAA J. Vol. 3 (1965) No. 3, pp. 506/70.

    MathSciNet  Google Scholar 

  12. Thurston, G.A.: A numerical solution of the nonlinear equations for axisymmetric bending of shallow spherical shells. J. Appl. Mech. Vol. 28 (1961) pp. 557/62.

    MathSciNet  Google Scholar 

  13. Holston, A. Jr. Approximate analytical solution of the finite difference equations for a shallow spherical shell. J. Appl. Mech. Vol. 34, Ser. E (1967) No. 1, pp. 65/67.

    Google Scholar 

  14. Soper, W.G.: Large deflection of stiffened plates. J. Appl. Mech. Vol. 25 (1958) pp. 444/48.

    Google Scholar 

  15. Wemper, G.A., andR. Schmidt: Large symmetric deflections of annular plates. J. Appl. Mech. Vol. 25 (1958) pp. 449/52.

    Google Scholar 

  16. Reis, E.L.: Axially symmetric buckling of shallow spherical shells under external pressure J. Appl. Mech. Vol. 25 (1958) pp. 556/60.

    Google Scholar 

  17. Nash, W.A., andI.D. Cooley: Large deflection of a clamped elliptical plate subjected to uniform pressure. J. Appl. Mech. Vol. 26, Ser E (1959) No. 2.

  18. Nath, Y., andR.K. Jain: Nonlinear dynamic analysis of orthotropic annular plates resting on elastic foundations. Earthquake Engng. and Structural Dynamics Vol. 11, (1983) pp. 785/96.

    Google Scholar 

  19. Dumir, P.C., M.L. Gandhi andY. Nath: Axisymmetric static and dynamic buckling of orthotropic shallow spherical caps with flexible supports. Acta Mechanica Vol. 52 (1984) pp. 93/106.

    Article  Google Scholar 

  20. Dumir, P.C., Y. Nath andM.L. Gandhi: Nonlinear transient response of isotropic circular plates. Computer and Structures Vol. 18 (1984) pp. 1008/18.

    Article  Google Scholar 

  21. Nath, Y., P.C. Dumir andM.L. Gandhi: Choice of collocation points for axisymmetric nonlinear two-point boundary value problems in statics of shallow spherical shells. Engng. Trans. Vol. 31, No. 3 (1983) pp. 331/40.

    Google Scholar 

  22. Alwar, R.S., Y. Nath andB.S. Reddy: Axisymmetric dynamic buckling of shallow spherical shells. ZAMM Vol. 60 (1980) pp. 108/20.

    Google Scholar 

  23. Sepetoski, W.K., C.E. Pearson, I.W. Dingwell andZ.W. Adkins: A computer program for the generally axially symmetric thin shell problem. J. Appl. Mech. Vol. 29, Ser. E (1962) pp. 655/61.

    Google Scholar 

  24. Patel, H.P., andR.H. Kennedy: Nonlinear finite element analysis for composite structures for axisymmetric geometry and loading. Computers and Structures Vol. 15 (1982) No. 1, pp. 79/84.

    Article  Google Scholar 

  25. Reissner, E.: On axisymmetrical deformations of thin shells of revolution. Proc. Symposia Appl. Math. Vol. 3, McGraw-Hill 1950, pp. 27/52.

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Bangladesh University of Engineering & Technology, Dhaka, Bangladesh

    Md. Wahhaj Uddin

Authors
  1. Md. Wahhaj Uddin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Uddin, M.W. Large deflection analysis of conical head pressure vessels. Forsch Ing-Wes 52, 146–152 (1986). https://doi.org/10.1007/BF02560921

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02560921

Keywords

Search

Navigation