Skip to main content
Log in

Existence and stability of axisymmetric buckled states of spherical shells

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. L. Bauer, H.B. Keller & E. L. Reiss, “Axisymmetric buckling of hollow spheres and hemispheres,” Comm. Pure Appl. Math. 23 (1970), 529–568.

    Google Scholar 

  2. M.S. Berger & P.C. Fife, “On von Kármán's equations and the buckling of a thin elastic plate,” Bull. Amer. Math. Soc. 72 (1966), 1006–1011.

    Google Scholar 

  3. M.S. Berger, “On the existence of equilibrium states of thin elastic shells (I),” Indiana Math. J. 20 (1971), 591–602.

    Google Scholar 

  4. R. Courant & D. Hilbert, “Methods of Mathematical Physics,” vol. I, Interscience Publishers, New York, 1953.

    Google Scholar 

  5. G.H. Knightly & D. Sather, “Nonlinear axisymmetric buckling of shallow spherical caps,” SIAM J. Math. Anal. 6 (1975), 913–924.

    Google Scholar 

  6. W.T. Koiter, “The nonlinear buckling problem of a complete spherical shell under uniform external pressure,” Proc. Kon. Nederl. Akad. Wet. Amsterdam B72 (1969), 40–123.

    Google Scholar 

  7. C.G. Lange & G. A. Kriegsmann, “The axisymmetric branching behavior of complete spherical shells,” preprint, 1974.

  8. H.E. Rauch, “Instability of thin-walled spherical structures under external pressure,” Contributions to Analysis, Academic Press, New York, 1974, 357–373.

    Google Scholar 

  9. E. Reissner, “On the axisymmetrical deformation of thin shells of revolution,” Proc. Symposia in Appl. Math. 3 (1950), 27–52.

    Google Scholar 

  10. E.H. Rothe, “Completely continuous scalars and variational methods,” Ann. of Math. 49 (1948), 265–278.

    Google Scholar 

  11. D. Sather, “Bifurcation and stability for a class of shells,” Arch. Rational Mech. Anal., 63 (1976), 295–304.

    Google Scholar 

  12. D. Sather, “Branching of solutions of nonlinear equations,” Proc. Seminar on Nonlinear Eigenvalue Problems, Santa Fe, 1971, Rocky Mtn. J. Math. 3 (1973), 203–250.

  13. D. Sather, “Branching of solutions of an equation in Hubert space,” Arch. Rational Mech. Anal. 36 (1970), 47–64.

    Google Scholar 

  14. D.H. Sattinger, “Stability of bifurcating solutions by Leray-Schauder degree,” Arch. Rational Mech. Anal. 43 (1971), 154–166.

    Google Scholar 

  15. I. Stakgold, “Branching of solutions of nonlinear equations,” SIAM Review 13 (1971), 289–332.

    Google Scholar 

  16. J.M.T. Thompson, “The rotationally-symmetric branching behavior of a complete spherical shell,” Proc. Kon. Nederl. Akad. Wet. Amsterdam B67 (1964), 295–311.

    Google Scholar 

  17. J.M.T. Thompson & G. W. Hunt, “A General Theory of Elastic Stability,” John Wiley and Sons, London, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J.B. McLeod

The research of G. H. Knightly reported here was supported in part by a grant from the U.S. National Science Foundation, No. MPS 75-07579; that of D. Sather was supported in part by U.S. National Science Foundation Grant No. MPS 73-08948 and in part by the Council on Research and Creative Work of the University of Colorado.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knightly, G.H., Sather, D. Existence and stability of axisymmetric buckled states of spherical shells. Arch. Rational Mech. Anal. 63, 305–319 (1976). https://doi.org/10.1007/BF00279990

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00279990

Keywords

Navigation