Spherical Shells

  • Jack R. Vinson
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 18)


Having the general governing equations for shells of revolution under axially symmetric loads developed in Chapter 4, it is straightforward to specify them for a spherical shell.


Cylindrical Shell Axial Load Spherical Shell Stress Couple Conical Shell 
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  1. 6.1.
    Reissner, E., “Stresses and Small Displacements of Shallow Spherical Shells, I and II”, Journal of Mathematics and Physics, Vol. 25, 1946, pp. 80–85, 279300, 1948.MathSciNetGoogle Scholar
  2. 6.2.
    Carr, J. H., “Analysis of Head Failure in Aircraft Torpedoes”, Navord Report 1019, May, 1948.Google Scholar
  3. 6.3.
    Vinson, J. R., “Analysis of Maximum Stresses in Elastic Spherical Shells During High Speed Water Entry”, Proceedings of the Second Annual Technical Symposium on Ballistic Missiles, (USAF and Ramo-Wooldridge, Corp), Los Angeles, June 13–14, 1957 and Transactions of the 12th Southeastern Conference on Applied Mechanics, Calloway Gardens, May 10–11, 1984.Google Scholar
  4. 6.4.
    Seigel, A. E., “A Method of Calculating Forces Upon a Body During its Entry Into Water from the Atmosphere”, Navord Report 4180, 24 January 1956.Google Scholar
  5. 6.
    International Critical Tables Vol. 3, pp. 40 and 440, National Bureau of Standards.Google Scholar

Suggested further study for spherical shells

  1. 6.6.
    Kalnins, A. and J. F. Lestingi, “On Nonlinear Analysis of Elastic Shells of Revolution”, Journal of Applied Mechanics, pp. 59–64, March, 1967.Google Scholar
  2. 6.7.
    Weinitschke, H. J., “On the Nonlinear Theory of Shallow Spherical Shells”, Journal of the Society of Industrial and Applied Mathematics, Vol. 6, pp. 209232, 1958.Google Scholar
  3. 6.8.
    Thurston, G. A., “A Numerical Solution of the Nonlinear Equations for Axisymmetric Bending of Shallow Spherical Shells”, Journal of Applied Mechanics, Vol. 28, pp. 557–563, 1961.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 6.9.
    Famili, J. and R. R. Archer, “Finite Asymmetric Deformation of Shallow Spherical Shells”, AIAA Journal, Vol. 3, pp. 506–510, 1965.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 6.10.
    Wilson, P. E. and E. E. Spier, “Numerical Analysis of Large Axisymmetric Deformations of Thin Spherical Shells, AIAA Journal, Vol. 3, pp. 1716–1725, 1965.CrossRefGoogle Scholar
  6. 6.11.
    Wilkinson, J. P. and A. Kalnins, “Deformation of Open Spherical Shells Under Arbitrarily Located Concentrated Loads”, Journal of Applied Mechanics, pp. 305–312, June, 1966.Google Scholar
  7. 6.12.
    Koiter, W. T., “A Spherical Shell Under Point Loads at its Poles”, Advances in Applied Mechanics, Prager Anniversary Volume, pp. 155–169, 1963.Google Scholar
  8. 6.13.
    Berry, J. G., “On Thin Hemispherical Shells Subjected to Concentrated Edge Moments and Forces”, Proceedings of the Second Midwestern Conference on Solid Mechanics, pp. 489–494, 1955.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Jack R. Vinson
    • 1
  1. 1.Department of Mechanical Engineering and the Center for Composite MaterialsUniversity of DelawareNewarkUSA

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