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Shells of Revolution Subjected to Axially Symmetric Loads

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

Abstract

Shells in which the middle surface is generated by rotating a generator about an axis are called shells of revolution. A closed cylindrical shell is the simplest case, and the analysis of stresses and deformations in such cylindrical shells was treated in Chapter 3. Due to Reissner, Meissner, and Naghdi, a generalized method of analysis can be employed for all shells of revolution subjected to axially symmetric loads without dealing with each shell geometry specifically. This treatment is presented below, because of its extreme usefulness.

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References

  1. 4.1.
    Reissner, E., “On the Theory of Thin Elastic Shells,” H. Reissner Anniversary Volume, J. W. Edwards, Ann Arbor, Michigan, 1949, pp. 231–247.Google Scholar
  2. 4.2.
    Naghdi, P. M., and C. N. De Silva, “On the Deformation of Elastic Shells of Revolution,” Quarterly Journal of Applied Mathematics, Volume 12, 1954.Google Scholar
  3. 4.3.
    Meissner, E., “Über Elastizität and Festigkeit dünner Schalen”, Vierteljahrsschrift der Naturforschende Gesellschaft, Zurich, 60, 1915.Google Scholar
  4. 4.4.
    Hildebrand, F. B., “On Asymptotic Integration in Shell Theory,” Proceedings of the 3rd Symposium in Applied Mathematics, pp. 53–66, McGraw Hill, 1950.Google Scholar
  5. 4.5.
    Novozhilov, V. V., “Thin Shell Theory,” E. P. Noordhoff, Ltd., Groningen, The Netherlands, 1964.Google Scholar
  6. 4.6.
    Langer, R. E., “On the Asymptotic Solutions of Ordinary Differential Equations with an Application to the Bessel Function of Large Order,” American Mathematical Society Transactions, 33, 1931.Google Scholar
  7. 4.7.
    Langer, R. E., “On the Asymptotic Solution of Ordinary Differential Equations with Reference to the Stokes Phenomenon about a Singular Point,” American Mathematical Society Transaction, 37, 397–416, 1935.Google Scholar
  8. 4.
    Maison, J. R., “Stresses In Cyclide Shells,” MMAE Thesis, Department of Mechanical and Aerospace Engineering, University of Delaware, 1968.Google Scholar
  9. 4.9.
    Maison, J. R., “Stresses in Rotation Cyclide Shells”, Ph.D. Dissertation, Department of Mechanical and Aerospace Engineering, University of Delaware, 1970.Google Scholar
  10. 4.10
    Maison, J. R. and J. R. Vinson, “The Use of Rotation Cyclides in Underwater Structures”, Proceedings of the IASS Pacific Symposium on Hydromechanically Loaded Shells, Honolulu, University Press of Hawaii, 1974.Google Scholar

Other suggested reading for shells of revolution subjected to asymmetric loads

  1. 4.11.
    Steele, C. R., “Shells of Revolution with Edge Loads of Rapid Circumferential Variation”, Journal of Applied Mechanics, Vol. 29, pp. 701–707, 962.Google Scholar
  2. 4.12.
    Schile, R. D., “Asymptotic Solution of Nonshallow Shells of Revolution Subjected to Nonsymmetric Loads”, Journal of the Aerospace Sciences, Vol. 29, pp. 1375–1379, 1962.zbMATHCrossRefGoogle Scholar
  3. 4.13.
    Kalnins, A., “Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads, Journal of Applied Mechanics, 1964.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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