Shells Of Other Shapes

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


In the preceding chapters, cylindrical shells, general shells of revolutions, conical shells and spherical shells have been treated, and some solutions were obtained. In this chapter the governing equations and geometric relations for some other shell shapes are provided, with no solutions, as an aid to solving problems, and giving insight as to how to approach these other problems.


Cylindrical Shell Spherical Shell Conical Shell Shell Shape Transverse Shear Deformation 
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  1. 7.1.
    Naghdi, P. M., and C. N. De Silva, “Deformation of Elastic Ellipsoidal Shells of Revolution”, Proceedings of the Second U.S. National Congress of Applied Mechanics, pp. 333–343, 1954.Google Scholar
  2. 7.2.
    Daugherty, R. L., “Stresses and Displacements in Shells of Revolution of Composite Materials”, Ph.D. Dissertation, Department of Mechanical and Aerospace Engineering, University of Delaware, June, 1971.Google Scholar
  3. 7.3.
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  4. 7.4.
    Naghdi, P.M., “The Effect of Transverse Shear Deformation on the Bending of Elastic Shells of Revolution”, Quarterly Journal of Applied Mathematics, pp. 41–52, 1957.Google Scholar
  5. 7.5.
    Kayran, A. and J. R. Vinson, “Torsional Vibrations of Layered Composite Paraboloidal Shells”, Journal of Sound and Vibration, Vol. 141 (2), pp. 231244, July 1990.Google Scholar
  6. 7.6.
    Kayran, A. and J. R. Vinson, “The Effect of Transverse Shear Deformation on the Natural Frequencies of Layered Composite Paraboloidal Shells”, ASME Journal of Vibration and Acoustics, Vol. 112, pp. 429–439 October, 1990.Google Scholar
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Suggested further reading

  1. 7.11.
    Galletly, G. D., W. T. Kyner and C. E. Moller, “Numerical Methods and the Bending of Ellipsoidal Shells”, Journal of the Society of Industrial and Applied Mathematics, Vol. 9, pp. 489–513, 1961.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 7.12.
    Sanders, J. L., Jr., and A. Liepins, “Toroidal Membrane Under Internal Pressure”, AIAA Journal, Vol. 1, pp. 2105–2110, 1963.zbMATHCrossRefGoogle Scholar
  3. 7.13.
    Reissner, E., “On Stresses and Deformations in Toroidal Shells of Circular Cross Section Which Are Acted Upon By Uniform Normal Pressure”, Quarterly of Applied Mathematics, Vol. 21, pp. 177–187, 1963.MathSciNetzbMATHGoogle Scholar
  4. 7.14.
    Clark, R. A., “On the Theory of Thin Elastic Toroidal Shells”, Journal of Mathematics and Physics, Vol. 29, pp. 146–178, 1950.zbMATHGoogle Scholar
  5. 7.15.
    Jordan, P. F., “Stresses and Deformations of the Thin-Walled Pressurized Forces”, Journal of the Aerospace Sciences, Vol. 29, pp. 213–225, 1962.zbMATHCrossRefGoogle Scholar
  6. 7.16.
    Rossettos, J. N. and J. L. Sanders, Jr., “Toroidal Shells Under Internal Pressure in the Transition Range”, AIAA Journal, Vol. 3, pp. 1901–1909, 1965.CrossRefGoogle Scholar
  7. 7.17.
    Colbourne, J. R. and W. Flügge, “The Membrane Theory of the Toroidal Shell–A Singular Perturbation Problem”, International Journal of Non-Linear Mechanics, 2, 1, pp. 39–53, March, 1967.zbMATHGoogle 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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