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
Reissner, E., “On the Theory of Thin Elastic Shells,” H. Reissner Anniversary Volume, J. W. Edwards, Ann Arbor, Michigan, 1949, pp. 231–247.
Naghdi, P. M., and C. N. De Silva, “On the Deformation of Elastic Shells of Revolution,” Quarterly Journal of Applied Mathematics, Volume 12, 1954.
Meissner, E., “Über Elastizität and Festigkeit dünner Schalen”, Vierteljahrsschrift der Naturforschende Gesellschaft, Zurich, 60, 1915.
Hildebrand, F. B., “On Asymptotic Integration in Shell Theory,” Proceedings of the 3rd Symposium in Applied Mathematics, pp. 53–66, McGraw Hill, 1950.
Novozhilov, V. V., “Thin Shell Theory,” E. P. Noordhoff, Ltd., Groningen, The Netherlands, 1964.
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.
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.
Maison, J. R., “Stresses In Cyclide Shells,” MMAE Thesis, Department of Mechanical and Aerospace Engineering, University of Delaware, 1968.
Maison, J. R., “Stresses in Rotation Cyclide Shells”, Ph.D. Dissertation, Department of Mechanical and Aerospace Engineering, University of Delaware, 1970.
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.
Other suggested reading for shells of revolution subjected to asymmetric loads
Steele, C. R., “Shells of Revolution with Edge Loads of Rapid Circumferential Variation”, Journal of Applied Mechanics, Vol. 29, pp. 701–707, 962.
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.
Kalnins, A., “Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads, Journal of Applied Mechanics, 1964.
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© 1993 Springer Science+Business Media Dordrecht
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Vinson, J.R. (1993). Shells of Revolution Subjected to Axially Symmetric Loads. In: The Behavior of Shells Composed of Isotropic and Composite Materials. Solid Mechanics and Its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8141-7_4
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DOI: https://doi.org/10.1007/978-94-015-8141-7_4
Publisher Name: Springer, Dordrecht
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