Derivation of the Governing Equations for Thin Shells

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

Abstract

After the brief introduction to curvilinear coordinates in Chapter 1, one can now describe the equations of elasticity in curvilinear coordinates, and systematically reduce them to the governing equations for shells in curvilinear coordinates, employing the assumptions of shells in the process.

Keywords

Stress Equation Thin Shell Middle Surface Covariant Component Elastic Shell 
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References

  1. 2.1.
    Love, A. E. H., “The Small Free Vibrations and Deformation of a Thin Elastic Shell”, Philosophical Transactions of the Royal Society London, Vol. 17, pp. 491–546, 1888.ADSGoogle Scholar
  2. 2.2.
    Reissner, E., “A New Derivation of the Equations for the Deformation of Elastic Shells”, American Journal of Mathematics, 63, pp. 177–184, 1941.MathSciNetCrossRefGoogle Scholar
  3. 2.3
    Flügge, W., “Statik und Dynamik der Schalen”, Edwards Brothers, Inc, Ann Arbor, 1943.Google Scholar
  4. 2.4.
    Love, A.E.H., “A Treatise on the Mathematical Theory of Elasticity”, Dover Publications, New York, 1944.Google Scholar
  5. 2.5.
    Sokolnikoff, I.S., “Mathematical Theory of Elasticity”, McGraw-Hill Book Company, Inc., Second Ed., 1956.Google Scholar
  6. 2.6.
    Goldenveizer, A. L. and Lourye, A. I., “On the Mathematical Theory of Equilibrium of Elastic Shells”, Prild: Mat. 11, pp. 565–592, 1947.Google Scholar
  7. 2.7.
    Reissner, E., “On the Theory of Thin Elastic Shells”, H. Reissner Anniversary Volume, pp. 231–247, 1949.Google Scholar
  8. 2.8.
    Hildebrand, F. B., “On Asymptotic Integrations in Shell Theory”, Proceedings of Symposium Applied Mathematics, 53–66, McGraw Hill, 1950.Google Scholar
  9. 2.9.
    Vlasov, V. S., “Basic Differential Equations in General Theory of Elastic Shells”, NASA TM 1241, 1951.Google Scholar
  10. 2.10.
    Reissner, E., “Stress-Strain Relations in the Theory of Thin Elastic Shells, J. Math. Phys. 31, pp. 109–119, 1952.MathSciNetMATHGoogle Scholar
  11. 2.11.
    Goldenveizer, A. L., “Theory of Thin Shells”, Pergamon Press, New York, 1961.Google Scholar
  12. 2.12.
    Nash, W. A.;, “Bibliography on Shells and Shell-Like Structures, U.S. Navy David W. Taylor Model Basin Report 863, Nov. 1954.Google Scholar
  13. 2.13.
    Reissner, E., “On Some Aspects of the Theory of Thin Elastic Shells”, J. Boston Soc. Civil Engineers, 42, pp. 100–133, 1955.MathSciNetGoogle Scholar
  14. 2.14.
    Naghdi, P. M., “A Survey of Recent Progress in the Theory of Elastic Shells”, Applied Mechanics Reviews Vol. 9, No. 9, pp. 365–368, September 1956.Google Scholar
  15. 2.15.
    Mushtari, Kh. M. and K. Z. Galimov, “Non-Linear Theory of Thin Elastic Shells”, Editors and Publishers of Scientific and Technical Literature, Kazam, 1957.Google Scholar
  16. 2.17.
    Timoshenko, S. and Woinowsky-Krieger S., Theory of Plates and Shells, McGraw-Hill Book Company, Inc., 2nd Ed., New York, 1959.Google Scholar
  17. 2.18.
    Goldenveizer, A. L., “Theory of Elastic Thin Shells”, Pergamon Press, New York, 1961.Google Scholar
  18. 2.
    Flügge, W., “Stresses in Shells”, Springer-Verlag, Berlin/Göttingen/Heidelberg, 1962 (2nd Edition).Google Scholar
  19. 2.20.
    Vlasov, V. S., “General Theory of Shells and its Applications in Engineering”, NASA TTF 99, April, 1964.Google Scholar
  20. 2.21.
    Luré, A. I., “Three Dimensional Problems of the Theory of Elasticity”, Interscience Publishers, New York, 1964.Google Scholar
  21. 2.22.
    Sokolnikoff, I. S., “Tensor Analysis”, John Wiley and Sons, New York, 1964.Google Scholar
  22. 2.23.
    Vlasov, V. S. and N. N. Leont’ev, “Beams, Plates and Shells on Elastic Foundations”, Israel Program for Scientific Translations, Jerusalem, 1966.Google Scholar
  23. 2.24.
    Ogibalov, P. M., “Dynamic and Strength of Shells”, Israel Program for Scientific Translations, Jerusalem, 1966.Google Scholar
  24. 2.25.
    Durgar’ yan, S. M. (Ed.), “Theory of Shells and Plates”, Israel Program for Scientific Translations, Jerusalem, 1966.Google Scholar
  25. 2.26.
    Savin, G. N. and N. P. Fleischman, “Rib-Reinforced Plates and Shells”, Israel Program for Scientific Translations, Jerusalem, 1967.Google Scholar
  26. 2.27.
    Kraus, H., “Thin Elastic Shells”, John Wiley and Sons, Inc., New York, 1967.Google Scholar
  27. 2.28.
    Calcote, L. R., “The Analysis of Laminated Composite Structures”, Van Nostrand Reinhold Company, New York, 1969.Google Scholar
  28. 2.29.
    Baker, E. H., L. Kovalovsky and R. L. Rish, “Structural Analysis of Shells”, McGraw Hill, New York, 1972.Google Scholar
  29. 2.30.
    Flügge, W., “Tensor Analysis and Continuum Mechanics”, Springer-Verlag, Berlin, 1972.Google Scholar
  30. 2.31.
    Leissa, A.W., “Vibration of Shells”, NASA SP-288, U. S. Government Printing Office, 1973.Google Scholar
  31. 2.32.
    Dym, C. L., “Introduction to the Theory of Shells”, 1st ed., Pergamon Press, Inc., Glasgow, 1974.Google Scholar
  32. 2.33.
    Libai, A. and J. G. Simmonds, “The Nonlinear Theory of Elastic Shells”, Academic Press, 1988.Google Scholar
  33. 2.34.
    Voyiadjis, G. Z. and D. Karamanlides (Eds.), “Advances in the Theory of Plates and Shells” Elseviers, Amsterdam, 1990.Google Scholar
  34. 2.35.
    Palazotto, A. N. and S. T. Dennis, “Analysis of Nonlinear Shell Structures”, AIAA, 1991.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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