Energy Methods for Shells

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


In structural mechanics three energy principles are used Minimum Potential Energy, Minimum Complementary Energy, and Reissner’s Variational Theorem. The first two are discussed at length in Sokolnikoff [10.1] and many other references. The Reissner Variational Theorem, likewise, is widely referenced. In solid mechanics, Minimum Complementary Energy is rarely used, because often it requires assuming continuous functions for all stresses which satisfy the boundary conditions, are continuous and satisfy equilibrium. It is usually far easier to make a guess at the displacement functions which must be continuous and satisfy the boundary conditions. These displacement functions are needed to utilize the Theorem of Minimum Potential Energy.


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  1. 10.1.
    Sokolnikoff, I. S., “The Mathematical Theory of Elasticity”, McGraw-Hill Book Company, Inc., Second Edition, 1956.Google Scholar
  2. 10.2.
    Vinson, J. R., “The Behavior of Thin Walled Structures: Beams Plates and Shells”, Kluwer Academic Publishers, Dordrecht, 1989.zbMATHGoogle Scholar
  3. 10.3.
    Vinson, J. R. and R. L. Sierakowski, “The Behavior of Structures Composed of Composite Materials”, Martinus-Nijhoff Publishers (now Kluwer Academic Publishers, Dordrecht, 1986.zbMATHGoogle Scholar
  4. 10.4.
    Mura, T. and T. Koya, “Variational Methods in Mechanics”, Oxford University Press, March, 1992.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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