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Archive for Rational Mechanics and Analysis

, Volume 18, Issue 2, pp 83–96 | Cite as

Saint-Venant's Principle

  • R. A. Toupin
Article

Abstract

The principle of the elastic equivalence of statically equivalent systems of load, or Saint-Venant's Principle, is given a precise mathematical formulation and proof. Counterexamples to traditional verbal statements of the principle are given, and the results are compared with previous mathematical work on the Saint-Venant principle.

Keywords

Neural Network Complex System Nonlinear Dynamics Mathematical Formulation Electromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Saint-Venant, A.-J.-C. Barré de, Mémoire sur la torsion des prismes, avec des considérations sur leur flexion ... (Read June 13, 1853). Mém. Divers Savants 14, 233–560 (1855). Also issued separately: De la Torsion des Prismes ... Paris: Imprimérie Impériale (1855).Google Scholar
  2. [2]
    Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Fourth Edition. Cambridge: The University Press 1927.zbMATHGoogle Scholar
  3. [3]
    Diaz, J. B., & L. E. Payne, Mean Value Theorems in the Theory of Elasticity. Proceedings of the Third U.S. National Congress of Applied Mechanics, 293–303 (1958).Google Scholar
  4. [4]
    Filon, L. N. G., On the Elastic Equilibrium of Circular Cylinders under Certain Practical Systems of Load. Phil. Trans. Roy. Soc. (Ser. A) 198, 147 (1902).ADSCrossRefGoogle Scholar
  5. [5]
    [5]Bramble, J. H., & L. E. Payne, Some Inequalities for Vector Functions with Applications in Elasticity. Arch. Rational Mech. Anal. 11, 16–26 (1962).ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    Boussinesq, M. J., Applications des potentiels à l'étude de l'équilibre et du mouvement des solides élastiques. Paris: Gauthier-Villars 1885.zbMATHGoogle Scholar
  7. [7]
    von Mises, R., On Saint-Venant's Principle. Bull. Amer. Math. Soc. 51, 555–562 (1945).MathSciNetCrossRefGoogle Scholar
  8. [8]
    Sternberg, E., On Saint-Venant's Principle. Quart. of Appl. Math. 11, 393–402 (1954).MathSciNetCrossRefGoogle Scholar
  9. [9]
    Zanaboni, O., Dimostrazione generale del Principio del de Saint-Venant. Atti. Acc. Naz. Lincei 25, 117–120 (1937).zbMATHGoogle Scholar
  10. [10]
    Dou, A., On the Principle of Saint-Venant. Mathematics Research Center, U.S. Army, The University of Wisconsin, Tech. Report No. 472 (1964).Google Scholar
  11. [11]
    Gould, S., Variational Methods for Eigenvalue Problems. Math. Expositions 10, Toronto (1957).Google Scholar
  12. [12]
    Truesdell, C., & R. Toupin, The Classical Field Theories. Handbuch der Physik, Vol. III/1. Berlin-Göttingen-Heidelberg: Springer 1960.CrossRefGoogle Scholar
  13. [13]
    Truesdell, C., The Rational Mechanics of Materials—Past, Present, Future. Appl. Mech. Rev. 12, 75–80 (1959).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1965

Authors and Affiliations

  • R. A. Toupin
    • 1
  1. 1.IBM Watson Research CenterYorktown Heights

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