Archive for Rational Mechanics and Analysis

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

Saint-Venant's Principle

  • R. A. Toupin


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.


Neural Network Complex System Nonlinear Dynamics Mathematical Formulation Electromagnetism 
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  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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