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On Saint-Venant's principle in the two-dimensional linear theory of elasticity

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References

  1. Saint-Venant, B. de, Mémoire sur la torsion des prismes. Mém. savants étrangers 14, 233 (1856).

    Google Scholar 

  2. Boussinesq, M. J., Application des Potentiels. Paris: Gauthier-Villars 1885.

    Google Scholar 

  3. Mises, R. von, On Saint-Venant's principle. Bull. Amer. Math. Soc. 51, 555 (1945).

    Google Scholar 

  4. Sternberg, E., On Saint-Venant's principle. Q. Appl. Math. 11, 393 (1954).

    Google Scholar 

  5. Keller, H. B., Saint-Venant's procedure and Saint-Venant's principle. Q. Appl. Math. 22, 293 (1965).

    Google Scholar 

  6. Horvay, G., Saint-Venant's principle: a biharmonic eigenvalue problem. J. Appl. Mech. 24, 381 (1957).

    Google Scholar 

  7. Horvay, G., Biharmonic eigenvalue problem of the semi-infinite strip. Q. Appl. Math. 15, 65 (1957).

    Google Scholar 

  8. Horvay, G., Some aspects of Saint-Venant's principle. J. Mech. and Phys. of Solids 5, 77 (1957).

    Google Scholar 

  9. Babuška, I., K. Rektorys & F. Vyčichlo, Mathematische Elastizitätstheorie der ebenen Probleme. Berlin: Akademie-Verlag 1960.

    Google Scholar 

  10. Goodier, J. N., A general proof of Saint-Venant's principle. Phil. Mag., series VII, 23, 607 (1937).

    Google Scholar 

  11. Goodier, J. N., Supplementary note on “A general proof of Saint-Venant's principle”. Phil. Mag., series VII, 24, 325 (1937).

    Google Scholar 

  12. Goodier, J. N., An extension of Saint-Venant's principle, with applications. J. Appl. Phys. 13, 167 (1942).

    Google Scholar 

  13. Southwell, R., On Castigliano's theorem of least work and the principle of Saint-Venant. Phil. Mag., series VI, 45, 193 (1923).

    Google Scholar 

  14. Biezeno, C. B., & R. Grammel, Engineering Dynamics, vol. 1. Glasgow: Blackie & Son, Ltd. 1955.

    Google Scholar 

  15. Zanaboni, O., Dimostrazione generale del principio del De Saint-Venant. Atti Acad. Naz. dei Lincei, Rendiconti 25, 117 (1937).

    Google Scholar 

  16. Zanaboni, O., Valutazione dell'errore massimo cui dà luogo l'applicazione del principio del De Saint-Venant. Atti Acad. Naz. dei Lincei, Rendiconti 25, 595 (1937).

    Google Scholar 

  17. Zanaboni, O., Sull'approssimazione dovuta al principio del De Saint-Venant nei solidi prismatici isotropi. Atti Acad. Naz. dei Lincei, Rendiconti 26, 340 (1937).

    Google Scholar 

  18. Toupin, R. A., Saint-Venant's principle. Arch. Rational Mech. & Anal. 18, 83 (1965).

    Google Scholar 

  19. Mindlin, R. D., & M. G. Salvadori, Analogies, in: Handbook of experimental stress analysis, edited by M. Hetényi. New York: John Wiley & Sons 1950.

    Google Scholar 

  20. Temple, G., & W. G. Bickley, Rayleigh's principle and its applications to engineering. New York: Dover Publications, Inc. 1956.

    Google Scholar 

  21. Hardy, G. H., J. E. Littlewood, & G. Pólya, Inequalities. Cambridge: University Press 1959.

    Google Scholar 

  22. Johnson, M. W. Jr., & R. W. Little, The semi-infinite elastic strip problem. Q. Appl. Math. 22, 335 (1965).

    Google Scholar 

  23. Fadle, J., Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe. Ingenieur-Archiv 11, 125 (1940).

    Google Scholar 

  24. Nicolesco, M., Les fonctions polyharmoniques. Actualites Scientifique et Industrielles 331, Paris (1936).

  25. Diaz, J. B., & L. E. Payne, Mean value theorems in the theory of elasticity. Proc., Third U.S. Nat'l Cong. Appl. Mech., Brown Univ., Providence, R.I., p.293 (1958).

    Google Scholar 

  26. Sokolnikoff, I. S., Mathematical Theory of Elasticity. New York: McGraw-Hill Book Co. 1956.

    Google Scholar 

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Communicated by E. Sternberg

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Knowles, J.K. On Saint-Venant's principle in the two-dimensional linear theory of elasticity. Arch. Rational Mech. Anal. 21, 1–22 (1966). https://doi.org/10.1007/BF00253046

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