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Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem

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References

  1. Saint-Venant, A.-J.-C. B. de, Mémoire sur la torsion des prismes. Mémoires des Savants étrangers 14, 233 (1856).

    Google Scholar 

  2. Saint-Venant, A.-J.-C. B. de, Mémoire sur la flexion des prismes. Journal de Mathématiques de Liouville, Ser. II, 1, 89 (1856).

    Google Scholar 

  3. Toupin, R. A., Saint-Venant's principle. Archive for Rational Mechanics and Analysis 18, 2, 83 (1965).

    Google Scholar 

  4. Knowles, James K., On Saint-Venant's principle in the two-dimensional linear theory of elasticity. Archive for Rational Mechanics and Analysis 21, 1 (1966).

    Google Scholar 

  5. Clebsch, A., Theorie der Elasticität fester Körper. Leipzig: B. G. Teubner 1862.

    Google Scholar 

  6. Voigt, W., Theoretische Studien über die Elasticitätsverhältnisse der Krystalle. Göttinger Abhandlungen 34, 53 (1887).

    Google Scholar 

  7. Grioli, G., Sullo stato tensionale dei continui in equilibrio e sulle deformazioni nel caso elastico. Conferenze del Seminario di Matematica, Bari 35/36, 3 (1958).

    Google Scholar 

  8. Grioli, G., Mathematical Theory of Elastic Equilibrium. Berlin-Göttingen-Heidelberg: Springer 1962.

    Google Scholar 

  9. Kellogg, O. D., Foundations of Potential Theory. Berlin: Springer 1929.

    Google Scholar 

  10. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Fourth Edition. New York: Dover 1944.

    Google Scholar 

  11. Sokolnikoff, I. S., Mathematical Theory of Elasticity, Second Edition. New York: McGraw-Hill 1956.

    Google Scholar 

  12. Fichera, G., Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno relativi all'equilibrio di un corpo elastico. Annali della Scuola Normale Superiore di Pisa, Ser. III, 4, 35 (1950).

    Google Scholar 

  13. Truesdell, C., The rational mechanics of materials — past, present, future. Applied Mechanics Reviews 12, 2, 75 (1959).

    Google Scholar 

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The results contained in this paper were obtained in the course of research conducted under Contract Nonr-220(58) with the Office of Naval Research in Washington, D.C.

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Sternberg, E., Knowles, J.K. Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem. Arch. Rational Mech. Anal. 21, 89–107 (1966). https://doi.org/10.1007/BF00266569

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