On Saint-Venant’s principle
Author:
E. Sternberg
Journal:
Quart. Appl. Math. 11 (1954), 393-402
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/58414
MathSciNet review:
58414
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Additional Information
B. de Saint-Venant, “Mémoire sur la torsion des prismes,” Mém. Savants étrangers, Paris, 1855.
M. J. Boussinesq, “Application des potentiels,” Gauthier-Villars, Paris, 1885.
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
- R. v. Mises, On Saint Venant’s principle, Bull. Amer. Math. Soc. 51 (1945), 555–562. MR 12567, DOI https://doi.org/10.1090/S0002-9904-1945-08394-3
C. B. Biezeno and R. Grammel, “Technische Dynamik,” J. W. Edwards, Ann Arbor, Michigan, 1944.
R. Southwell, “On Castigliano’s theorem of least work and the principle of Saint-Venant,” Phil. Mag. (6) 45, 193 (1923).
J. N. Goodier, “A general proof of Saint-Venant’s principle,” Phil. Mag. (7) 23, 607 (1937).
J. N. Goodier, “Supplementary note on ’A general proof of Saint-Venant’s principle’,” Phil. Mag. (7) 24, 325 (1937).
O. Zanaboni, “Dimostrazione generale del principio del De Saint-Venant” Atti Acc. Naz. Lincei 25, 117 (1937).
O. Zanaboni, “Valutazione dell’ errore massimo cui dà luogo l’applicazione del principio del De Saint-Venant,” Atti Acc. Naz. Lincei 25, 595 (1937).
- J. N. Goodier, An extension of Saint-Venant’s principle, with applications, J. Appl. Phys. 13 (1942), 167–171. MR 6313
K. Erim, “Sur le principe de Saint-Venant,” Proc., Seventh Int. Cong. for Appl. Mech., London, 1948.
O. D. Kellogg, “Foundations of potential theory,” The Murray Printing Company, New York, 1929.
- J. L. Synge, Upper and lower bounds for the solutions of problems in elasticity, Proc. Roy. Irish Acad. Sect. A 53 (1950), 41–64. MR 0039484
- C. Weber, Kugel mit normalgerichteten Einzelkräften, Z. Angew. Math. Mech. 32 (1952), 186–195 (German, with English, French and Russian summaries). MR 50469, DOI https://doi.org/10.1002/zamm.19520320605
- E. Sternberg and F. Rosenthal, The elastic sphere under concentrated loads, J. Appl. Mech. 19 (1952), 413–421. MR 0054482
N. J. Hoff, “The applicability of Saint-Venant’s principle to airplane structures,” J. Aero. Sci. 12, 455 (1945).
- Piero Locatelli, Estensione del principio di St. Venant a corpi non perfettamente elastici, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 75 (1940), 502–510 (Italian). MR 4582
B. de Saint-Venant, “Mémoire sur la torsion des prismes,” Mém. Savants étrangers, Paris, 1855.
M. J. Boussinesq, “Application des potentiels,” Gauthier-Villars, Paris, 1885.
A. E. H. Love, “A treatise on the mathematical theory of elasticity,” 4th ed., Dover Publications, New York, 1944.
R. v. Mises, “On Saint-Venant’s principle,” Bull. Amer. Math. Soc., 51, 555 (1945).
C. B. Biezeno and R. Grammel, “Technische Dynamik,” J. W. Edwards, Ann Arbor, Michigan, 1944.
R. Southwell, “On Castigliano’s theorem of least work and the principle of Saint-Venant,” Phil. Mag. (6) 45, 193 (1923).
J. N. Goodier, “A general proof of Saint-Venant’s principle,” Phil. Mag. (7) 23, 607 (1937).
J. N. Goodier, “Supplementary note on ’A general proof of Saint-Venant’s principle’,” Phil. Mag. (7) 24, 325 (1937).
O. Zanaboni, “Dimostrazione generale del principio del De Saint-Venant” Atti Acc. Naz. Lincei 25, 117 (1937).
O. Zanaboni, “Valutazione dell’ errore massimo cui dà luogo l’applicazione del principio del De Saint-Venant,” Atti Acc. Naz. Lincei 25, 595 (1937).
J. N. Goodier, “An extension of Saint-Venant’s principle, with applications,” J. Appl. Phys. 13, 167, 1942.
K. Erim, “Sur le principe de Saint-Venant,” Proc., Seventh Int. Cong. for Appl. Mech., London, 1948.
O. D. Kellogg, “Foundations of potential theory,” The Murray Printing Company, New York, 1929.
J. L. Synge, “Upper and lower bounds for the solution of problems in elasticity,” Proc., Royal Irish Ac. (A) 53, 41 (1950).
C. Weber, “Kugel mit normalgerichteten Einzelkräften,” Z. Angew. Math. Mech. 32, 186 (1952).
E. Sternberg and F. Rosenthal, “The elastic sphere under concentrated loads,” J. Appl. Mech. 19, 413 (1952).
N. J. Hoff, “The applicability of Saint-Venant’s principle to airplane structures,” J. Aero. Sci. 12, 455 (1945).
P. Locatelli, “Extensione del principio di St. Venant a corpi non perfettamente elastici,” Atti R. Acc. delle Sci. Torino 75, 502 (1940).
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Article copyright:
© Copyright 1954
American Mathematical Society
