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Kirchhoff’s theory of rods. (English) Zbl 0762.01012
“The purpose of this paper is to examine the classical theory of finite displacements of thin rods as developed by Kirchhoff [1859, 1876] and Clebsch [1862], and presented by Love [1892, 1906]. In their work, a rod is a three-dimensional body with two dimensions which are very small compared to the third ... We will re-examine in this paper the general ideas of Kirchhoff-Clebsch-Love within the framework of modern continuum mechanics”.

MSC:
01A55 History of mathematics in the 19th century
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74-03 History of mechanics of deformable solids
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[1] 1859 Kirchhoff, G.: Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. f. reine. angew. Math. (Crelle) 56 (1859) 285-313. · ERAM 056.1494cj · doi:10.1515/crll.1859.56.285
[2] 1862 Clebsch, A.: Theorie der Elasticität Fester Körper. B. G. Teubner, Leipzig, 1862.
[3] 1876 Kirchhoff, G.: Vorlesungen über mathematische Physik, Mechanik (Vorl. 28). B. G. Teubner, Leipzig, 1876.
[4] 1883 Clebsch, A.: Théorie de l’Elasticité des Corps Solides. Translated by B. de Saint-Venant and Flamant, Dunod, Paris, 1883. Reprinted by the Johnson Reprint Corp., NY, 1966.
[5] 1892 Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity. First Edition, Cambridge Univ. Press, 1892.
[6] 1893 Todhunter, Isaac, & Karl Pearson: A History of the Theory of Elasticity and of the Strength of Materials from Galilei to Lord Kelvin. Vol. II, Part II. Cambridge University Press, 1893. Dover edition, 1960.
[7] 1906 Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity. Second Edition, Cambridge Univ. Press, 1906. Fourth Edition 1927, reprinted by Dover Publications. · JFM 37.0822.01
[8] 1954 Green, A. E., & W. Zerna: Theoretical Elasticity. Oxford University Press, London.
[9] 1965 Truesdell, C., & W. Noll: The Non-linear Field Theories of Mechanics. Encyclopedia of Physics, ed. S. Flügge. Springer-Verlag. · Zbl 0779.73004
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