zbMATH — the first resource for mathematics

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”.

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
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.