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THE GENERAL THEORY OF ELASTIC STABILITY AT THE END OF THE 19th CENTURY

LUIS A. GODOY

Department of Structures, FCEFyN, Universidad Nacional de Cordoba and CONICET, Cordoba, P.O. Box 916, Correo Central, Cordoba, Argentina

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https://doi.org/10.1142/S0219455411004191Cited by:0 (Source: Crossref)

Abstract

This paper reviews the research on the theory of elastic stability published at the end of the 19th century, with emphasis on the work by G. H. Bryan in Cambridge. The state of the studies on structural stability previous to Bryan is reviewed, and two lines of work are identified: one is a general stability of rigid bodies and the other is a collection of case studies of elastic stability. Bryan's theory is discussed next, presenting his arguments based on first energy principles, which led him to strong conclusions. The importance of the word "general" and the idea of having solved the problem in each case are explained. The impact of the contributions made by Bryan, together with the critiques that this generated, is also discussed.

An earlier version of this paper was presented at the ICSSD meeting to honor the 60th anniversary of Prof. J. N. Reddy, Orlando, FL, June 2005.

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References

W. T. Koiter, Over de stabiliteit van het elastisch evenwich (in Dutch), Doctoral Thesis, Polytechnic Institute of Delft, Delft (published by H. J. Paris, Amsterdam, 1945). English translation On the stability of elastic equilibrium, NASA, TTF10, 833, Washington, 1967. Second English translation at Palo Alto, California, 1970 . Google Scholar
L. A. Godoy, Anales de la Academia Nacional de Ciencias Exactas, Físicas y Naturales de Argentina 55, 99 (2003). Google Scholar
J. M. T. Thompson and G. W. Hunt , A General Theory of Elastic Stability ( Wiley , London , 1973 ) . Google Scholar
R. V. Southwell, Philosophical Transactions of the Royal Society 213, 187 (1913). Crossref, Google Scholar
J. Larmor, Cambridge Philosophical Proceedings IV, 410 (1883). Google Scholar
A. G. Greenhill, Cambridge Philosophical Proceedings IV, 65 (1881). Google Scholar
A. G. Greenhill, On the strength of shafting when exposed both to torsion and to end thrust, Proc. Institution of Mechanical Engineers (1883) pp. 182–209. Google Scholar
S. P. Timoshenko , History of Strength of Materials ( McGraw-Hill , New York , 1953 ) . Google Scholar
G. H. Bryan, Obituary Notices of Fellows of the Royal Society (1932–1954) 1(2) (1933) 139–142 . Google Scholar
G. H. Bryan , Stability in Aviation ( Macmillan , London , 1911 ) . Google Scholar
G. H. Bryan, Proceedings Cambridge Philosophical Society 6, 199 (1888). Google Scholar
G. R. Kirchhoff , Vorlesungen uber Mathematische Physik ( Leipzig German , 1876 ) . Google Scholar
A. E. H. Love , A Treatise on the Mathematical Theory of Elasticity 2 ( Cambridge University Press , Cambridge , 1893 ) . Google Scholar
G. H. Bryan, Proceedings Cambridge Philosophical Society 6, 287 (1888). Google Scholar
W. Fairnbairn, Philosophical Transactions of the Royal Society 148, 389 (1858). Crossref, Google Scholar
W. C. Unwin, Proceedings of Institution of Civil Engineers 46, 225 (1875). Google Scholar
G. H. Bryan, Proceedings London Mathematical Society 22, 54 (1891). Google Scholar
I. Todhunter and K. Pearson , A History of the Theory of Elasticity and of the Strength of Materials 2 ( Cambridge University Press , Cambridge , 1893 ) . Google Scholar
H. Reissner, Zeitschrift für Angewandte Mathematik und Mechanik 5, 475 (1925). Google Scholar
C. B. Biezeno and H. Hencky, On the general theory of elastic stability, Proceedings of the Academy of Sciences, Amsterdam 31 (1928) 569–578; Second part in 32 (1929) 444–456 . Google Scholar
V. E. Trefftz, Zeitschrift für Angewandte Mathematik und Mechanik 13, 160 (1933), DOI: 10.1002/zamm.19330130224. Crossref, Web of Science, Google Scholar