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Paul Ehrenfest (left) and Stephen Timoshenko in St. Petersburg


Isaac Elishakoff (Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, USA), “Who developed the so-called Timoshenko beam theory?”, Mathematics and Mechanics of Solids, 2019, DOI: 10.1177/1081286519856931
ABSTRACT: The use of the Google Scholar produces about 78,000 hits on the term ‘‘Timoshenko beam.’’ The question of priority is of great importance for this celebrated theory. For the first time in the world literature, this study is devoted to the question of priority. It is that Stephen Prokofievich Timoshenko had a co-author, Paul Ehrenfest. It so happened that the scientific work of Timoshenko dealing with the effect of rotary inertia and shear deformation does not carry the name of Ehrenfest as the co-author. In his 2002 book, Grigolyuk concluded that the theory belonged to both Timoshenko and Ehrenfest. This work confirms Grigolyuk’s discovery, in his little known biographic book about Timoshenko, and provides details, including the newly discovered letter of Timoshenko to Ehrenfest, which is published here for the first time over a century after it was sent. This paper establishes that the beam theory that incorporates both the rotary inertia and shear deformation as is known presently, with shear correction factor included, should be referred to as the Timoshenko-Ehrenfest beam theory.
(Isaac Elishakoff wrote the following for an announcement of a lecture on this topic given at the Mechanics and Computation Seminar (ME395) in 2019 at Stanford University: “At the first glance there might be a confusion about the question in the title. One could retort: “Naturally, it was Timoshenko (1878-1972) who developed this theory!” In his 1977 paper, W.T. Koiter claimed that the Timoshenko beam theory is the illustration of the fact that the theory bearing someone’s name is usually by someone else. Koiter did not know how right he was. Hold your breath: Timoshenko WAS one of the developers of this theory! What is not known widely is that he had a collaborator, namely famous Austrian-Dutch physicist Paul Ehrenfest (1880-1933) whose dissertation was in classical mechanics. How did we find this fact? In defiance of the famous cynical definition by Mark Twain, “Classical work is the work that everyone cites but nobody reads,” this author read original papers and autobiographical book by Timoshenko, many times, as well as widely consulted with Archive of S.P. Timoshenko and Archive of P. Ehrenfest that are housed at Stanford and Leiden universities, respectively. In his forthcoming book titled “Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories” (World Scientific, Singapore, 2019) author shows that this theory ought to be called Timoshenko-Ehrenfest beam theory. Author conducted an ‘archeological’ dig as it were, to illuminate the fact that, as the ancient saying states “truth sprouts from the earth.” It is also shown that the Timoshenko-Ehrenfest beam theory is unnecessarily overcomplicated. Simplest possible version of the beam theory that takes into account both shear deformation and rotary inertia is suggested. Dr. Elishakoff is preparing another book tentatively titled “S.P. Timoshenko at 140: Going Strong,” and will appreciate any comment on Timoshenko’s life and/or work.”)

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