An “Optimal” Solution of Saint-Venant’s Flexure Problem for a Circular Cylinder

[+] Author and Article Information
David B. Bogy

California Institute of Technology, Division of Engineering and Applied Science, Pasadena, Calif.

J. Appl. Mech 34(1), 175-183 (Mar 01, 1967) (9 pages) doi:10.1115/1.3607620 History: Received March 07, 1966; Revised July 18, 1966; Online September 14, 2011


In a recent paper, Sternberg and Knowles characterized implicitly the solution of a relaxed Saint-Venant flexure problem that is associated with the absolute minimum of the total strain energy among all solutions of this relaxed problem that correspond to a fixed resultant load and to the normal tractions on the ends of the cylinder inherent in Saint-Venant’s solution. In the present investigation, this optimal flexure solution is determined explicitly for a circular cylinder by means of the Papkovich-Neuber stress functions. The results obtained, which are in infinite-series form, are evaluated numerically and compared with the analogous results of Saint-Venant. The solution deduced here also supplies a quantitative illustration of Saint-Venant’s principle.

Copyright © 1967 by ASME
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