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.
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An “Optimal” Solution of Saint-Venant’s Flexure Problem for a Circular Cylinder
David B. Bogy
California Institute of Technology, Division of Engineering and Applied Science, Pasadena, Calif.
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Bogy, D. B. (March 1, 1967). "An “Optimal” Solution of Saint-Venant’s Flexure Problem for a Circular Cylinder." ASME. J. Appl. Mech. March 1967; 34(1): 175–183. https://doi.org/10.1115/1.3607620
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