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Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem

Sternberg, Eli and Knowles, James K. (1966) Minimum energy characterizations of Saint-Venant's solution to the relaxed Saint-Venant problem. Archive for Rational Mechanics and Analysis, 21 (2). pp. 89-107. ISSN 0003-9527. doi:10.1007/BF00266569.

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The singular importance, in both theory and practice, of SAINT-VENANT'S celebrated memoirs [1], [2] on what has long since become known as SAINTVENANT'S problem, requires no emphasis. Indeed, a comprehensive bibliography of the vast and varied literature to which the work contained in [1], [2] has given impetus would multiply the length of this rather limited study. With a view toward describing the aim of the present investigation we recall first that SAINT-VENANT'S problem consists in the determination of the stresses and deformations in an elastic cylinder (or prism), which - in the absence of body forces - is subjected to surface tractions arbitrarily prescribed over its ends and which is free from lateral loading. In this formulation the problem, even within the linearized equilibrium theory of homogeneous and isotropic elastic solids, has remained one of undiminished notoriety. SAINT-VENANT'S treatment of the foregoing problem rests on a relaxed formulation in which the detailed assignment of the terminal tractions is abandoned in favor of prescribing merely the appropriate stress resultants.

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Additional Information:© 1966 Springer. (Received September 15, 1965) The results contained in this paper were obtained in the course of research conducted under Contract Nonr-220(58) with the Office of Naval Research in Washington, D.C.
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Office of Naval Research (ONR)Nonr-220(58)
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Record Number:CaltechAUTHORS:20150811-131727884
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59423
Deposited By: George Porter
Deposited On:11 Aug 2015 21:18
Last Modified:10 Nov 2021 22:20

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