A Consistent Theory for Elastic Deformations With Small Strains

[+] Author and Article Information
R. T. Shield

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Ill. 61801

J. Appl. Mech 51(4), 717-723 (Dec 01, 1984) (7 pages) doi:10.1115/1.3167714 History: Received July 01, 1983; Online July 21, 2009


A consistent theory is developed for linear elastic behavior in which the strains are small but in which no restriction is placed on the magnitudes of the displacements or the rotations of elements of the body. The theory reduces to the classical theory for infinitesimal deformations when the rotations are small. Pure torsion of a long cylinder and the bending of a beam by a terminal load are treated in order to illustrate the application of the theory. The bending solution agrees with the St. Venant flexure solution when the deflections are small and with the theory of the elastica when the deflections are large.

Copyright © 1984 by ASME
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