Finite Deflections of a Nonlinearly Elastic Bar

[+] Author and Article Information
J. T. Oden

Research Institute, University of Alabama, Huntsville, Ala.

S. B. Childs

Department of Mechanical Engineering, University of Houston, Houston, Texas

J. Appl. Mech 37(1), 48-52 (Mar 01, 1970) (5 pages) doi:10.1115/1.3408488 History: Received August 20, 1968; Online July 12, 2010


The problem of finite deflections of a nonlinearly elastic bar is investigated as an extension of the classical theory of the elastica to include material nonlinearities. A moment-curvature relation in the form of a hyperbolic tangent law is introduced to simulate that of a class of elastoplastic materials. The problem of finite deflections of a clamped-end bar subjected to an axial force is given special attention, and numerical solutions to the resulting system of nonlinear differential equations are obtained. Tables of results for various values of the parameters defining the material are provided and solutions are compared with those of the classical theory of the elastica.

Copyright © 1970 by ASME
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