Application of a Perturbation Technique Based on the Method of Characteristics to Axisymmetric Plasticity

[+] Author and Article Information
O. Richmond, H. L. Morrison

United States Steel Corporation, Edgar C. Bain Laboratory for Fundamental Research, Monroeville, Pa.

J. Appl. Mech 35(1), 117-122 (Mar 01, 1968) (6 pages) doi:10.1115/1.3601123 History: Received August 10, 1966; Revised August 23, 1967; Online September 14, 2011


A perturbation technique is described which may be used for obtaining approximate solutions in plasticity when the field equations are hyperbolic. The characteristic parameters of the exact equations are employed as independent variables. The technique has been used to a limited extent in supersonic fluid mechanics, but not fully exploited. It apparently has not been used before in plasticity. As an example, an upper-bound solution is obtained to an axisymmetric problem: Expansion of a circular hole in a finite flat plate. The accuracy of the technique is illustrated by comparing the stresses with those obtained by a well-known finite-difference method. The advantages of the technique over an earlier perturbation method based on approximate characteristics are demonstrated by a comparison with a solution to the same problem obtained by that method.

Copyright © 1968 by ASME
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