Reconsideration of the Stress-Focusing Effect in a Uniformly Heated Solid Cylinder

[+] Author and Article Information
T. Hata

Department of Technology, Faculty of Education, Shizuoka University, Shizuoka City 422, Japan

J. Appl. Mech 61(3), 676-680 (Sep 01, 1994) (5 pages) doi:10.1115/1.2901513 History: Received October 30, 1992; Revised June 22, 1993; Online March 31, 2008


The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the cylinder result in very high stresses at the center. Ho solved the problem by using Laplace transform on time and presented the solution as infinite series summations, which converge very slowly for certain combinations of time and the radius of a cylinder. However, adopting a concept of the ray theory, the solution of stress waves in the cylinder is sorted out into rays according to the ray path of multiply reflected waves. The results expressed in an infinite series reveal that stresses peak out periodically at a constant period and the order of singularity of the stresses in a cylinder is O (ρ −2 ).

Copyright © 1994 by The American Society of Mechanical Engineers
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