Stress-Focusing Effect in a Uniformly Heated Solid Sphere

[+] Author and Article Information
Toshiaki Hata

Shizuoka University, Shizuoka City, 422, Japan

J. Appl. Mech 58(1), 58-63 (Mar 01, 1991) (6 pages) doi:10.1115/1.2897179 History: Received December 06, 1988; Revised January 08, 1990; Online March 31, 2008


The ray theory is applied to the stress-focusing effects in a uniformly heated solid sphere. The stress-focusing effect is the phenomenon that, under an instantaneous heating, stress waves reflected from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Laplace transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply-reflected waves. Inverse transform of each ray gives rise to the exact solution of the transient response up to the arrival time of the next ray. The numerical results reveal that stresses peak out periodically at a constant period and, unlike the case of cylinder, the radial stress at the center of the sphere is bounded.

Copyright © 1991 by The American Society of Mechanical Engineers
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