Stress-focusing effect due to an instantaneous concentrated heat source in a sphere

The stress-focusing effect is the phenomenon in which, due to an instantaneous concentrated heat source, stress waves propagating from the free surface of the sphere result in very high stresses at the center. Using the ray theory, the Fourier transformed solution of stress waves in the sphere is sorted out into rays according to the ray path of multiply reflected waves. In the study, in order to denote the strength of the stress focusing, we introduce the stress-focusing intensity factor, S-Fi, which is defined by the relation sigma(i) = S-Fi/r(-3) (i = r, theta, phi) at the focusing point. The numerical results reveal that stresses peak out periodically with a constant period.