STRESS-FOCUSING EFFECT IN A UNIFORMLY HEATED TRANSVERSELY ISOTROPIC SPHERE

The ray theory is applied to the stress-focusing effects in a uniformly heated transversely isotropic 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 Fourier transformed solution of stress waves in the sphere is sorted into rays according to the ray path of multiply-reflected waves. The 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 results reveal that stresses peak periodically at regular intervals and the stress peak at the center of the sphere depends on the anisotropy of the sphere.