DYNAMIC THERMOSTRESS-CONCENTRATION EFFECT IN A SPHERICALLY ISOTROPIC SPHERE
球面各向同性球体内的动态热应力集中

The dynamic response of thermal stresses in a sphere made of different kinds of materials is very useful for the fracture analysis of brittle material subjected to a rapid change in temperature. Hata (1991b) get a solution to the problem of stress-concentration effects in an isotropic sphere subjected to thermal shock. In this paper, we decompose the complete solution for a spherically isotropic sphere subjected to thermal shock into a thermoelastic solution satisfying the homogeneous equation with the in- homogeneous boundary conditions and an elastodynamic solution satisfying the inhomogeneous equation with the homogeneous boundary conditions. Through a direct integral and a finite integral transform, we obtain the thermoelastic solution and the elastodynamic solution respectively. Finally the analytical expression of the exact solution for a sphere made of different Kinds of material under thermal shock is obtained. From the analytical solution obtained, the discussions about the stress--concentration effect in a spherically isotropic sphere and an isotropic sphere, respectively are much more easy and clear than existed results. This major objective of this paper has been in gaining an effectively solving method and a better understanding for the dynamic stress-concentration effect in a spherically isotropic sphere under thermal shock.