Thermal stress-focusing in a transversely isotropic sphere and an isotropic sphere

Elastodynamic theory is applied to solve the dynamic thermal stress-focusing effect in a transversely isotropic sphere and an isotropic sphere. Using a finite integral transform [G. Cinelli, Int, J. Engng. Sci, vol. 3, pp. 534-550, 1965] and Laplace transform, the exact expression of dynamic thermal stress in the sphere is obtained. Based on the analytical expression of this solution, it is observed that the thermal stress-focusing effect in a transversely isotropic sphere is obviously different from that in an isotropic sphere. The results show that there exists a thermal stress-focusing phenomenon in a sphere under a uniformly thermal shock, which results in a very, high thermal stress-peak. Finally, it is discussed that some phenomena of the stress-focusing effect at the center of a sphere mainly depend on the material properties of the sphere.