Abstract: This paper presents an analytical method of solving the elastodynamic problem of a solid sphere.The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions.By utilizing the variable transform, the dynamic equation may be transformed into Bassel equation.By defining a finite Hankel transform, we can easily obtain the dynamic solution for the inhomogeneous dynamic equation.Thereby, the exact elastodynamic solution for a solid sphere can be obtained.From results carried out, we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.

Key words: solid sphere, elastodynamics, dynamic stress-focusing