By using the separation of variables technique, the dynamic thermal stress responses in an isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface are performed successfully. The analytical solutions of the radial and hoop dynamic stresses at the center are also obtained. By means of the present method, integral transform can be avoided. Numerical results denote that a very high dynamic stress peak appears periodically at the center of the isotropic solid sphere subjected to uniform temperature rise all over the sphere and a sudden constant pressure at the external surface.

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