One-Dimensional Thermal Stresses in Spheres

Synonyms

Hollow spheres; Infinite medium with a cavity; Solid spheres; Static and quasi-static thermal stresses

Definition

Let us consider the thermal stresses in a spherical symmetric body with radial temperature variation. In this case, all displacements and their derivatives in the $\theta$ and $\phi$ directions are not appeared in the equations of motion because of the symmetry to the origin of the spherical coordinate. Therefore, the equation of motion is dependent only on the radial variable of $r$ in the static problem or on the radial variable of $r$ and time $t$ in the quasi-static and dynamic cases.

Overview

Consider the simple case of a temperature symmetrical with respect to the center of the spherical symmetric body and so a function of $r$, the radial distance, only. Under this simplest assumption, it is possible to analyze the several interesting thermal stress problems in the spherical symmetric body. For example, the thermal stress problems in a sphere, a...