Abstract
This paper contains an exact solution for the state of stress in an elastic circular cylinder with an oblate spheroidal cavity or an internal penny-shaped crack, the surface of which is subjected to a prescribed temperature distribution. The solution is deduced. with the aid of thermoelastic displacement potentials and Dougall's displacement potentials. Two sets of harmonic functions and two sets of biharmonic functions are given by simple expressions referring to cylindrical and oblate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and the cavity are satisfied by using the relations between the cylindrical and oblate spheroidal harmonics and biharmonics. The solution for an internal penny-shaped crack is also given by regarding as a limited case of an oblate spheroidal cavity. Numerical results for stress distributions, stress concentration factors and stress intensity factors are shown graphically.
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