Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution (Q1434733)

The authors derive a general solution expressed by four quasi-harmonic functions by the introduction of two displacement functions and using the operator theory. The form of the solution is very simple in that it does not contain a particular part related to the temperature field. Using this general solution, the potential theory method is extended to solve the problem of a penny-shaped crack subjected to temperature load in an infinite transversely isotropic medium. A new potential is introduced to take thermal effect into account. Two governing integral or integro-differential equations are derived. It is found that the structure of the integral equation is the same as that for crack problems in elasticity and that the integro-differential equation is identical to that for contact problems in elasticity. For the problem of a penny-shaped crack subjected to point surface temperature, a complete and exact fundamental solution of the thermoelastic field is derived.