Point temperature solution for a penny-shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium

The solution of an impermeable penny-shaped crack subjected to a concentrated thermal load (prescribed point temperature) applied arbitrarily at the crack surfaces is derived using the generalized potential theory method. The integral equation governing the temperature field is found to have the same structure as that for the elastic punch problem and the integro-differential equations related to the electroelastic field are similar to that reported for the elastic crack problem. Significant solutions to these integro-differential equations are obtained by generalizing the previous results available in literature. Exact three-dimensional expressions for the full-space thermo-electro-elastic field are finally obtained by simple differentiation, all in terms of elementary functions. The exact analysis for a permeable crack is also presented and discussed. The obtained point temperature solutions play an important role in the related BEM analysis.