Exact fundamental thermo-elastic solutions of a transversely isotropic elastic medium with a half infinite plane crack

Abstract

This paper presents three-dimensional (3D) exact fundamental solutions of the thermoelastic field in a transversely isotropic elastic medium weakened by a half infinite plane crack subjected to a pair of point thermal loadings symmetrically acting on the crack surface. In view of the symmetric condition, the original problem is transformed into a mixed boundary value problem of a half space. By means of the general solutions conjugated with the generalized potential theory method, the problem is exactly solved and the corresponding Green's functions are derived, for the first time. Complete and exact fundamental solutions are expressed in terms of elementary functions. The singular behavior of the crack tip is discussed and the stress intensity factor is given explicitly.