In this paper, we present Green's functions for a two-phase transversely isotropic elastic solid due to a steady heat source in the lower half-spae. The functions of displacements and stresses are derived in closed forms, which include the special cases such as the case for an infinite transversely isotropic elastic solid with a steady heat source and the case for a semi-infinite transversely isotropic elastic solid with a steady heat source. Furthermore, numerical results for magnesium-titanium composite are given.

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