A general solution in terms of the Stroh-type formalism for quasicrystals is developed for two-dimensional thermoelastic deformation. The solution is then applied to analyze the deformation of a conductive elliptic hole embedded in the decagonal quasicrystal plane which is under a remotely uniform heat flow. The hoop stresses around the elliptic hole are derived in an exact closed form. When the thermal conductivity inside the hole is neglected, the present results are reduced to the existing solutions in the literature. Some numerical examples are provided to show the effects of the geometrical shape of the hole and the thermal conductivity inside the hole on the hoop stresses. The results show that along the hole the variations of the hoop stress of the phonon field are completely different from those of the phason field. Compared to the corresponding insulated case, consideration of a conductive elliptic hole would lead to very different and interesting thermoelastic behaviors.
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