Using the method of the boundary integral equation, a set of singular integral equations of the heat transfer problems and the thermo_elastic problems of a crack embedded in a two_dimensional finite body is derived, and then its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main_part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples are calculated.
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