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A boundary element formulation for the analysis of two-dimensional and three-dimensional steady state thermo-elastic problems involving arbitrary non-uniform heat sources is presented. All domain integrals are expressed in terms of a heat source function instead of a temperature function. The proposed method alleviates the difficulty associated with finding the temperature distribution throughout the domain. A simple, yet robust, method referred to as the Cartesian transformation method (CTM) is developed that allows boundary-only evaluation of domain integrals. Unlike other transformation methods the CTM does not require the introduction of a domain point for the transformation. Domain heat sources defined either over the whole domain or over a specific part of the domain can be treated by the proposed method. Three examples including different forms of heat sources are analysed to show the validity and efficiency of the presented methods.

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