本文主要推導含點熱源兩相異圓形異質之彈性場通解，並計算圓邊界正向應力與切向應力。首先利用保角映射法將兩相異圓形異質問題轉換成兩同心圓異質問題，將實際求解之物理平面轉換至數學平面；藉由複變函數理論，結合解析連續法、交替法等技巧，幫助計算所需函數。由於本研究為受一點熱源之應力分析，需先求得整體溫度場，由邊界上的溫度連續及熱流連續，藉由交替法，解析連續條件，反覆疊代得到每一層所屬溫度函數，由循環方程式表示得到整體溫度場。再將溫度場函數代入應力函數運算，根據Muskhelishvili等向性二維彈性力學基本公式，藉由邊界上應力連續及位移連續條件，並定義一輔助應力函數，此輔助應力函數可幫助簡化計算。同樣藉由交替法，解析連續條件，由兩邊界之連續條件不斷地疊代，得到每一層所屬應力函數，再藉由循環方程式表示可得到整體應力場。利用應力公式可計算出圓邊界上之正向應力與切向應力，並探討改變異質材料參數對於應力的影響。

This study presents in-plane elasticity problem of the two bonded circular inclusions subjected to an arbitrary point heat source. Based on the technique of comform mapping and the method of analytical continuation in conjunction with the alternation technique, the temperature, displacements and stresses are in terms of the Muskhelishvili’s complex potentials, such that the continuity conditions of the temperature, heat flow, displacements and result forces are forced to satisfy along the interface. Numerical results of both temperature and stresses are calculated using the programing language to obtain the normal stress and tangential stress. The interaction between a point heat source and circular inclusions is also discussed for different material properties. The effect of the distance between two bonded circular on interfacial stresses is also discussed. The results show that the normal stresses have symmetric characteristics and the tangential stresses have antisymmetric characteristics. It is clear that both the normal stress and shear stress increase with the difference of the shear modulus and thermal expansion coefficients of the neighboring materials.

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