本文主要求解受到均勻分布熱流作用於含有塗層三角形孔洞之無窮平板的問題，並計算孔洞邊界正向應力與切向應力。利用保角映射法將塗層三角形孔洞問題轉換成同心圓孔洞問題，由物理平面轉換至數學平面，再藉由解析連續以及交替法等方法，計算所需函數。為了計算塗層三角形孔洞邊界之應力，必須先取得整體溫度場分布，藉由邊界上的溫度連續以及熱流連續等條件，利用交替法反覆疊代求得整體溫度場，再引入應力函數運算。研究中根據Muskhelishvili等向性二維彈性力學基本公式，藉由邊界上的應力連續以及位移連續等條件，同樣利用交替法計算求得應力場，其中利用到輔助函數，用途為簡化計算。已知應力函數後，藉由應力公式計算邊界上正向應力以及切向應力，探討改變材料參數對於應力之影響。

This study presents thermoelasticity problem of a coated triangular hole embedded in an infinite matrix subjected to uniform heat flow. Using the technique of conformal mapping, analytical continuation in conjunction with alternating technique, a convergent series solution is derived in a compact form. The complex functions are solved by satisfying the continuity conditions of heat flow, temperature, displacements and traction forces across the interface between two different materials. Calculating interfacial stresses by using MATLAB. Using COMSOL to check the numerical analysis results. The effect of shear modulus and thermal expansion coefficients on the interfacial stress are discussed. The results show that both interfacial normal stresses and interfacial shear stresses increase with increasing the different of shear modulus and thermal expansion coefficients between the matrix and a coated layer.

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