本論文主要在推導塗層三角形孔洞受遠域均勻應力作用之彈性場通解。首先，利用保角映射法先將塗層三角形轉換成圓形界面的異質問題，將實際求解之物理平面轉換至數學平面以利求解，使用Muskhelishvili二維平面等向彈性力學理論為基礎，藉由適當的定義輔助應力函數 簡化求解過程，再來使用複變函數理論並結合解析連續法與交替技巧，即可求得在複合材料系統下受無窮遠處均勻應力作用下之全場應力函數之級數解，經由上述之方法了解塗層之特性可以以此特性設計三角形複合材料，有助於提高複合材料的界面強度。本研究界面應力之數值計算使用MATLAB R2015b軟體作為本文計算工具，以及使用有限元數法ANSYS (APDL 15.0)作為驗證工具。

This study presents plane elasticity problems of a triangle coated hole embedded in an infinite plane subjected to a remote infinite uniform load. Based on the method of analytical continuation in conjunction with the alternating technique and the technique of conformal mapping, both the displacements and stresses are derived explicitly in terms of the Muskhelishvili complex potential functions. Through the above method, we found that the presence of a coating layer can effectively reduce the interfacial stress by properly selecting the material constant. The interfacial stresses are calculated by using MATLAB R2015b software and the finite element method ANSYS (APDL 15.0) to verify the numerical solution.

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