本論文主要是探討差排對四邊形塗層孔洞之影響。首先，利用保角映射法先將四邊形異質轉換成圓形界面的異質問題，這個步驟會將物理平面傳換到數學平面，並使用Muskhelishvili二維平面等向彈性力學理論，且定義輔助應力函數 來簡化過程，使用複變函數理論、解析連續法及交替法來求得塗層材料在差排影響中的全場應力函數級數解，經由此方法可以得知塗層四邊形中的應力分布，進而提升材料介面的強度。本研究界面應力之數值計算使用MATLAB R2014a軟體作為本文計算工具，以及使用有限元素法COMSOL作為驗證工具。

This study mainly investigates the interaction between a coated square hole and an edge dislocation. Based on the analytical continuation theorem and the alternating technique in conjunction with the method of conformal mapping, a series solution of both the displacement and stresses is derived in terms of a homogeneous potential function. The force on the dislocation is also calculated. Examples for various coating thickness and material constant combinations are given and discussed.

中文摘要 I
ABSTRACT II
致謝 III
Nomenclature 1
Chapter 1 Introduction 2
1.1 Background 2
1.2 Literature study 2
1.3 Method 4
Chapter 2 Basic equations 5
2.1 Two-dimensional isotropic elasticity theory 5
2.2 Conformal mapping method 5
2.3 Analytical continuation 6
2.3.1 Analytical continuation theorem 6
2.3.2 Analytic functions 6
2.4 Stress calculation formula 7
Chapter 3 Stress field 12
3.1 Problem statement 12
3.2 Stress field function derivation 12
Chapter 4 Finite element method 21
4.1 Model establishment 21
4.2 Material parameters setting 21
4.3 Boundary conditions setting 21
Chapter 5 Numerical results 24
5.1 Image force 24
5.2 The results of dislocation on the x-axis 25
Chapter 6 Conclusions 41
Chapter 7 Future prospects 43
References 44
Appendix A 46
Appendix B 50

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