# 臺灣博碩士論文加值系統

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 基於二維等向性反平面之彈線性理論及複變理論的框架下，本文主旨在求解塗層多邊形孔洞受到無窮剪應力之應力強度因子解析，並對基材上的裂紋產生何種影響及變化進行討論。透過保角映射法將塗層孔洞轉換成同心圓孔洞，可將物理平面轉換至為數學平面，再利用解析連續以及交替法等方法計算出所需函數。研究中藉由界面上應力連續以及位移連續之條件，使用交替法反覆疊代求得完整之應力場級數解。再利用未定係數插植公式、疊加法滿足其沿著裂紋之差排分佈及表面無曳引力條件下，對應力勢能函數透過Gauss-Chebyshev數值積分求得差排密度，繼而求得應力強度因子。最後探討不同剪力模數、形狀因子及塗層形狀對應力強度因子之影響以了解塗層特性對含裂紋孔洞彈性體之整體穩定度評。
 Based on two-dimensional isotropic anti-plane elasticity and complex variable theory, a general analytical solution to a coated arbitrary shape hole interacted with a crack embedded in an infinite matrix under a remote uniform shear load is provided in this article. According to the approach of conformal mapping and the method of analytical continuation theorem in conjunction with alternating technique, a convergent series solution in the reinforcement layer and the matrix for both the displacement and stress functions is expressed in terms of the corresponding homogeneous complex potential. By using the superposition method, a singular integral equation (SIE) satisfying the traction-free condition along the crack surface is then established. The effects of material properties and geometric configurations of a coating layer on the mode-III stress intensity factors (SIFs) are discussed in detail and shown in graphic form.
 中文摘要 IABSTRACT II致謝 IIIList of figures VIList of tables XIExplanation of Symbols XIIChapter 1 Introduction 11.1 Research motivation 11.2 Literature review 11.3 Research method 4Chapter 2 Problem formulation 52.1 Stress potential energy function 52.2 Mapping function 62.3 Analytic functions 72.4 Analytic continuation theorem 72.5 The interpolation formula 82.6 Stress intensity factors 9Chapter 3 Stress field solution 153.1 Problem Description 153.2 Derivation of stress field 15Chapter 4 Numerical solution 204.1 The singular integration 204.2 Superposition 204.3 The superposition of the crack in the matrix 214.4 Single value condition 214.5 The flow chart 23Chapter 5. Results and discussion 245.1 Results of stress field 245.2 A coated arbitrary shape hole with a crack in the matrix 245.2.1 Convergence analysis 245.2.2 The SIFs with the different iteration steps 265.2.3 The SIFs with the different shear moduli 265.2.4 The SIFs with the different shape factors 285.2.5 The SIFs with the different radii 285.3 In comparison with different coated arbitrary shape holes 29 Chapter 6 Conclusion and future prospects 576.1 Conclusion 576.2 Future prospects 58References 59
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 1 多邊形塗層孔洞承受點熱源之熱應力分析 2 邊界積分方程中雙退化機制在反平面問題之研究 3 四邊形塗層孔洞承受均勻熱流之應力分析 4 四邊形塗層孔洞承受差排之應力分析 5 塗層三角形孔洞之熱彈性分析 6 任意傾斜多裂縫受反平面動態載重之暫態分析 7 纖維狀複合材料受遠端均勻剪應力作用下之模態三應力強度因子 8 兩相異圓形異質與裂紋交互作用之平面彈性問題解析 9 含披覆層橢圓孔洞與裂紋交互作用之反平面彈性問題解析 10 表面裂縫與螺旋差排之間的交互作用

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