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研究生:郭哲源
研究生(外文):Jhe-Yuan Guo
論文名稱:多邊形塗層孔洞承受遠端均勻負載之應力強度因子分析
論文名稱(外文):Mode-III Stress Intensity Factors for a Coated Arbitrary Shape Hole Subject to a Remote Uniform Shear Load
指導教授:趙振綱
指導教授(外文):Ching-Kong Chao
口試委員:黃榮芳張瑞慶
口試委員(外文):Rong-Fung HuangRwei-Ching Chang
口試日期:2021-01-22
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:77
中文關鍵詞:反平面複變理論多邊形塗層孔洞應力強度因子交替法保角映射法
外文關鍵詞:Anti-planeComplex variable theoryA coated arbitrary shape holeStress intensity factorsAlternation techniqueConformal mapping
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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 I
ABSTRACT II
致謝 III
List of figures VI
List of tables XI
Explanation of Symbols XII
Chapter 1 Introduction 1
1.1 Research motivation 1
1.2 Literature review 1
1.3 Research method 4
Chapter 2 Problem formulation 5
2.1 Stress potential energy function 5
2.2 Mapping function 6
2.3 Analytic functions 7
2.4 Analytic continuation theorem 7
2.5 The interpolation formula 8
2.6 Stress intensity factors 9
Chapter 3 Stress field solution 15
3.1 Problem Description 15
3.2 Derivation of stress field 15
Chapter 4 Numerical solution 20
4.1 The singular integration 20
4.2 Superposition 20
4.3 The superposition of the crack in the matrix 21
4.4 Single value condition 21
4.5 The flow chart 23
Chapter 5. Results and discussion 24
5.1 Results of stress field 24
5.2 A coated arbitrary shape hole with a crack in the matrix 24
5.2.1 Convergence analysis 24
5.2.2 The SIFs with the different iteration steps 26
5.2.3 The SIFs with the different shear moduli 26
5.2.4 The SIFs with the different shape factors 28
5.2.5 The SIFs with the different radii 28
5.3 In comparison with different coated arbitrary shape holes 29

Chapter 6 Conclusion and future prospects 57
6.1 Conclusion 57
6.2 Future prospects 58
References 59
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[21] Chao, C. K., & Wikarta, A. (2012). Mode-iii stress intensity factors of a three-phase composite with an eccentric circular inclusion. Computer Modeling in Engineering and Sciences, 84(5), 439.
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[25] Tseng, S. C., Chao, C. K., & Chen, F. M. (2020). Stress Field for a Coated Triangle-Like Hole Problem in Plane Elasticity. Journal of Mechanics, 36(1), 55-72.
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[27] Wang, S., Xing, S., Chen, Z., & Gao, C. (2019). A nanoscale hole of arbitrary shape with surface elasticity. Journal of Elasticity, 136(2), 123-135.
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