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研究生:李威穎
研究生(外文):Wei-Ying Li
論文名稱:四邊形塗層孔洞承受差排之應力分析
論文名稱(外文):Stress Analysis of a Coated Square Hole Subject to an Edge Dislocation
指導教授:趙振綱
指導教授(外文):Ching-Kong Chao
口試委員:應宜雄黃榮芳
口試委員(外文):Yi-Shyong IngRong-Fung Huang
口試日期:2019-07-04
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:2019
畢業學年度:107
語文別:英文
論文頁數:61
中文關鍵詞:交替法四邊形塗層孔洞保角映射法
外文關鍵詞:Alternating techniqueCoated square holeConformal mapping
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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
A. K. Head, "The Interaction of Dislocations and Boundaries," Philosophical Magazine, vol. 44, pp. 92-94, 1953.
J. Dundurs and T. Mura, "Interaction between an edge dislocation and a circular inclusion," Journal of the Mechanics and Physics of Solids, vol. 12, pp. 177-189, 1964.
L. Stangni and R. Lizzio, "Shape effects in the interaction between an edge dislocation and an elliptical inhomogeneity," Applied Physics A, vol. 30, pp. 217-221, 1983.
L. Stagni, "Edge dislocation near an elliptic inhomogeneity with either an adhering or a slipping interface," Pilosophical Magazine A, vol. 68, pp. 49-57, 1993.
W. E. Warren, "The edge dislocation inside an elliptical inclusion," Mechanics of Materials, vol. 2, pp. 319-330, 1983.
Z. M. Xiao and B. J. Chen, "On the interaction between an edge dislocation and a coated inclusion," International Journal of Solids and Structures, vol. 38, pp. 2533-2548, 2001.
F. M. Chen, "Edge dislocation interacting with a nonuniformly coated circular inclusion," Archive of Applied Mechanics, vol. 81, pp. 1117-1128, 2011.
H. A. Luo and Y. Chen, "An edge dislocation in a three-phase composite cylinder model," ASME Journal of Applied Mechanics, vol. 58, pp. 75-86, 1991.
C. K. Chao, F. M. Chen and M. H. Shen, "Circularly cylindrical layered media in plane elasticity," International Journal of Solids and Structures, vol. 43, pp. 4739-4756, 2006.
S. X. Gong and S. A. Meguid, "A screw dislocation interacting with an elastic elliptical inhomogeneity," International Journal of Engineering Science, vol. 32, pp. 1221-1228, 1994.
M. H. Santare and L. M. Keer, "Interaction between an edge dislocation and a rigid elliptical inclusion," ASME Journal of Applied Mechanics, vol. 53, pp. 382-385, 1986.
C. K. Chao, L. M. Lu, C. K. Chen and F. M. Chen, "Analytical solution for a reinforcement layer bonded to an elliptic hole under a remote uniform load," International Journal of Solids and Structures, vol. 46, pp. 2959-2965, 2009.
C. K. Chao, C. K. Chen, F. M. Chen and M. A. Korsunsky, "Green’s function for a coated elliptic hole problem in plane elasticity," International Journal of Theoretical and Applied Multiscale Mechanics, vol. 1, pp. 281-307, 2010.
F. M. Chen, C. K. Chao and C. K. Chen, "Interaction of an edge dislocation with a coated elliptic inclusion," International Journal of Solids and Structures, vol. 48, pp. 1451-1465, 2011.
J. C. Luo and C. F. Gao, "Stress field of a coated arbitrary shape inclusion," Meccanica, vol. 46, pp. 1055-1071, 2011.
C. K. Chao and M. H. Shen, "On bonded circular inclusions in plane thermoelasticity," ASME Journal of Applied Mechanics, vol. 64, pp. 1000-1004, 1997.
J. Q. Tarn and Y. M. Wang, "Thermal stresses in anisotropic bodies with a hole or a rigid inclusion," Journal of Thermal Stresses, vol. 16, pp. 455-471, 1993.
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