三角形塗層孔洞承受點熱源支應力分析｜國立臺灣科技大學博碩士論文系統

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研究生：	張季婷 Chi-Ting Chang
論文名稱：	三角形塗層孔洞承受點熱源支應力分析 Stress Analysis of a Coated Triangle Hole Subject to a Point Heat Source
指導教授：	趙振綱 Ching-Kong Chao
口試委員:	黃榮芳 Rong-Fung Huang 應宜雄 Yi-Shyong Ing
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	83
中文關鍵詞：	點熱源、三角形塗層孔洞、保角映射法
外文關鍵詞：	Alternating technique, Point heat source, Coated triangle hole, Conformal mapping
相關次數：	點閱：292 下載：11
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本文主要在求解塗層三角形孔洞受到單一點熱源之熱彈性解析，並計算孔洞邊界正向應力與切向應力。利用保角映射法將塗層三角形孔洞轉換成同心圓孔洞意旨由物理平面轉換至數學平面，再藉由解析連續以及交替法等方法，計算所需函數。為了計算塗層三角形孔洞邊界之應力，須先利用邊界上的溫度連續以及熱流連續之條件，取得整體溫度場分布再使用交替法反覆疊代求得整體溫度場即可求得溫度勢能函數，並運用在計算介面應力上。研究中根據 Muskhelishvili等向性二維彈性力學基本公式，藉由邊界上的應力連續以及位移連續之條件，利用交替法計算求得應力場。得到應力函數後，藉由應力公式計算邊界上正向應力以及切向應力，探討改變材料參數對於應力之影響以及了解塗層之特性。

A general analytical solution for thermoelastic response of a coated triangle hole under the application of a point heat source is investigated in this article. This problem is solved by the method of conformal mapping and the analytical continuation theorem. A rapidly convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is solved. Numerical results for temperature contour plot and the interfacial normal and shear stresses along the interface for different shape factors and various material combinations are discussed in detail. The solution obtained can be treated as Green’s function which enables us to calculate an integral equation for a coated triangle hole embedded in an infinite medium with a crack.

中文摘要 I ABSTRACT II 致謝 III List of figures VI List of tables IX Explanation of Symbols X Chapter 1 Introduction 1 1.1 Research motivation 1 1.2 Literature review 1 1.3 Research method 3 Chapter 2 Problem formulation 4 2.1 Two-dimensional isotropic thermoelasticity theory 4 2.2 Temperature potential energy function 4 2.3 Auxiliary stress function 5 2.4 Mapping function 5 2.5 Analytic functions 6 2.6 Analytic continuation theorem 6 2.7 Stress calculation formula 7 Chapter 3 Temperature field solution 11 3.1 Problem Description 11 3.2 Derivation of temperature field 11 Chapter 4 Stress field solution 16 4.1 Problem Description 16 4.2 Derivation of temperature field 16 4.3 Numerical solution 26 Chapter 5. Finite Element Method 27 5.1 Modeling 27 5.2 Material parameters and grid 27 5.3 Boundary conditions 28 5.4 Post processing 28 Chapter 6 Result & Discussion 32 6.1 Result of temperature field 32 6.1.1 Analytical solution of temperature field 32 6.1.2 Verification of temperature field by finite element analysis 33 6.2 Result of interfacial stresses 33
V
6.2.1 Verification result of interfacial stresses ............................................................................ 33 6.2.2 Analytical solution of interfacial stresses ........................................................................ 34 6.3 Convergence analysis .............................................................................................................................................................. 35 6.4 Discussion of the result ........................................................................................................................................................ 36 6.4.1 Discussion of temperature field ...................................................................................................... 36 6.4.2 Discussion of stress field .......................................................................................................................... 36 Chapter 7 Conclusion and Future prospects ................................................................................................................................ 55 7.1 Conclusion .............................................................................................................................................................................................. 55 7.2 Future prospects .............................................................................................................................................................................. 56 References ........................................................................................................................................................................................................................................ 57 Appendix A .................................................................................................................................................................................................................................... 59 Appendix B .................................................................................................................................................................................................................................... 64 Appendix C .................................................................................................................................................................................................................................... 69
                                

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[15] Chao C.K., Chen C.K. and Chen F.M., Analytical exact solutions of heat conduction problems for a three-phase elliptical composite, CMES: Computer Modeling in Engineering & Sciences, vol. 47, pp. 283-298, 2009. [16] Chen F.M. and Chao C.K., Stress analysis of an infinite plate with a coated elliptic hole under a remote uniform heat flow, Journal of Thermal Stresses, vol.31, pp. 599-613, 2008. [17] Chao C.K., Lu L.M., Chen C.K. and Chen F.M., 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. [18] Chao C.K., Chen C.K. and Chen F.M., Interfacial stresses induced by a point heat source in an isotropic plate with a reinforced elliptical hole, Computer Modeling in Engineering & Sciences 63(1): pp. 1-28,2010. [19] Chang Y.C., Thermolelasticity analysis of an infinite plate with a coated triangular hole under a remote uniform heat flow, Master’s Thesis, NTUST, 2018. [20] Shen C.H., Stress Analysis of a Coated Triangle Hole a Remote Uniform Load, Master’s Thesis, NTUST, 2018.

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