多邊形塗層孔洞承受點熱源之熱應力分析｜國立臺灣科技大學博碩士論文系統

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研究生：	邱唯家 Wei-Chia Chiu
論文名稱：	多邊形塗層孔洞承受點熱源之熱應力分析 Thermal Stress Analysis of a Coated Arbitrary Shape Hole Subject to a Point Heat Source
指導教授：	趙振綱 Ching-Kong Chao
口試委員:	陳明志 Ming-Jyh CHERN 陳富謀 FU-MOU CHEN 趙振綱 Ching-Kong Chao
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：	120
中文關鍵詞：	點熱源、多邊形塗層孔洞、保角映射法
外文關鍵詞：	Coated Arbitrary Shape Hole
相關次數：	點閱：265 下載：6
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上一筆

在熱彈性線性理論的框架下，本文主要在求解塗層多邊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。先利用保角映射法將塗層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出所需函數。為了計算塗層孔洞邊界之應力，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。再將溫度是能函數做積分運算，並應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。

This paper presents an effective method for interfacial stresses induced by a point heat source in an isotropic plate with a reinforced arbitrary shape hole. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with alternating technique, the general expressions of the temperature and stresses in the reinforcement layer and the matrix are derived explicitly in a series form. Numerical results are presented graphically to investigate the effects of the material combination and geometric configuration on the interfacial normal stress and shear stress. It is interesting to see that the nature of intense fluctuation of the interfacial stresses occurs near the corner of a coated hole due to geometric discontinuities around the corner. The solution provided in this work can be treated as a Green’s function that can be used to solve the corresponding problem with a crack embedded in an infinite matrix.

中文摘要    I
ABSTRACT    II
致謝    III
List of figures    VI
List of tables    XII
Explanation of Symbols    XIII
Chapter 1 Introduction    1
1.1    Research motivation    1
1.2    Literature review    1
1.3    Research method    1
Chapter 2 Problem formulation    5
2.1    Two-dimensional isotropic thermoelasticity theory    5
2.2    Temperature potential energy function    5
2.3    Auxiliary stress function    6
2.4    Mapping function    6
2.5    Analytic functions    7
2.6    Analytic continuation theorem    7
2.7    Stress calculation formula    8
Chapter 3 Temperature field solution    13
3.1    Problem Description    13
3.2    Derivation of temperature field    13
Chapter 4 Stress field solution    19
4.1    Problem Description    19
4.2    Derivation of temperature field    19
4.3    Numerical solution    36
Chapter 5. Finite Element Method    37
5.1    Modeling    37
5.2    Material parameters and grid    37
5.3    Boundary conditions    37
5.4    Post processing    38
Chapter 6 Result & Discussion    43
6.1    Result of temperature field    43
6.1.1    Analytical solution of temperature field    43
6.1.2    Verification of temperature field by finite element analysis    44
6.2    Result of interfacial stresses    44
6.2.1    Verification result of interfacial stresses    45
6.2.2    Analytical solution of interfacial stresses    45
6.3    Convergence analysis    47
6.4    Discussion of the result    48
6.4.1    Discussion of temperature field    48
6.4.2    Discussion of stress field    48
Chapter 7 Conclusion and Future prospects    90
7.1    Conclusion    90
7.2    Future prospects    91
References    92
Appendix A    94
Appendix B    100
Appendix C    105


                                

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