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研究生： 陳宜暄
Yi-Hsuan Chen
論文名稱： 四邊形塗層孔洞承受均勻熱流之應力分析
Stress Analysis of a Coated Square Hole Subject to a Remote Uniform Heat Flow
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： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 58
中文關鍵詞： 交替法 、熱流 、四邊形塗層孔洞 、保角映射法
外文關鍵詞： alternating technique, heat flow, coated square hole, conformal mapping
相關次數： 點閱：250  下載：2 
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    • 在熱彈性線性理論的框架下，本文為含有四邊形塗層孔洞的無窮平板承受遠端均勻熱流之熱應力問題提供解析解。利用保角映射法將塗層四邊形轉換為圓形界面的異質問題，再經由解析連續法及交替法計算出所需的函數。由於此研究為受遠端均勻熱流之應力分析，首先須利用交替法及解析連續條件求得溫度場，再
    以 Muskhelishvili 等向性二維彈性力學基本公式為基礎，藉由輔助應力函數 w 來簡化求解過程，同樣使用交替法及解析連續條件求得應力場。利用應力公式可計算出邊界上之正向應力與切向應力，並探討改變異質材料參數對於應力的影響。本研究界面應力的數值計算使用 MATLAB R2014a 軟體作為計算工具，以及使用有限元素法 COMSOL 軟體作為驗證工具。

    Within the framework of the linear theory of thermoelasticity, this article provides an analytical solution for thermal stress problem of a coated square hole embedded in an infinite isotropic medium under a remote uniform heat flow. Based upon the technique of conformal mapping and the method of analytical continuation, the series solutions for both the temperature and stress functions are obtained in terms of a homogenous potential function. Numerical results for interfacial stresses between the coated layer and the matrix due to the application of a remote uniform heat flow are provided in graphic form to elucidate the effect of material property and geometric configuration. Comparison of the present results with finite element method shows that our derived solutions are exact. This study will be helpful in understanding of an optimum design for a square coated hole under a remote uniform heat flow.

    中文摘要 ABSTRACT Table of Contents List of Figure List of Table Nomenclature Chapter 1 Introduction 1.1 Research motivation 1.2 Literature study 1.3 Research method Chapter 2 Problem formulation 2.1 Two-dimensional isotropic thermoelasticity theory 2.2 Temperature potential function 2.3 Mapping function 2.4 Auxiliary stress function 2.5 Analytic functions 2.6 Analytic continuation theorem 2.7 Interfacial stresses Chapter 3 Temperature field solution 3.1 Problem description 3.2 Derivation of temperature field Chapter 4 Stress field solution 4.1 Problem description 4.2 Derivation of temperature field 4.3 Numerical solution Chapter 5 Finite Element Method 5.1 Modeling 5.2 Material parameters and grid pattern 5.3 Boundary conditions 5.4 Post processing Chapter 6 Result and discussion 6.1 Result of temperature field 6.1.1 Analysis result of temperature field analytical solution 6.1.2 Verification of temperature field by finite element analysis 6.2 Result of interfacial stresses 6.2.1 Verification result of interfacial stresses 6.2.2 Analytical solution of interfacial stresses 6.3 Convergence analysis 6.4 Discussion of the result Chapter 7 Conclusion and future research 7.1 Conclusion 7.2 Future research References Appendix-A Appendix-B Appendix-C

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