臺灣博碩士論文加值系統

本論文提供一等向性或異向性材料無窮平板含界面部份嵌入物之橢圓孔洞其承受無窮遠均勻熱流作用下之解析解。首先求解等向性材料時，可利用複變函數的解析連續性質來滿足界面的連續條件並以保角轉換之技巧為基礎，接著以希爾伯特問題的推導將界面嵌入物上的邊界條件表成柯西奇異積分並配合留數定理求得積分值即完成解析解，此溫度與應力之全場解可由簡潔之複數形式表示，受無窮遠熱流作用影響，洞上部份嵌入物之旋轉角可藉由材料特性、幾何特性與作用力大小來決定。最後，將各應力分佈、應力強度因子求出並以圖形展示出。其次求解異向性材料時以史磋公式為基礎，並引用解析連續方法來求解二維異向性彈性體在橢圓邊界上的混合型邊界值問題。另外也應用保角轉換來處理曲線邊界問題，最後我們將所得的解析解化為等向性材料問題之解，以驗證其正確性。此外，界面上之應力數值結果也以圖例方式來輔助說明上述問題的物理行為。

This paper provides an analytical exact closed-form solution for a partially reinforced elliptic hole embedded in an infinite isotropic or anisotropic medium under a remote uniform heat flow. Based on the method of analytical continuation which can staisfy the boundary conditions and the technique of conformal mapping, the full field solutions for the temperature and stresses are obtained in compact complex form. The rotation angle of a reinforced portion on the hole due to the application of a remote uniform heat flow is determined analytically which is dependent of the material property, geometric configuration and the magnitude of applied loading. Comparison of the present results with the existing ones shows that our derived solutions are exact and general. Finally, in order to check answer correctness the stress functions corresponding to anisotropic problems are successfully reduced to those corresponding to isotropic problems. Some numerical results are carried out and shown in graphic form to illustrate the physic behavior of the present problem.

中文摘要 ……………………………………………………………….….I
英文摘要 …………………………………………………………………..II
誌謝 ..….…………………………………………………………………...III
目錄 ..….…………………………………………………………………..IV
圖表索引 …..……………………………………………………….……...VII
符號索引 …………………………………………………………….……IX
第一章 緒 論 ....…………………………………………………….….…1
1.1 前言 ..……………………………………………………………...1
1.2 文獻回顧 .………………………………………………………….2
1.3 本文作法.…………………………………………………………..4
第二章 等向性熱彈性問題之求解………………………………………...6
2.1 基本方程式 ………………………………………………………..6
2.1.1 保角轉換…………….……………………………….………..7
2.1.2 無窮平板含絕熱橢圓洞之溫度函數 …………………………7
2.2 等向性熱應力函數求解 .………………………………………….9
2.2.1 基本方程式….……………………………….……………….9
2.2.2 混合邊界值問題…….……………………………….………..11
第三章 異向性熱彈性力學理論基礎 ……………………………………..24
3.1 Stroh公式之概述………………………………………………….24
3.2 恆等式……………………....……………………………………..28
第四章 異向性熱彈性問題求解……………………………….…………..30
4.1 前言 ……………………………………………………………...30
4.2 溫度函數推導 ……………………………………………………30
4.2.1 保角轉換 ……………………….…………………………...31
4.2.2 異向性無窮平板含絕熱橢圓洞之溫度場…….………….…..32
4.3 熱應力函數 ………………………………………….…………..34
4.4 界面應力 ………………………………………………….……51
第五章 數值解與討論………………………………………….………….55
5.1 應力強度因子之探討……………………………………………..55
5.2 熱應力分佈探討…………………………………………..……...56
5.3 嵌入物之旋轉角………………………………………….………57
第六章 結 論………………………………………….…………….…….68
6.1 結 論……………………………………………………………..68
6.2 未來展望 ………………………………………………………..70
參考文獻 ………………………………………………………………….71
附錄A ……………………………………………………………….…….74
附錄B ………………………………………………………………….….76
作者簡介 ………………………………………………………………….82

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