臺灣博碩士論文加值系統

近年來所發展之高性能複材，常採用全異向物性材料作為加強結構之方法。而在分析超薄物件時，最常見的問題便是內部熱傳導問題。邊界元素法分析超薄物件內之熱傳時，由於源點太靠近被積函數(D>>L)(圖1.4)，熱傳導之邊界積分式會產生近似奇異積分現象。過去文獻中，邊界元素法已運用分部積分將積分式正規化，以解決二維熱傳導問題。而三維熱傳導問題，在本篇論文將以參考文獻【16】之理論，將近似奇異積分視為瑕積分，以非線性轉換的方式處理被積函數奇異性的問題。此法的好處，可同時解決奇異積分以及近似奇異積分的問題。本研究以MathCAD為驗證工具，將界元素法之FORTRAN程式碼連結由Ian Robinson & Michael Hill【16】兩位學者所撰寫之C++程式碼，用以分析介質內部接近邊界之溫度場分佈。此外，為驗證分析結果之正確，並採用有限元素法之套裝軟體ANSYS做分析比對。

In recent years, generally anisotropic materials have been extensively applied to reinforce the strength of structures. The common problem is the treatment of the thermal field in thin structures. When analyzing the thermal field inside thin media, the boundary element method shall have a problem of “nearly singular integral” due to the source point too that are too close to the boundary. In the past, the scheme of integration by parts has been applied for regularizing the integrands for the problem of 2D heat conduction. For the 3D anisotropic heat conduction, this thesis employs the scheme developed by Robinson and Hill【16】using nonlinear transformation to resolve the problem of nearly singular integral, treated as an improper integral. An additional advantage of such an approach is that the scheme also applies to evaluating singular integrals when the source point lies on the element under integration. With verification by MathCAD, this thesis proposes a methodology analyzing the thermal field near the boundary of an 3D anisotropic medium by linking the FORTRAN program of BEM with the C++ code developed by Robinson and Hill【16】. Also, for further verification of the BEM results, the sample problems have been analyzed by means of ANSYS for comparison.

目錄
致謝 I
摘要 II
目錄 IV
圖目錄 VI
表目錄 IX
第一章 導論 1
1.1 前言 1
1.2 研究動機 2
1.3 文獻回顧 3
第二章 理論回顧 9
2.1 3-D 多域異向熱傳導理論 9
2.2 BEM 之映射域論述 14
2.3 r2d2lri：二維立方體全自動計算方法 18
第三章 邊界溫度場與溫度梯度之邊界積分 21
3.1 溫度平面與曲線元素邊界積分式 21
3.1.1溫度平面元素邊界積分式 31
3.1.2 溫度曲面元素邊界積分式 33
3.2溫度梯度平面與曲面元素邊界積分式 35
第四章 內部溫度場與溫度梯度之邊界積分整理 41
4.1 內部溫度邊界積分整理 41
4.2 內部溫度梯度邊界積分整理 48
第五章 數值範例 55
5.1 範例一 熱傳之統御方程式-驗證平面元素奇異性現象 55
5.2 範例二 熱傳之統御方程式-驗證曲面元素奇異性現象 61
5.3 範例三 67
5.4 範例四 69
第六章 結論與未來展望 121
參考文獻 123

參考文獻
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