臺灣博碩士論文加值系統

在邊界元法的研究中，暫態熱問題已被廣泛應用於等向性材料進行討論，甚至有人使用於非線性熱傳導分析。但目前較少有人研究全異向性材料的暫態熱傳導，本文使用於亥姆霍茲方程式定義下的暫態基礎解分析，可以有效準確的求解暫態熱傳導分析，並加入用夏育群博士所提出的映像法，可以由異向性熱傳導係數來定義新的映像區域，並將在新的座標系下求解的溫度解，映像回原本的座標，來達到異向性熱傳導分析的目的，在將兩個方法合併來求解暫態異向性熱傳導，並比較有限元素方法。

Despite the extensive study of the transient thermal conduction analysis for isotropic media by the boundary element method, its relevant researches in anisotropic transient heat conduction still remain extremely scarce indeed. In the thesis, the author applies the time-stepping scheme [2] for the transient effect and also the domain mapping scheme proposed by Shiah and Tan [4] to treat the anisotropy. For the transient analysis, the fundamental solution of the Helmholz equation is applied. For the domain mapping scheme, coordinates of the boundary are transformed to a new coordinate system by the anisotropic heat conductivities, where the transformed domain is considered to have equivalent isotropic heat conduction. Thus, the anisotropic thermal field in the original domain can be directly obtained via solving the corresponding isotropic one in the distorted domain. For the present boundary element analysis, the both schemes are jointly applied to solve for the problem of transient heat conduction in anisotropic media. In the end, a few benchmark examples are studied by the proposed schemes and the results are compared with finite element analysis.

中文摘要 I
英文摘要 II
誌謝 VIII
圖目錄 XI
表目錄 XV
⻣符號說明 XVI
第一章 1
導論 1
1.2研究動機 1
1.3文獻回顧 2
1.4研究流程與內容簡介 3
第二章 理論回顧 4
2.1勢能理論 4
2.2格林定理 5
2.3泊松方程式 7
2.4邊界積分式 9
2.5映像法 11
第三章 暫態異向性熱傳導分析 15
3.1二維暫態熱傳導之基礎解推導 15
3.2邊界網格化 19
第四章節 數值範例 22
4.1解題步驟 22
4.2暫態矩形等向性熱傳導 22
4.3暫態中空圓形等向性熱傳導 23
4.4異向二維矩形穩態異向性熱傳導之邊界元素法分析 24
4.5異向二維中空矩形穩態異向性熱傳導之邊界元素法分析 24
4.6異向二維中空圓形穩態異向性熱傳導之邊界元素法分析 25
4.7異向二維矩形暫態異向性熱傳導之邊界元素法分析 25
4.8異向二維中空矩形暫態異向性熱傳導之邊界元素法分析 26
4.9二維中空圓形暫態異向性熱傳導之邊界元素法分析 27
第五章節 結果與未來展望 28
參考文獻 29

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