臺灣博碩士論文加值系統

利用邊界元素法分析彈性力學問題且一併考慮熱效應對材料的影響時，則其邊界積分式中會產生一體積分項，目前最完善之解仍是將此體積分項完全轉換為面積分項。然而如果集中熱源出現在內部時，此熱源點將導致於分析時產生奇異性，造成數值運算上的困難。在本文中此問題藉由移除奇異點並使用靜偶合之方式得以解決，使其重新將體積分項轉換成面積分項，並加以驗証其結果是否正確。
在許多工程問題上，如主機版上之點焊問題、版金雷射切割…等問題皆屬於點熱源問題，在這些問題的數值模擬上，如果以有限元方式來模擬時會產生許多的問題。以ANSYS模擬為例，由於軟體沒有支援點熱源的設置，因此則必須使用非常精細的網格來模擬點熱源，除了造成網格的切割困難，計算時間也相對提高，這時如果利用邊界元素法來模擬時則可以克服這些問題。除了在建模速度上提升不少，計算時間也大幅的降低許多，針對此類的二維問題的分析使用邊界元素法分析為一項非常有力的工具。
當使用邊界元素法來求解工程問題之邊界值時，雖然於分析時間及效能上較有限元素法為快，但由於邊界元素的前處理邊界模型以及後處理器在目前本實驗室中仍是使用人工處理階段，於建模上及後處理分析上耗時甚多，而本論文中另針對邊界元素法套裝軟體，開發其相關圖形化界面以期使用者可以快速上手且進行分析。

When analyzing elasticity problem in conjunction with the material thermal effect, the boundary integral equation will generate one volume integral and as of now, the most complete solution is to convert the volume integral into surface integral. However, if the concentrated heat source emerges from within, then this heat source will create singularity and subsequently, difficulties in numerical calculations. In this article, the problem was solved by removing the singularity and applying the statically coupled method, reconvert the volume integral into the surface integral and verify the result.

Among many engineering problems, subjects like spot welding of motherboard, metal laser cutting, and many others can all be categorized under the spot heat source, which under the FEM; their data simulations can generate a lot of problems. Take ANSYS simulation as an example, the software is not equipped for supporting the spot heat source and must simulate them with very fine mesh, which in term created problems of difficulties associated with mesh cutting and increased calculation time. On the hand, problems can be resolved if BEM were to be used for simulation, much more efficient model building and greatly reduced calculation time. The BEM can also be a very powerful tool when comes to analysis for this kind of two dimensional problems.

When applying the boundary element method for solving the boundary value in engineering problems, though the analysis is much quicker and efficient, the preprocessing boundary model and the post processor are still manually processed in the lab. It is time consuming building the model and conducting the post processing analysis. In addition, this thesis had also developed a graphic interface for the boundary element method applications to facilitate users’ operation and analysis.

第1章 引言 1
第1.1節 前言 1
第1.2節 研究動機及目的 3
第1.3節 文獻回顧 6
第2章 基本理論 10
第2.1節 前言 10
第2.2節 域映射法 11
第2.3節 分域法 14
第2.4節 體積分之邊界積分轉換 16
第3章 二維異向性熱場之點熱源 28
第4章 二維異向性材點熱源之熱彈性力學 33
第5章 數值範例 46
第5.1節 ANSYS模型分析映射域理論應用 46
第5.2節 範例一：等向性材料圓盤 48
第5.3節 範例二：異向性材料圓盤 49
第5.4節 範例三：異向性材料平板 50
第6章 BEM前處理程式開發 65
第6.1節 程式開發目的 65
第6.2節 程式功能說明 66
第6.3節 模型建構法則 68
第6.4節 模型建構指令說明 69
第6.5節 點熱源設定 74
第6.6節 邊界條件設定 74
第6.7節 視窗功能表 79
第6.8節 材料性質及相關分析參數設定 80
第6.9節 材質資料庫 81
第6.10節 範例說明 82
第6.11節 BEM程式發展說明 91
第7章 結論 92

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