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研究生:李政錡
研究生(外文):Chen-ChiLi
論文名稱:多孔洞異向性板之邊界元素設計
論文名稱(外文):Boundary Element Design for Multiple Holes in Anisotropic Plates
指導教授:胡潛濱
指導教授(外文):Chyan-Bin Hwu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:60
中文關鍵詞:異向性孔洞邊界元素法組合區域法
外文關鍵詞:AnisotropicHolesBEMSubregions
相關次數:
  • 被引用被引用:2
  • 點閱點閱:119
  • 評分評分:
  • 下載下載:12
  • 收藏至我的研究室書目清單書目收藏:0
針對異向性平板含有不同形狀之孔洞問題,本研究利用多邊形孔洞之基本解配合邊界元素法與組合區域法,來解析平板的應力場以及位移場。以往多孔洞之研究大多為橢圓形孔洞居多,因幾何形狀受到限制使得能探討的問題不夠廣泛,因此本研究將孔洞形狀推廣為任意多邊形包含裂縫、圓洞、橢圓洞、三角形洞等等,並且配合組合區域法,使得介面上結點之位移與應力連續,來探討平板中多孔洞同時存在對彼此的影響。
由於基本解已滿足孔洞的邊界條件,無須在孔洞邊界取元素,而且基本解是以多邊形為基礎,對於不同形狀只須改變形狀參數即可。因此,本研究以多邊形孔洞之基本解為出發點,解析更為廣泛的多孔洞問題。

With respect to the problems of anisotropic plates containing multiple various holes, this research solves the stress and strain fields numerically by embedding the fundamental solutions of polygonal holes into boundary element method(BEM), and using the technique of subregion. In the literature, most of the examples of multi-holes consider elliptical holes due to the geometry restraints, it limits the range of the problems. In this study we like to extend the hole shape to the general polygon-like shapes.
Since the fundamental solutions have satisfied the boundary condition for holes, it’s unnecessary to discretize the hole boundary. Since, the fundamental solutions are for the polygon-like holes, their associated BEM would be able to solve multi-holes much more effectively and generally.

中文摘要
英文摘要
致謝
目錄 i
表目錄 iv
圖目錄 v
符號說明 vii
第一章 緒論 1
1.1前言 1
1.2研究動機 1
1.3研究目的 4
第二章 孔洞問題 5
2.1 史磋公式(Stroh Formalism) 5
2.2 多邊形孔洞受均佈拉伸問題 6
2.3 多邊形孔洞之映射值選取 7
2.3.1 映射問題 7
2.3.2 映射值選取 8
第三章 邊界元素法 13
3.1邊界積分方程式 13
3.2基本解 17
3.3內部之應力 18
3.4組合區域法與座標轉換 21
3.4.1組合區域法 21
3.4.2 座標轉換 22
3.5程式之建立 23
第四章 結果與討論 25
4.1含單一孔洞之平板數值驗證 25
4.1.1 含單一圓形孔洞之平板 26
4.1.2 含單一三角形孔洞之平板 26
4.1.3 含單一四邊形孔洞之平板 26
4.2含多孔洞之邊界元素分析 27
4.2.1 兩個相同的圓形洞 27
4.2.2 兩個相同的三角形洞 27
4.2.3 兩個相同的四邊形洞 28
4.3含多圓洞之邊界元素分析 28
4.3.1 一橢圓孔洞與兩對稱之圓洞 29
4.3.2 四個相同圓洞 32
第五章 結論 36
參考文獻 37
附圖 42
附表 56


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