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研究生:吳承峰
研究生(外文):Cheng-FengWu
論文名稱:三維邊界元素法探討異向性岩石內圓形裂縫之應力強度因子
論文名稱(外文):Determination of the SIFs of Circular Cracks in Anisotropic Rocks Using 3D BEM
指導教授:陳昭旭陳昭旭引用關係
指導教授(外文):Chao-Hsu Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資源工程學系碩博士班
學門:工程學門
學類:材料工程學類
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:119
中文關鍵詞:異向性岩石應力強度因子單圓裂縫雙圓裂縫邊界元素法裂縫前緣9節點單邊弧形元素
外文關鍵詞:anisotropic rockstress intensity factor (SIF)single/dual -crackboundary element methodcrack frontnine-node unilateral curved elements
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本研究的目的為將特殊九節點四邊形元素應用在離散未開裂邊界以及九節點單邊弧形元素應用在異向性岩石性質的矩形體中的雙/單圓裂縫,使用Fortran語言撰寫程式,利用三維單域邊界元素法(或稱對偶邊界元素法)探討三維情況下異向性岩石的混合模態應力強度因子。
本文中使用了特殊的9節點單邊弧形元素,克服了邊界為弧形的圓形裂縫,在邊界利用此元素排列不僅大大減少了元素的數目,更使程式運算快速有效率。元素敏感度分析找出CN(Crack Front Number)=32、EN(Element Number)=48的排列方式,此排列方式與前人解析解作數值驗證,相當吻合結果。
在本文中,針對異向性岩石性質的矩形體單、雙圓裂縫試體,模擬在受到垂直張力加載情況下,觀察應力強度因子之趨勢。單圓裂縫下探討裂縫在不同垂直高度以及水平距離時應力強度因子變化,在深入探討在不同層面角度以及異向性程度(E/E')改變狀況下的趨勢;雙圓裂縫探討水平雙裂縫-垂直間距及水平間距時應力強度因子的變化,在深入探討在不同層面傾角以及異向性程度(E/E')改變狀況下的趨勢,以及針對雙同斜和雙異斜裂縫於不同層面傾角的變化趨勢。

The purpose of this study is to present the nine-node quadrilateral elements to discretize the un-cracked boundary and the nine-node curved elements to discretize dual/single circular-crack in an anisotropic cuboid rocks. The Fortran program developed is to determine the three-dimensional(3D) mixed–mode stress intensity factors(SIFs) by using 3D single-domain boundary element method(BEM) or dual-BEM.
In order to overcome the curved boundary of circular crack, using a special nine-node unilateral curved elements. The use of this element is arranged not only greatly reduce the number of elements, the program operator to quickly and efficiently. In element sensitivity analysis to identify CN (Crack Front Number)= 32, EN(Element Number) = 48 arrangement which is with the previous analytic resolution as a numerical verification and fairly consistent results.
In this article, we observe the trend of the stress intensity factor that single, dual circular-crack in an anisotropic rock on vertical tension loading. In single circular-crack, It discusses the change of stress intensity factor on cracks in the vertical height and horizontal distance, and then observe the trend in different orientation angle and anisotropy(E/E'). In dual circular-crack, It discusses the change of stress intensity factor on cracks in the vertical and horizontal spacing, and then observe the trend in different orientation angle and anisotropy(E/E').

目錄
摘要 I
ABSTRACT II
誌謝 III
表目錄 VII
圖目錄 VIII
符號表 XIV
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究內容 5
第二章 文獻回顧 8
2.1 破壞力學 8
2.2 邊界元素法 11
2.3 應力強度因子 17
2.4 圓形裂縫 23
2.5 小結 25
第三章 理論模式 26
3.1 材料座標系統和基本方程式 26
3.2 異向性彈性體之基本解 29
3.3 邊界積分方程式 30
3.4 數值離散 32
3.5 應力強度因子 37
第四章 數值驗證 39
4.1均佈載重 39
4.1.1 不同層面角度的位移量,不同深度位移與應力情形 39
4.1.2 均佈垂直載重與重力下,不同層面角度位移情形 41
4.2 裂縫元素敏感度分析 43
4.3 矩形元素與單邊弧形元素 49
4.4 半無限邊域內之試體內圓裂縫 54
4.5 小結 55
第五章 案例分析 57
5.1矩形體內部圓裂縫 57
5.1.1 裂縫在不同垂直距離 57
5.1.2 裂縫在不同水平距離 62
5.1.3 內部裂縫在不同材料層面傾角 66
5.2矩形體內部雙圓裂縫 78
5.2.1 水平雙圓裂縫-垂直間距 78
5.2.2 水平雙圓裂縫-水平間距 84
5.2.3 雙水平圓裂縫不同材料層面傾角 89
5.2.4 雙垂直圓裂縫不同材料層面傾角 91
5.2.5 雙同斜圓裂縫不同材料層面傾角 94
5.2.6 雙異斜圓裂縫不同材料層面角度 97
第六章 結論與建議 101
6.1 結論 101
6.2 建議 103
參考文獻 104
附錄A 116

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