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研究生:劉全益
研究生(外文):Chuan-I Liu
論文名稱:異種非等向性楔形結構之應力奇異性分析
論文名稱(外文):Study of Stress Singularity in Dissimilar Anisotropic Wedges
指導教授:褚晴暉褚晴暉引用關係
指導教授(外文):Ching-Hwei Chue
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:90
語文別:中文
中文關鍵詞:應力奇異性異種楔形結構非等向性複合材料
外文關鍵詞:stress singularity orderdissimilar wedgesanisotropiccomposite
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  • 被引用被引用:1
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  • 收藏至我的研究室書目清單書目收藏:0
本論文以Lekhnitskii複變函數為基礎,分析非等向性楔形結構尖端r (
 Re[  ) 型式之應力奇異性,其中應力奇異性階數 (  1) 與材料
性質、幾何形狀和邊界條件有關。若使用纖維強化複合材料,纖維方向亦會影響
奇異性強弱。
文中探討非等向性單一楔形結構或異種楔形結構其空間中所有纖維方向之應力奇
異性分佈。文中定義空間中之纖維方向,並分別於四分之一圓圖形和全圓圖形以
等高線描述所對應之應力奇異性階數 ()。利用所得的圖形等高線之分
佈,便可直接瞭解最強、最弱、甚至應力奇異性消失之之最佳纖維方向,以作為
安全設計之參考。此外,文中並研究材料係數(楊氏係數、剪力係數)對應力奇異
性的影響。
由於對整體纖維方向與應力奇異性之瞭解,本文發現了一些規律的對稱關係,並
針對面外問題來證明此對稱性,且進一步的得到簡化的面外應力奇異性之特徵方
程式及其解。藉由方程式推導出奇異性消失之條件,以增加結構設計的安全性。
此外,並提出一套『圖解法』來尋找面外應力奇異性與纖維方向之對稱性。
Based on the anisotropic elasticity theory and Lekhnitskii’s complex
potential functions, the r type (  Re[  ) stress
singularities occurring near the apex of anisotropic wedges are
studied. It is known that the stress singularity orders depend on the
wedge angles, edge boundary conditions, composite material properties,
and fiber orientations.
The fiber orientations are defined. For single-wedge problem, a
one-quarter circular region is proposed in which the contours of
singularity order are plotted for all fiber orientation and a certain
wedge angle. For dissimilar wedge problem, a full circular region is
presented, similarly. The numerical results agree well with existing
results for special cases. Some interesting new results for engineering
applications are obtained in this study, such as the disappearance of
stress singularity and fiber orientation corresponding to minimum
singularity order. The effects of the material properties on stress
singularity are also discussed.
For anisotropic dissimilar wedges in antiplane shear, the analytical
eigen-equations of the antiplane stress singularity are derived in very
simple forms. The wedge edges are free and/or clamped. The repeated
occurrence of stress singularity orders will be examined. The
disappearance conditions of the stress singularity are analytically
determined.
摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VIII
圖目錄 X
符號說明 XIX
第一章 緒 論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 等向性材料 2
1.2.2 非等向性材料 4
1.2.3 工程上之應用 8
1.3 研究目的及本文架構 9
第二章 Lekhnitskii複變函數 12
2.1 應力場及位移場 12
2.2 廣義平面應變 22
第三章 單一楔形結構之應力奇異性 26
3.1 特徵方程式 26
3.2 面內與面外非耦合之探討 30
3.3 四分之一圓 32
3.3.1 纖維方向(, )之定義 32
3.3.2 四分之一圓之定義 36
3.4 結果分析 37
3.4.1 任意纖維方向之單一楔形結構 37
3.4.2 裂縫問題 39
3.4.3 等向性問題 39
3.4.4 最弱奇異性之纖維方向(*, *) 40
3.4.5 材料性質之影響 40
第四章 異種楔形結構接合之應力奇異性 57
4.1 特徵方程式 57
4.2 面內與面外非耦合之探討 61
4.3 全圓圖形之定義 63
4.4 結果比較 64
4.4.1 異種等向性楔形 65
4.4.2 纖維落在x-y平面 65
4.4.3 纖維落在y-z平面 65
4.4.4 纖維落在x-z平面 66
4.4.5 界面裂縫 67
4.4.6 退化至單一材料 68
4.5 90-180接合之應力奇異性 68
4.5.1 對稱性之探討 68
4.5.2 最弱奇異性之纖維方向(*, *) 71
4.5.3 材料性質之影響 73
4.6 半平面接合之應力奇異性 77
4.6.1 對稱性之探討 77
4.6.2 範例及應力奇異性消失之探討 79
4.6.3 應力奇異性在複合層板之應用 83
第五章 異種楔形結構面外問題之探討 150
5.1 異種非等向性楔形結構奇異性之特徵方程式 150
5.1.1 自由-自由之邊界條件 154
5.1.2 固定-固定之邊界條件 157
5.1.3 固定-自由之邊界條件 158
5.1.4 自由-固定之邊界條件 159
5.2 含傾斜角k之正交性複材應力奇異性分析 160
5.3 主幅角 k() 之定義 163
5.4 特殊楔形結構奇異性之對稱性分析 166
5.4.1 半平面接合之應力奇異性 167
5.4.2 脫膠全平面之楔形結構 176
5.4.3 楔形角為90倍數之楔形結構 182
5.4.3.1 模數Rk(90) 與主幅角 k(90) 之特性 183
5.4.3.2 90- 90楔形結構 184
5.4.3.3 90- 270楔形結構 185
5.4.3.4 90- 180楔形結構 185
5.4.3.5 180- 180楔形結構 191
5.5 任意楔形結構奇異性之對稱性分析 192
第六章 結論 218
參考文獻 225
附錄 237
近期論文著作 241
自述 243
著作權聲明 244
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