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研究生:李侑昀
研究生(外文):Yu-Yun Lee
論文名稱:含裂縫異向性彈性板受彎矩作用之破壞力學分析
論文名稱(外文):Fracture Mechanics Analysis for Bending Problems of Anisotropic Plates with Cracks
指導教授:吳光鐘
指導教授(外文):Kuang-Chong Wu
口試委員:張正憲陳正宗陳俊杉陳世豪
口試日期:2015-07-23
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
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:2015
畢業學年度:103
語文別:中文
論文頁數:101
中文關鍵詞:邊界積分法裂縫異向彈性板Stroh法
外文關鍵詞:boundary integral equationscracksanisotropic platesStroh-like formalism
相關次數:
  • 被引用被引用:2
  • 點閱點閱:161
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
本文發展一種新的積分方程式,用於分析二維含裂縫異向性彈性板彎矩作用之問題上。此法的推導是先利用Stroh理論求得單一旋錯(disclination)的基本解,再利用旋錯會造成旋轉角不連續的特性,將受力矩作用的裂縫視為連續分佈的旋錯,來建構相關的積分方程式。該積分方程式可經由高斯-謝比雪夫積分法轉化為線性代數方程式求解。此法的優點是不論邊界條件、材料常數為何,其裂縫尖端之應力強度因子都可求得;即使在少數的積分點下,也可達到很高的精確性。本文之算例使用之材料有等向性與正交性兩種,計算的模型有單裂縫、雙裂縫、多裂縫、弧形裂縫之無限板受均勻力矩或剪力問題等,其中部分結果參考其他文獻之解析解,驗證其有效性與精確性。

A new integral equation method is developed in this paper for the analysis of two-dimensional general anisotropic cracked elastic plates under bending. Integral equation are constructed by considering cracks as continuous distributions of disclination. Using Gauss-Chebyshev integration formulas, the integral equations can be transformed into the form of algebraic equations, with which the disclination densities and the stress intensity factors associated with each crack tip can be computed. An advantage of the method is that we can get the stress intensity factors regardless of the boundary conditions and material parameters. Another advantage is that accurate results may be obtained with relatively few integration points. Numerical examples are provided for isotropic or orthotropic plates with a single line or arc crack, double line cracks, multiple line cracks, under uniform bending, twisting moments or shearing force. The some results are compared with those in the literature whenever possible to verify their accuracy.

致謝 i
中文摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 viii
表目錄 xiii
第1章 導論 1
1.1 研究動機與文獻回顧 1
1.2 本文大綱 3
第2章 薄板理論 4
2.1 古典板假設 4
2.2 應力應變關係 5
2.3 應變與位移關係 6
2.4 組成律 7
2.5 平衡方程式 9
2.6 統御方程式 9
第3章 Stroh理論 10
3.1 薄板之Stroh-Like理論 10
3.2 Stroh-Like理論之特性 15
第4章 數值方法 18
4.1 旋錯(disclination)基本解 18
4.2 含多裂縫板之積分方程式 21
4.3 旋錯法與謝比雪夫多項式 23
4.4 應力強度因子計算 27
4.5 解析解 30
第5章 數值方法 33
5.1 材料常數 33
5.1.1 等向性材料與正交性材料 33
5.2 水平單裂縫之無限板受均勻力矩與剪力 35
5.2.1 水平單裂縫之無限板受均勻扭矩 與 35
5.2.2 水平單裂縫之無限板受均勻彎矩 37
5.2.3 水平單裂縫之無限板受均勻剪力 39
5.3 傾斜單裂縫之無限板受均勻力矩 41
5.3.1 傾斜單裂縫之無限板受均勻扭矩 與 41
5.3.2 傾斜單裂縫之無限板受均勻彎矩 45
5.4 雙裂縫之無限板受均勻力矩 49
5.4.1 水平雙裂縫之無限板受均勻彎矩 49
5.4.2 傾斜雙裂縫之無限板受均勻彎矩 54
5.4.3 傾斜雙裂縫之無限板受均勻彎矩 58
5.4.4 傾斜雙裂縫之無限板受均勻扭矩 與 62
5.4.5 修正常數 66
5.5 多裂縫之無限板受均勻力矩 68
5.5.1 三裂縫之無限板受均勻彎矩 68
5.5.2 三裂縫之無限板受均勻彎矩 71
5.5.3 三裂縫之無限板受均勻彎矩 與 74
5.5.4 多裂縫之無限板受均勻彎矩 與 76
5.5.5 多裂縫之無限板受均勻扭矩 與 81
5.6 弧形裂縫之無限板受均勻力矩 87
5.6.1 弧狀裂縫之數值方法 87
5.6.2 弧狀裂縫之無限板受均勻彎矩 與 88
5.6.3 弧狀裂縫之無限板受均勻扭矩 與 92
第6章 結論與未來展望 95
6.1 結論 95
6.2 未來展望 96
參考文獻 97


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