博碩士論文 973202006 詳細資訊


姓名 康宇權(Yu-chien Kang)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 混合載重下的三維多裂縫問題之M-積分
(Using M-integral to calculate multiple cracks problem in mixed-mode in 3D)
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摘要(中) M-積分是研究物體具有裂縫之破壞行為的重要參數。本論文結合有限元素法研究針對三維線彈性材料具有裂縫之物體受混合載重作用計算其M-積分的數值分析。首先依序針對具有任意形狀之二維裂縫問題以及具有任意形狀之三維裂縫問題,進行M-積分式的理論推導,其次証明M-積分具有與積分曲面無關的性質。
在三維問題,對單裂縫的M-積分計算結果顯示與積分曲面無關和具有與原點無關的特性;多裂縫問題的M-積分計算,則需對所有裂縫的幾何形狀中心做計算,並且裂縫的幾何位置亦會影響M-積分。
此外,三維的有限元素網格遠比二維的複雜,因此有效的試體網格
是本論文研究的重點。關於三維單裂縫和多裂縫問題M-積分的積分區域在定義上有所不同,因此本論文將對三維單裂縫和多裂縫問題所對應的M-積分進行數值分析。
關鍵詞:M-積分、有限元素法、與積分曲面無關、原點無關、幾何形狀中心
摘要(英) The M-integral is the one of major parameter for the fracture behavior. In this paper, a numerical procedure, incorporated with the finite element method, is developed for calculation of the 3D linear elastic solid is subjected to mixed-mode load with 3D cracks. First, verify M-integral for the arbitrary shaped cracks in 2D problem and the arbitrary shaped cracks in 3D problem. Second, verify the property of surface independent.
In the 3D single crack problem, M-integral computation result can verify the property of surface independent and origin independent. In the 3D multiple cracks problem, M-integral computation result is associated with geometric center, and cracks geometric position influence computation result.
Furthermore, 3D FEM mesh is more complicated than 2D FEM mesh, so testing a good and useful mesh is also important in this research. The definition of integral region is different between the single crack and multiple cracks in 3D, and therefore calculate M-integral for the single crack problem and multiple cracks problem in this research.
Keywords : M-integral, finite element method, surface independent, origin independent, geometric center
關鍵字(中) ★ M-積分
★ 有限元素法
★ 與積分曲面無關
★ 幾何形狀中心
★ 原點無關
關鍵字(英) ★ origin independent
★ geometric center
★ surface independent
★ finite element method
★ M-integral
論文目次 摘 要 i
Abstract ii
誌 謝 iii
目 錄 I
表目錄 IV
圖目錄 V
第一章 緒 論 1
1.1研究動機與目的 1
1.2文獻回顧與探討 2
1.3論文內容 6
第二章 文獻回顧:二維M-積分的分析理論與推導 7
2.1 前言 7
2.2 二維單裂縫的M-積分理論及路徑無關特性 7
2.2.1 二維單裂縫的M-積分理論 7
2.2.2 M-積分之物理意義 9
2.2.3 與積分路徑無關特性 11
2.3 二維多裂縫的M-積分理論及與積分路徑無關特性 12
2.3.1 二維多裂縫的M-積分理論 12
2.3.2 與積分路徑無關特性 13
第三章 M-積分分析計算三維單裂縫問題 14
3.1 前言 14
3.2 三維單裂縫的M-積分理論與推導 14
3.2.1 理論與推導 14
3.2.2 與積分曲面無關特性(surface-independent) 16
3.3 數值計算範例:圓盤形裂縫位於圓柱體內部中央處 17
3.4 有限元素計算結果 18
3.4.1 M-積分 18
3.4.2 與原點無關的特性 19
3.4.3 三維M-積分與J1-積分之關係 20
3.4.4 有限元素網格分析 21
第四章 M-積分分析計算三維多裂縫問題 23
4.1前言 23
4.2三維多裂縫的M-積分理論與推導 23
4.2.1 理論與推導 23
4.2.2 與積分曲面無關特性(surface-independent) 24
4.3 受混合載重作用的水平排列雙圓盤形裂縫 25
4.4 有限元素計算結果 25
4.4.1 三維多裂縫M-積分 26
4.4.2 三維多裂縫不具與原點無關的特性 27
4.4.3 有限元素網格分析 27
第五章 結論與建議 29
5.1結論 29
5.2建議 30
參考文獻 32
附 錄 I M -積分之詳細推導 35
附 錄 II M -積分與積分路徑及與積分曲面無關之證明 38
附 錄 III Jk -積分與積分路徑及與積分曲面無關之證明 41
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指導教授 張瑞宏(Jui-Hung Chang) 審核日期 2011-3-13
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