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Student Number 973202006
Author Yu-chien Kang(康宇權)
Author's Email Address 973202006@cc.ncu.edu.tw
Statistics This thesis had been viewed 515 times. Download 243 times.
Department Civil Engineering
Year 2010
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title Using M-integral to calculate multiple cracks problem in mixed-mode in 3D
Date of Defense 2010-10-20
Page Count 79
Keyword
  • finite element method
  • geometric center
  • M-integral
  • origin independent
  • surface independent
  • Abstract 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
    Table of Content 摘 要i
    Abstractii
    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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    葉俊彬,「應用Jk積分於均質與非均質材料在裂縫延伸時之能量釋放計算」,碩士論文,國立中央大學土木工程研究所,中壢(1996)。
    陳哲彬,「複合材料垂直於介面上裂縫之Jk積分計算」,碩士論文,國立中央大學土木工程研究所,中壢(1997)。
    鄔德傳,「三維裂縫之Jk積分與應力強度因子之數值計算」,博士論文,國立中央大學土木工程研究所,中壢(2005)。
    Advisor
  • Jui-Hung Chang(張瑞宏)
  • Files
  • 973202006.pdf
  • approve immediately
    Date of Submission 2011-03-13

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