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研究生： 張連達
Chang, Lian-Da
論文名稱： 界面裂紋漸近場高階參數之數值分析
Numerical analysis of higher order parameters for the near-tip fields of an interface crack
指導教授： 宋見春
Sung, Jen-Chun
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2011
畢業學年度： 99
語文別： 中文
論文頁數： 65
中文關鍵詞： 高階項係數 、裂縫 、有限元素分析 、FEOD方法 、應力強度因子
外文關鍵詞： coefficient of the higher-order terms, crack, finite element analysis, FEOD method, stress intensity factor
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    • 本文旨在研究雙層材料界面含一裂縫，受到拉應力或剪應力的作用下計算Williams expansion高階項係數。文中先推導雙層材料界面含一裂縫之位移漸近場表達式，接著說明有限元素超定(FEDO)方法的原理與使用。其次介紹奇異元素的原理與ABAQUS軟體的使用。最後應用FEOD方法求得係數並且針對影響收斂性和精確度的因素做討論與比較。

    This thesis aims to study the parameters of the higher-order terms in the Williams expansion of an interface crack in a bi-material subjected to tensile stress or shear stress load. First, the asymptotic displacement fields of an interface crack are introduced, and then the principle of the Finite Element Over-Deterministic (FEOD) method is introduced. The singularity element as well as the ABAQUS software is also introduced. Finally, the FEOD method is employed to calculate the higher-order parameters in the Williams expansion, and the effects of convergence and accuracy are discussed and compared.

    摘要 I Abstract II 誌謝 III 目錄 IV 表目錄 VI 圖目錄 VII 第一章 緒論 1 1-1 前言 1 1-2 文獻回顧 1 1-3 本文綱要 3 第二章 基本公式 5 2-1 雙層材料界面含一中央裂縫之位移漸近場公式 5 2-2 有限元素超定方法 14 第三章 有限元素分析 22 3-1 奇異元素(Singularity element) 22 3-2 套裝軟體：ABAQUS 6.8-1 26 第四章 數值模擬結果與討論 33 4-1 驗證基準問題 33 4-2 驗證中央裂縫平板(Center-cracked plate)問題 34 4-2-1 均質材料純Mode I範例 34 4-2-2 均質材料純Mode II範例 37 4-2-3 驗證他人之相關研究 39 4-3 雙層材料在非均質的情況下計算高階項係數 41 4-3-1 非均質材料Mode I範例 42 4-3-2 非均質材料Mode II範例 45 4-4 項數多寡與節點數量對係數收斂性與準確性的影響 48 4-4-1 環狀取點 48 4-4-2 徑向取點 52 4-5網格切割的疏密對Williams expansion係數的影響 56 第五章 結論 59 參考文獻 61 附錄A 64

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