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研究生:沈國瑞
論文名稱:無元素分析之積分權值調整法
指導教授:盛若磐,王仲宇
學位類別:博士
校院名稱:國立中央大學
系所名稱:土木工程研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:133
中文關鍵詞:無元素法積分權值調整法高斯積分無網格法元素釋放法
相關次數:
  • 被引用被引用:14
  • 點閱點閱:137
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  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
無元素法( Element Free method,EFM)處理網格邊界與材料邊界不一致的不規則邊界問題,常以高斯積分點在材料邊界內外做為取捨標準,容易造成數值誤差。 本論文提出積分權值調整觀念,由高斯積分的幾何意義著手,將積分網格中積分點與權的值拓展成積分面積的觀念,處理邊界網格積分時直接估算材料邊界內的高斯積分面積,使能量計算誤差降低,取代以往以高斯積分點點位座落於介質體內外為取捨的積分觀念。數值範例顯示積分權值調整觀念處理網格邊界與材料邊界不一致的邊界積分,不必細分網格也可以達到相當的分析精度,不論處理傾斜邊界或曲線邊界均呈現出穩定而且良好的分析結果。運用本法結合J積分計算版裂縫應力強度因子與運用完整高斯積分法情況所得相近。積分權值調整觀念使用於裂縫拓展分析中也相當便利,由彈性樑垂直邊裂縫拓展與版雙裂縫拓展分析顯示本法可以在處理移動性邊界問題時真正做到不必網格重建。此一新的積分法以簡單有效的權值調整觀念處理複雜的邊界網格積分問題,不僅符合無元素法的原創精神,也確保了無元素法能量積分的正確性。
目錄
摘要 I
A Weighting Adjustment Scheme of Gauss Integration in Element Free Method II
目錄 III
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 論文內容 4
第二章 文獻回顧 6
2.1無網格法的發展 6
2.2 斷裂損傷力學上的應用 10
2.3無元素法的邊界與介面處理 15
2.4 無元素法的積分處理 17
第三章 無元素法之基本理論 19
3.1 移動式最小平方(MLS)內插法之應用 19
3.1.1 一致性(Consistency)檢驗 23
3.1.2 形狀函數(Shape Function)之性質 24
3.1.3 加權函數(Weight Function)之探討 26
3.2變分原理 28
3.3離散方程式 30
第四章 無元素法的實行與積分改良 48
4.1無元素法的實行 48
4.2高斯積分的幾何新義 53
4.3不規則邊界處之積分處理 57
4.4 無元素法的積分改善 64
4.5權值調整法程式流程 67
第五章 裂縫拓展分析的基礎 69
5.1 應力強度因子的求法 69
5.2 裂縫拓展的原則 75
5.3 無元素法於裂縫處的影響圓建構 80
5.3.1不連續邊界處的影響圓決定方法 80
5.3.2通視法定影響圓 82
5.3.3繞射法定影響圓 84
5.3.4透明法定影響圓 85
5.4 權值調整法在裂縫處之應用 86
第六章 積分驗證與數值分析例 88
6.1積分驗證 88
6.1.1 一階多項式函數積分檢測 88
6.1.2 高階多項式函數積分檢驗 89
6.1.3指數函數積分檢驗 93
6.2一維微分方程數值例 96
6.2.1具一階線性解的一維微分方程問題 96
6.2.2 具較高階解的一維問題 107
6.3二維彈性介質數值例 112
6.3.1 拉桿 112
6.3.2 含圓孔之無限鈑 116
6.3.3 曲桿純彎曲 117
6.4 破壞力學數值例 118
6.4.1第一型應力強度因子分析 119
6.4.2複合型應力強度因子分析 121
6.4.3 含45度邊緣斜裂縫的版 123
6.4.4 樑三點彎曲試驗 125
6.4.5 含兩組圓孔與裂縫的版 129
第七章 結論與建議 136
7.1 結論 136
7.2建議 138
參考文獻 140
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