臺灣博碩士論文加值系統

利用有限元素法分析含有裂紋的結構時，在求解過程中，須在裂紋尖端附近建構大量元素，計算時必須耗費大量電腦容量及運算時間，此缺點在求解動態問題時會更加明顯。因此本文基於有限元素法，配合幾何形狀相似之等參元素理論，推導出含有慣性項的無限元素演算程序，使裂紋尖端眾多的元素可化簡為僅存周邊節點的廣義元素。本研究運用MATLAB軟體撰寫此分析方法之計算程式，並求解薄膜振動及平板之平面內振動問題之特徵值來驗證無限元素演算法之理論與程式的正確性。進而從分析中歸納出此方法相關之收斂條件，研究結果證實了無限元可適用區域須小於整體結構之十分之一。最後本研究將此分析方法應用於含裂紋之平板之平面內的動態特徵值分析上，並與有限元素套裝軟體ABAQUS做結合。由分析可知，不論是單裂紋或多裂紋的問題，應用此法均祇須計算一個裂紋元素而後與結構本體做組合，從而節省大量未知數的計算，並提升了無限元在動態問題上分析的能力。

表目錄………………………………………………….…....II
圖目錄……………………………………………….……...III
第一章 緒 論 1
1-1 研究動機與目的 1
1-2 文獻回顧 3
1-3 研究流程圖 6
第二章 動態無限元素法之推導 7
2-1 等參元素相似法則 7
2-2 無限元素法之公式推導 9
2-2-1 彈性問題 9
2-2-2 靜態公式推導[4] 14
2-2-3 動態公式推導(無限元素演算法) 19
第三章 無限元素演算法的程式驗證 32
3-1 薄膜振動例題 32
3-2 無限元素法之性質探討 35
3-3 平板之平面振動頻率 49
3-4 裂紋分析 62
第四章 結論與未來研究方向 67
4-1 結論 67
4-2 未來研究方向 69
參 考 文 獻 70

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