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中文論文名稱 應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究
英文論文名稱 Dynamic Fracture Analysis of a Piezoelectric Crack by Using Numerical Inversion of Laplace Transform
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 95
學期 2
出版年 96
研究生中文姓名 廖雪吩
研究生英文姓名 Hsueh-Fen Liao
學號 694370098
學位類別 碩士
語文別 中文
口試日期 2007-06-21
論文頁數 137頁
口試委員 指導教授-應宜雄
委員-馬劍清
委員-劉昭華
中文關鍵字 壓電材料  數值拉普拉斯逆轉換法  有限長裂紋  動力破壞  應力強度因子 
英文關鍵字 piezoelectric  numerical inversion of Laplace transform  finite crack  dynamic fracture 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究主題為應用數值拉普拉斯逆轉換法於無窮域內含不可誘電邊界靜止裂紋之壓電材料動力破壞問題,求解一含有限長靜止裂紋之壓電材料於裂紋面上受均佈反平面動態應力及平面動態電位移負載的暫態問題。本文運用了三種數值拉普拉斯逆轉換法分別為Durbin方法、趙氏方法ㄧ及趙氏方法二,首先利用簡單函數範例來比較這些數值法的準確性,並由計算經驗分別建議三種數值法的參數設定範圍;最後以數值拉普拉斯逆轉換法配合積分轉換技巧,解析含裂紋之壓電材料動力破壞問題,並將所求得之應力強度因子數值解做詳細的計算與討論。
英文摘要 In this study, the dynamic fracture analysis of an infinite piezoelectric material containing a finite crack with impermeable boundary conditions is investigated by using numerical inversion of Laplace transform. The finite crack is subjected to uniformly anti-plane stress and in-plane electric displacement impacts. Three numerical methods, Durbin’s method, Zhao’s method 1 and Zhao’s method 2 are used in this study. The accuracy is examined through some specified functions and the applicable numerical parameters are suggested respectively by the experience of calculation. Finally, the dynamic fracture analysis of a piezoelectric crack is carried out by numerical inversion of Laplace transform and the technique of integral transformation. Numerical solutions for dynamic stress intensity factors are evaluated and discussed in detail.
論文目次 目 錄
中文摘要 ……………………………………………………………… I
英文摘要 …………………………………………………………… II
目錄 ………………………………………………………………… IV
表目錄 …………………………………………………………… VI
圖目錄 …………………………………………………………… VIII
第一章 緒論 …………………………………………………………1
1.1 研究動機 ………………………………………………1
1.2文獻回顧 ………………………………………………3
1.3內容簡介 ………………………………………………6
第二章 數值拉普拉斯逆轉換………………………………………8
2.1 拉普拉斯轉換及逆轉換……………………………8
2.2 Durbin方法…………………………………………9
2.3 趙氏方法一 (Zhao’s method1)………………………19
2.4 趙氏方法二 (Zhao’s method2)………………………22
2.5 簡單數值範例…………………………………………27
第三章 壓電材料動力破壞之應用…………………………35
3.1 問題描述…………………………………………35
3.2 理論解析…………………………………………37
第四章 數值結果與討論………………………………………55
4.1 求解弗萊德積分方程式之數值法…………55
4.1.1 高斯積分法…………………………………55
4.1.2 L.U.法………………………………………56
4.1.3 求解弗萊德積分方程式………………………58
4.2 數值結果比較…………………………………63
第五章 結論與展望…………………………………………72
5.1 本文結論…………………………………………72
5.2 本文成果……………………………………………72
5.3 尚待研究的方向……………………………………73
參考文獻………………………………………………………………75

表 目 錄

表2-1 文獻範例 運用三種數值方法之結果………………………81
表2-2 文獻範例 運用三種數值方法之結果………………………82
表2-3 文獻範例 運用三種數值方法之結果………………………83
表2-4 文獻範例 運用三種數值方法於較佳設定參數之結果……84
表2-5 文獻範例 運用三種數值方法於較佳設定參數之結果………85
表2-6 文獻範例 運用三種數值方法於較佳設定參數之結果………86
表2-7 Durbin數值方法比較範例結果……………………………87
表2-8 Durbin方法比較 範例結果………………………………88
表2-9 趙氏數值方法一比較 範例結果……………………………89
表2-10 趙氏數值方法一比較 範例結果…………………………90
表2-11 趙氏數值方法二比較 範例結果…………………………91

圖 目 錄

圖2-1 及 、 、 之圖形…………………………92
圖2-2 及 、 、 之圖形…………………………93
圖2-3 發散及 、 、 之圖形……………………94
圖2-4 收斂及 、 、 之圖形……………………95
圖2-5 於Durbin方法逆轉換在不同週期 之比較圖……………96
圖2-6 於Durbin方法逆轉換在不同週期 之比較圖……………97
圖2-7 於Durbin方法逆轉換在不同 之比較圖…………………98
圖2-8 於Durbin方法逆轉換在不同 之比較圖…………………99
圖2-9 於Durbin方法逆轉換在不同項數 之比較……………100
圖2-10 於Durbin方法逆轉換在不同項數 之比較……………101
圖2-11 於趙氏方法一逆轉換在不同週期 之比較……………102
圖2-12 於趙氏方法一逆轉換在不同週期 之比較……………103
圖2-13 於趙氏方法一逆轉換在不同項數 之比較……………104
圖2-14 於趙氏方法一逆轉換在不同項數 之比較……………105
圖2-15 於趙氏方法二逆轉換在不同週期 之比較……………106
圖2-16 於趙氏方法二逆轉換在不同週期 之比較……………107
圖2-17 於趙氏方法二逆轉換在不同項數 之比較……………108
圖2-18 於趙氏方法二逆轉換在不同項數 之比較……………109
圖2-19 於三種數值法逆轉換之比較圖………………………110
圖2-20 於三種數值法逆轉換之比較圖………………………111
圖2-21 於三種數值法逆轉換之比較圖………………………112
圖2-22 三種數值法逆轉換結果之比較…………………………113
圖3-1 無窮域含裂紋壓電材料受反平面均佈應力及平面電位移負載之結構示意圖………………………………………………………114
圖4-1 無窮域含裂紋之彈性材料受反平面均佈應力運用不同數值法
之結果比較圖………………………………………………115
圖4-2 無窮域含裂紋之壓電材料運用Durbin方法於不同項數 時之比較圖………………………………………………116
圖4-3 無窮域含裂紋之壓電材料運用Durbin方法於不同項數 時之短時間比較圖………………………………………117
圖4-4 無窮域含裂紋之壓電材料運用趙氏方法一於不同項數 時之比較圖………………………………………………118
圖4-5 無窮域含裂紋之壓電材料運用趙氏方法一於不同項數 時之短時間比較圖………………………………………119
圖4-6 無窮域含裂紋之壓電材料運用趙氏方法二於不同項數 時之比較圖………………………………………………120
圖4-7 無窮域含裂紋之壓電材料運用趙氏方法二於不同項數 時之短時間比較圖………………………………………121
圖4-8 無窮域含裂紋之壓電材料運用Durbin方法於 不同時之比較圖………………………………………………………122
圖4-9 無窮域含裂紋之壓電材料運用趙氏方法一於 不同時之比較圖……………………………………………………123
圖4-10 無窮域含裂紋之壓電材料運用趙氏方法二於 不同時之比較圖……………………………………………………124
圖4-11 無窮域含裂紋之壓電材料運用不同數值法之長時間數值解比較圖…………………………………………………………125
圖4-12 無窮域含裂紋之壓電材料運用Durbin方法於不同電位移負載大小之比較圖……………………………………126
圖4-13無窮域含裂紋之壓電材料運用趙氏方法一於不同電位移負載大小之比較圖……………………………………127
圖4-14無窮域含裂紋之壓電材料運用趙氏方法二於不同電位移負載大小之比較圖……………………………………128
圖4-15無窮域含裂紋之壓電材料運用三種數值法之比較……129
圖4-16 Chen and Karihaloo(1999)之結果圖………………………130
圖4-17無窮域含裂紋之壓電材料受之電位移強度因子關係圖
……………………………………………………………131
圖4-18第一種負載函數之圖形……………………………………132
圖4-19無窮域含裂紋之壓電材料之三種數值法比較圖………133
圖4-20第二種負載函數之圖形……………………………………134
圖4-21 無窮域含裂紋之壓電材料受運用Durbin方法於不同加
載上升時間之比較圖…………………………………135
圖4-22無窮域含裂紋之壓電材料受運用趙氏方法一於不同加載上升時間之比較圖……………………………………136
圖4-23無窮域含裂紋之壓電材料運用趙氏方法二於不同加載上升時間之比較圖………………………………………137
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