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系統識別號 U0002-2407200920210100
中文論文名稱 含有限長裂紋之線彈性複合層板之暫態響應
英文論文名稱 Transient Response of a Finite Crack in Linearly Elastic Composite Strips
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 97
學期 2
出版年 98
研究生中文姓名 林世達
研究生英文姓名 Shih-Ta Lin
學號 696430718
學位類別 碩士
語文別 中文
口試日期 2009-07-01
論文頁數 73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 複合層板  應力強度因子  暫態響應  有限長裂紋 
英文關鍵字 Composite strips  Stress intensity factor  Transient response  Finite crack 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究雙異質線彈性複合層板之暫態響應,解析含有限長裂紋之線彈性複合層板受反平面均佈動力負載時裂紋尖端之應力強度因子。文中將問題分為兩個部份,問題一先求解不含裂紋之複合層板於自由表面受反平面動力負載時之解,問題二則於拉普拉斯轉換域中在複合層板的裂紋面上反加問題一所產生的剪應力。解析時將利用奇異積分方程與切比雪夫多項式來求得轉換域中之解,最後再利用Durbin數值拉普拉斯逆轉換法獲得應力強度因子之時域解。數值計算時,將與文獻上施加應力在裂紋面上之解析解作比較,並作詳細之討論。
英文摘要 In this study, the transient response of a finite crack lying on the interface of a linearly elastic composite strip is investigated. The laminate is subjected to uniformly dynamic anti-plane loading on the free surfaces. This transient problem can be treated as the superposition of two problems. Problem 1 considers a crack-free laminate subjected to uniformly dynamic anti-plane loading on the free surfaces. While problem 2 concerns a linearly elastic laminate containing an interfacial crack with the crack faces subjected to the loads that cancel out the shear stress induced by problem 1. The solution procedures are based on the use of integral transforms, singular integral equations and Chebyshev polynomial expansions. Durbin’s method is used to carry out the numerical inversion of Laplace transform. The numerical results are evaluated and discussed in detail. Furthermore, the accuracy is examined through some specified cases in the literature.
論文目次 目錄............................................I
圖目錄............................................III
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....................................5
第二章 理論基礎................................6
2.1線彈性材料之反平面控制方程與本構方程式......6
2.2拉普拉斯轉換及逆轉換........................7
2.3 傅立葉轉換及逆轉換 ........................7
2.4 Durbin 方法................................8
2.5奇異積分方程 (Singular Integral Equation)...8
2.6切比雪夫多項式..............................9
第三章 含有限長裂紋之複合層板之動力破壞........11
3.1 問題描述...................................11
3.2 無裂紋受反平面均佈應力之複合層板之問題描述..12
3.3 無裂紋之複合層板受反平面均佈應力之解析.....13
3.4含有限長裂紋於裂紋面承受負載複合層板之問題描述.............................................16
3.5 含有限長裂紋於裂紋面承受負載之複合層板之解析.............................................17
第四章 數值結果與討論.........................27
4.1數值計算時應注意事項..................27
4.2數值解結果比較........................30
第五章 結論與成果.............................35
5.1本文結論...............................37
5.2本文成果.............................................38
5.3尚待研究的方向.......................................................38
參考文獻.................40
附錄一 論文簡要版..............................................................................................66














圖 目 錄
圖3-1含有限長裂紋之複合層板受反平面均佈應力之圖形..…44
圖3-2無裂紋之複合層板受反平面均佈應力之圖形…...…...……45
圖3-3含有限長裂紋於裂紋面承受負載之複合層板之圖形..…46
圖4-1 於不同的Durbin項數之比較...............................................47
圖4-2應力強度因子於不同積分上限.............................................................48
圖4-3應力強度因子在不同的 級數項數.............................................49
圖4-4應力強度因子在不同的積分精確度...................................................50
圖4-5應力強度因子在Durbin的不同加總項數.........................................51
圖4-6應力強度因子在不同的 值.............................................52
圖4-7應力強度因子於不同週期之比較........................................................53
圖4-8應力強度因子於裂紋長度 時不同厚度之比較...............54
圖4-9應力強度因子於裂紋長度 時不同厚度之比較...............55
圖4-10 應力強度因子於裂紋長度 時不同厚度之比較...........56
圖4-11 應力強度因子於長時間的影響.........................................................57
圖4-12 應力強度因子於 之值的影響...........................................58
圖4-13於裂紋上施加均佈負載之複合層板之圖形................................59
圖4-14於裂紋上施加均佈負載的複合材料之應力強度因子................60
圖4-15為計算直接施加均佈負載於裂紋面上情況之應力強度因子 61
圖4-16 負載函數f(t)之圖形 62
圖4-17 於裂紋上施加f(t)形式負載之複合層版之圖形 63
圖4-18 於裂紋上施加f(t)型式負載的複合材料之應力強度因子 64
圖4-19 單一材料於裂紋上施加f(t)型式負載情況之應力強度因子 65
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廖雪吩 (2007),應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究,淡江大學航空太空工程學系碩士班碩士論文。

許吉勝 (2008),含有限長裂紋之彈壓電複合層板動力破壞分析,淡江大學航空太空工程學系碩士班碩士論文。
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