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系統識別號 U0026-2108201615290700
論文名稱(中文) 邊界元素法應用於薄層複材之界面應力分析
論文名稱(英文) Application of BEM on the analysis of interfacial stresses in thin anisotropic composite
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 104
學期 2
出版年 105
研究生(中文) 鍾竣宇
研究生(英文) Jun-Yu Zhong
學號 P46031220
學位類別 碩士
語文別 中文
論文頁數 102頁
口試委員 指導教授-夏育群
口試委員-胡潛濱
口試委員-楊文彬
中文關鍵字 全異向性彈性體複合材料  界面應力  邊界元素法  自正規化 
英文關鍵字 Anisotropic composites  interlaminar stresses  boundary element method  self-regularization. 
學科別分類
中文摘要 在工程產中, 異向性彈性體薄層複合材料已經被廣泛的應用。
一般的分析通常忽略了膠合層(黏著劑)的存在,由於非常薄的薄層有建模上的困難,所以一般的分析中通常忽略了膠合層(黏著劑)的存在,
但往往先造成破壞的就是膠合層(黏著劑),這將無法提供可靠的破壞(剝離)評估。
本文中研究的對象是對於三維全異向性彈性體,處理薄層複材之界面應力問題。因為要考慮破壞(剝離)的問題,邊界元模型也將各薄層間的膠合層(黏著劑)考慮進去。由於邊界元素法(BEM)在社會大眾所周知問題就是,當源點非常接近其邊界時,將產生近似奇異積分(nearly singular integration)的問題,進而產生不準確的數值積分。目前採用了自正規化(self-regularization)來解決此問題。
在本文中,自正規化(self-regularization)的邊界積分方程(BIE)之三維等向性彈性體之分析由He and Tan【1】提出,而2015年Shiah et al【2】將此方法擴展應用於三維異向性彈性體研究超薄幾何問題以及內部點靠近邊界的問題,已有相當不錯的結果,本研究將其應用於三維異向性彈性體薄層複材之界面應力問題,並且比較各種不同的例子來探討有無膠合層(黏著劑)的差別,再與ANSYS進行比對。
英文摘要 In engineering industries, composites made of thin anisotropic layers have been widely applied for various applications. The conventional analysis usually neglects the existence of adhesive material due to the modeling difficulty of very thin layers; however, this shall fail to provide reliable assessment of the potential debonding due to the fracture of the adhesive material. This work presents an analysis of interlaminar stresses in thin layered anisotropic composites by the boundary element method (BEM). For assessment of potential debonding, the BEM modeling also takes into account the presence of a thin adhesive layer. For the singular kernels in the boundary integrals, inaccurate numerical integrations shall occur for the conventional elastostatic BEM analysis of thin structures. The present work employs the self-regularization scheme presented very recently to analyze the interlaminar stresses in thin anisotropic composites and compare the cases of whether the adhesive epoxy layer is considered or not. In the end, a few benchmark examples are presented to show the applicability of the present approach.
論文目次 摘要 I
誌謝 XI
目錄 XII
表目錄 XV
圖目錄 XVI
第一章 導論 1
1.1 引言 1
1.2 研究動機與目的 5
1.3 文獻回顧 6
1.4 研究方法與流程 8
第二章 理論回顧 10
2.1 邊界積分方程式 10
2.2 異向性材料之位移解 10
2.3 異向性材料之應力解 13
第三章 格林函數 15
3.1 解析式 16
3.2 傅立葉級數 17
3.2.1 格林函數以傅立葉級數表示 17
3.2.2格林函數一階導數以傅立葉級數表示 19
3.2.3格林函數二階導數以傅立葉級數表示 21
3.3 簡化傅立葉級數 23
3.3.1格林函數以簡化後傅立葉級數表示 23
3.3.2格林函數一階導數以簡化後傅立葉級數表示 25
3.3.3格林函數二階導數以簡化後傅立葉級數表示 26
第四章 自正規化方法(SELF-REGULARIZED) 29
4.1 自正規化之邊界積分式 29
4.2 尋找投影點與判斷是否使用自正規化 33
第五章 應用分析範例 35
5.1格林函數效率比較 36
5.3雙材料-中間有無膠合層應用分析 43
5.3.1疊層板 45
5.3.2疊層圓柱 51
5.3.3疊層圓球 58
5.3.4 Lap joint 65
5.3.5 Double lap joint 71
5.3.6 孔洞 78
5.4 疊層板應用分析 83
5.4.1 五層對稱疊層板[90/45/0/45/90]拉伸 84
5.4.2五層對稱與非對稱疊層板 88
第六章 未來展望 95
參考文獻 96
附件A 100

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