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系統識別號 U0026-1808201620583300
論文名稱(中文) 廣義不完美介面效應之複合桿件扭轉行為探討
論文名稱(英文) General imperfect interfaces in Saint-Venant’s torsion
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 104
學期 2
出版年 105
研究生(中文) 胡智翔
研究生(英文) Chih-Hsiang Hu
學號 N66031150
學位類別 碩士
語文別 中文
論文頁數 88頁
口試委員 指導教授-陳東陽
口試委員-葉超雄
口試委員-馬劍清
口試委員-趙振綱
口試委員-吳光鐘
中文關鍵字 聖維南扭轉  廣義不完美介面  中性內含物  複合材料桿件 
英文關鍵字 Saint-Venant’s torsion  general imperfect interface  neutral inclusions  composite bars 
學科別分類
中文摘要 本文主要目的在於利用不含座標之介面微分算子與阿達馬關係式,並搭配泰勒展開式來推導出聖維南扭轉之廣義不完美介面關係式,此為不含特定座標之形式。此廣義不完美介面模型之概念為利用不具有厚度的不完美介面,來取代兩介質間的具有均勻微小厚度的交界區間,而此位於交界區間中間的不完美介面,其特色為翹曲函數與法向剪應力均不連續。接著,本文將廣義不完美介面應用於扭轉中性內含物的問題,主要分為兩部分:第一部分考慮基底為圓形桿時,利用廣義不完美介面來得到偏心圓形中性內含物之束制條件;第二部分在基底為橢圓桿件時,我們發現圓形中性內含物只能位於基底中心,必須用兩種材料並搭配廣義不完美介面才能找到偏心的圓性中性內含物,並推導出所需滿足之束制條件。
英文摘要 In numerous situations of practical interest, the interfaces between two phases of composite bars turn out to be imperfect, so the study of imperfect interfaces is of prime importance in mechanical and physical fields. The main purpose of this thesis is to use a coordinate-free differential geometry theory, asymptotic analysis, and Hadamard’s relation to derive the general imperfect interface relations in Saint-Venant’s torsion. The method for the derivation of general imperfect interface consists in replacing an interphase of small uniform thickness between two neighboring phases with an imperfect interface of null thickness, positioned at the middle surface of the original interphase and characterized by the warping function and shear traction jump relations. Also, we apply the general imperfect interface derived in the present work to construct neutral inclusions in torsion problems. The problems of finding neutral inclusions in torsion of composite bars can be divided into two parts. In the first part considering the homogeneous circular bar, we design an eccentric circular inclusion with the general imperfect interface such that the warping function within the host bar is undisturbed. In the second part concerned with the elliptical host bar, the circular neutral inclusion can only be located at the center of the matrix. We need a coating material to get the eccentric circular inclusion neutral applying the general imperfect interface. Moreover, constraint conditions are derived for the neutral inclusion in previous two cases.
論文目次 中文摘要 i
Abstract ii
誌謝 viii
目錄 ix
圖目錄 xi
符號表 xii
第一章 緒論 1
1.1 理論背景與文獻回顧 1
1.2 論文內容簡介 4
第二章 不完美介面與基本扭轉理論介紹 5
2.1 不完美介面 5
2.1.1 彈性力學之不完美介面 5
2.1.2 熱傳導之不完美介面 7
2.2 基本扭轉理論 9
2.2.1 翹曲函數形式 9
2.2.2 共軛諧和函數形式 14
2.2.3 應力函數形式 15
第三章 扭轉行為之廣義不完美介面 18
3.1 介面微分算子 18
3.2 阿達馬關係式(Hadamard’s relation) 21
3.3 廣義不完美介面模型 23
3.3.1 等向性廣義不完美介面 34
3.4 LS型與HS型不完美介面 35
3.4.1 LS型不完美介面 36
3.4.2 HS型不完美介面 37
3.5 基底型與內含物型不完美介面 38
3.5.1 基底型不完美介面 38
3.5.2 內含物型不完美介面 39
第四章 圓形桿件之中性內含物 41
4.1 偏心圓形中性內含物 41
4.2 數值分析 47
第五章 橢圓形桿件之中性內含物 52
5.1 偏心之圓形中性內含物 52
5.2 偏心之雙相圓形中性內含物 56
5.3 數值分析 61
5.3.1 介面厚度的影響 62
5.3.2 介面材料係數的影響 63
第六章 結論與未來展望 66
6.1 本文結論 66
6.2 未來展望及應用 66
參考文獻 68
附錄A 熱傳導之廣義不完美介面關係式推導 74
附錄B 廣義不完美介面之平行曲線座標系形式 81
附錄C 熱傳導之偏心圓形中性內含物 85

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