臺灣博碩士論文加值系統

隨著科技的進步，許多技術關注在微小產品的製成，考慮微小尺度下材料的特性，當物體尺寸逐漸縮小時，表面積對體積的比率逐漸增大，此時界面/表面應力對物體之力學行為有相當大的影響，因此不可忽略考慮。本文將以基本纖維複合材料問題為架構，考慮表面應力，引入界面條件，重新探討複合材料之反平面等效剪力模數。利用複變函數定義場量分析，選用幾何形狀較為廣義的橢圓形，透過廣義自洽法建立雙層共焦橢圓形模型，並藉由保角映射技巧和平均值定理求解代表整體材料之元素彈力特性，分析複合材料在奈米尺度下，尺寸、形狀、面積比和嵌入纖維強度對表面力的影響，透過等效剪力模數來觀察表面力在小尺度下的應力行為。

This study investigates the problem of nano composites with surface stress under antiplane shear deformation. The ratio of surface area to volume increases when the size of medium shrinks, thus the mechanical behavior of the medium will be greatly affected by the interface imperfection. Therefore, the interface/surface stress is not negligible for nano scale solids. The model we discuss is the basic fibrous composite. The cross section is a confocal elliptic subjected to an antiplane shear loading on the matrix in far field. The effective antiplane shear modulus is obtained through generalized self-consistent method. The boundary condition particularly leads into the interface condition that is traction force of discontinuous. The elastic field is defined by potential function, by applying the conformal mapping technique and average theorem to solve the effective antiplane shear modulus. Finally, we demonstrate numerical results to discuss the influences of size, shape, concentration factor and shear modulus of fiber inclusion on effective behavior. The results confirm that the surface effect is significant when the size scale approach to the order of nanometer.

摘要 i
致謝 vii
目錄 viii
圖目錄 x
表目錄 xi
符號表 xii
第1章 緒論 1
1.1 文獻回顧與研究動機 1
1.1.1 表面力 1
1.1.2 內含物尺寸的相依特性 3
1.1.3 非均質複合材料行為與場量 4
1.1.4 複合材料之等效模數 4
1.2 論文架構及內容介紹 6
第2章 三維正交曲線座標系統之固體介面行為 8
2.1 流體Young-Laplace equation介紹 8
2.2 陳述理論模型和正交曲線座標系統 10
2.3 界面行為推導結果 11
2.4 特定幾何形狀內含物的界面情況 12
第3章 反平面剪力等效模數 13
3.1 基本定義 13
3.1.1 問題描述及定義模型 13
3.1.2 定義場量及控制方程式 14
3.1.3 複變函數方程 15
3.1.4 反平面剪力問題之滿足條件 18
3.2 解決問題之技巧及運算 19
3.2.1 保角映射轉換(conformal mapping method) 19
3.2.2 勞倫級數(Laurent series)假設及邊界條件 22
3.3 分析有效反平面剪力模數 28
第4章 數值模擬與結果討論 31
4.1 反平面等效剪力模數 31
4.1.1 圓形複合材料問題 31
4.1.2 橢圓形複合材料 32
4.2 等效模數特性模擬 34
4.2.1 等效係數與內含物尺寸之相依特性 36
4.2.2 等效係數與內含物形狀之相依特性 38
4.2.3 等效係數與內含物體積比之相依特性 40
4.2.4 等效係數與內含物剪力模數之相依特性 42
第5章 結論與建議 43
5.1 結論 43
5.2 未來研究之方向與建議 44
參考文獻 45
附錄A 52
附錄B 58

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