臺灣博碩士論文加值系統

本文旨在探討磁電彈性螺旋差排與多層不完美界面交互作用的基本解及其應用。利用複變數理論與解析連續法，可求得磁電彈性場全場級數型式顯解，藉此，界面不完美程度對磁電彈性場的影響將被仔細討論。作用在差排之映射利可利用 Peach-Koehler 公式求得，而以級數型式顯解表示，並據此討論界面瑕疵程度與材料組合對映射力與差排平衡點的影響。接下來，吾人將利用之前所推導的解析解求解含不完美界面複合材料受遠域均勻磁電彈性負荷之裂縫問題，利用差排連續分佈以模擬裂縫，並以單一差排之解為奇異積分的核函數，藉由數值方法可解得差排密度函數，進而求得裂縫尖端之應力強度因子、電位移強度因子與磁感強度因子。此外，本文亦將討論材料組合與界面瑕疵程度對此磁電彈性場強度因子的影響。

This work investigated the analytic solution for a screw dislocation interacting with imperfect interfaces and its application to magnetoelectric solids. By means of a complex variable method and analytic continuation technique, the explicit solutions of magnetoelectric fields are obtained. With the aid of the Peach-Koehler formula, the explicit expression for the image forces exerted on the screw dislocation are derived. The effect of the interface imperfection on the magnetoelectroelastic fields in the multiply inclusion is investigated. The image force acting on the screw dislocation and its equilibrium positions near the imperfect interface is also discussed for variable parameters (interface imperfection, material magnetoelectroelastic mismatch). Next, we will apply the derived analytic solutions to solve the corresponding crack problem. In this case, a far-field loading condition is considered. By using the solution of a screw dislocation near a coated inclusion in magnetoelectric media as the Green function, the problem is formulated into a set of singular integral equations, which are solved by numerical method. The stress intensity factor, displacement intensity factor and magnetic induction intensity factor are derived in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Numerical examples are given for various material constants combinations and interface imperfection.

目錄
中文摘要 i
Abstract iii
誌謝 v
目錄 vi
圖目錄 viii
第一章緒 論 1
1.1研究動機與目的 1
1.2文獻回顧 2
1.3研究方法 4
1.4本文作法 5
第二章 問題描述與基本方程式 6
2.1 問題描述 6
2.2 解析連續 9
第三章 求解方法 14
3.1 奇異點位於中間層 14
3.2 奇異點位於外域基質中 20
3.3 奇異點位於心部圓盤中 24
3.4 裂縫問題 28
(I)無裂縫問題 29
(II)單一裂縫問題 30
第四章 結果與討論 35
第五章 結論與未來展望 44
參考文獻 45

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