本文旨在推導奇異點在兩相異圓形異質等向性彈性體平面場任一點之通解，本研究方法首先利用保角映射法(Conformal mapping)將實際求解之物理平面轉換至數學平面以利求解，並透過Muskhelishvili提出的基本應力函數且搭配解析連續交替法(Alternating technique)反覆跌代各層材料級數通解，而差排作用在複合材料上之映射力可根據Peach-Koehler Formula求得，並探討圓形異質中奇異點與幾何特徵及材料彈性係數比對於差排位置的關係，其中差排所受的映射力可得知其移動方向及受材料產生之動力，並藉由判斷平衡點位置與穩定藉此推測差排可能堆積的位置 。本研究差排映射力之數值計算使用MATLAB R2009b軟體作為本文計算工具。

This study presents in-plane elasticity problems of the two bounded circular inclusions subjected to an arbitrary singularity point. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, both the displacements and stresses are in terms of the Muskhelishvili’s complex potentials.The image forces acting on the dislocation are calculated through the Peach-Koehler formula. The interaction between an edge dislocation and circular inclusions is also discussed for different materials and geometry in this study.And the equilibrium position and subsequent stability of the dislocation are determined and the magnitude or direction of dislocation’s movement is discussed in detail. This study calculated the image forces acting on the dislocation using MATLAB R2009b software.

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