本文旨在研究無窮域壓電材料，內含一剛性絕緣線異質物與一裂紋，受到反平面應力及平面電位移作用下應力場和電位移場問題。此問題之探討，首先引用廣義點壓電螺旋差排作用之基本解，將分析之問題轉化為一連續廣義壓電螺旋差排密度作用於裂紋面上，從而建立了一組奇異積分方程式。其次經由數值方法求得此廣義壓電螺旋差排密度之數值解，由廣義差壓電螺旋排密度之數值解進一步求得其應力場的全場解和裂紋尖端處的應力與電位移強度因子。文中針對剛性絕緣線異質物與裂紋中心距離和裂紋傾角等參數變化對應力場和強度因子之影響進行了分析。

In this thesis, the interaction of the stress and electric displacement field between a rigid dielectric line and a crack, both embedded in an infinite piezoelectric medium is analyzed under remote anti-plane stress and in-plane electric displacement fields. Based on the Green’s function for a piezoelectric screw dislocation, a system of singular integral equations for the unknown piezoelectric screw dislocation densities defined on the crack faces is derived. Numerical method is then used to calculate the solutions to the system of equations. With the obtained piezoelectric screw dislocation density, the full field of stress field and the intensity factors are further computed and stress field contours are plotted. The influence of the geometry position between the crack and the rigid dielectric line on the full stress field is discussed.

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