本文針對含電極之半平面橫向等向性壓電材料受廣義集中力作用之問題進行探討。此問題可由半平面壓電材料內之電極位置上施加一未知廣義分佈力函數，並滿足電極軸向應變和等於零之邊界條件來模擬。將未知廣義分佈力函數沿著電極位置積分，並滿足邊界條件得到本文問題之柯西型奇異積分方程式，再搭配輔助方程式，即可求得此未知廣義分佈力函數。本文採用Gerasoulis(1982)的數值方法求廣義分佈力函數的數值解，進而求得電極尖端的廣義應力強度因子，即開裂型、滑移型、撕裂型及電位移應力強度因子。而數值分析中探討的材料為橫向等向性壓電材料，針對不同的電極旋轉角度、不同的電極深度及不同的集中力角度進行面內效應分析，對半平面邊界效應及彈電耦合效應也有討論。

In the present thesis, the problem of piezoelectric half-plane containing an electrode subjected to a generalized concentrated force is considered. This problem is analyzed by distributing unknown generalized distributed forces on the position of the electrode subjected to satisfaction of the boundary conditions. Based on the generalized Stroh(1958) formalism, the unknown generalized distributed forces can be formulated in terms of Cauchy-type singular integral equations. By using the numerical method proposed by Gerasoulis(1982), we can get not only the numerical solution of the unknown generalized distributed forces but the traction field of the problem. The traction at the tip of the electrode is what we are most concerned about. Because of the singularity of stress at the tip, the Generalized Stress Intensity Factors(GSIFs) are considered. There are four type of the GSIFs: open mode, sliding mode, tearing mode and electric displacement intensity factor. The piezoelectric ceramic material PZT-6B is used to analyze the problem in the present studied. PZT-6B is transverse-isotropic material, hence, the in-plane effect and out-of-plane effect are decoupled. Therefore, only the in-plane effect is analyzed. The influences of the depth of electrode, the tilted angle of the generalized concentrated force and the direction of the electrode on the GSIFs are discussed in the last chapter. Additionally, the difference between piezoelectric material and pure-elastic material are also discussed in this study.

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