一般壓電體的材料性質為非等向性，但是當極化方向與楔形結構之軸向方向平行時，會產生橫向等向性的特性。且面內機械場與面外機械場、面內電場會分解，即只有面外機械場會產生電彈耦合效應。本論文利用梅林轉換（Mellin transform），解析單一壓電材料楔形體及兩個等楔形角壓電材料結合而成之楔形體在受到一對面外集中力負載下之機電場。並由所得之機電場進一步探討強度因子、奇異性階數及其所對應之由解析之結果可知，對於單一壓電材料楔形體，面外應力場與面內電位移場互相分解。在所討論的兩種情況中，各場之奇異性階數及角函數皆相同並只與楔形角度有關。藉由所推導出之雙壓電材料楔形體的公式解，我們可以將兩材料之材料性質設為相同，其結果可退化為單一壓電材料的機電場。若將集中負荷之結果作為基本解，運用加權函數的方法可求得任意面外剪力負載下之機電場。本論文之結果也可以應用在含裂
縫之壓電體結構上，如單一壓電材料楔形結構退化為無限域中之半無限長裂縫；雙壓電材料結合之楔形結構退化為兩半無限域間之界面裂縫。此外，若忽略其壓電效應，可退化為純彈性體的問題。

This paper presents the general solutions of antiplane electro-mechanical field for two piezoelectric wedge problems: (1) a piezoelectric wedge subjected to a pair of concentrate forces and free charges; (2) a wedge of equal wedge angles bonded by two dissimilar piezoelectric materials.
Employing the Mellin transform method, the generalized stress, strain, and electrical displacement intensity factors are derived analytically. In addition,the singularity orders and the angular functions expressed in electro-mechanical field can also be obtained.
The accuracies of these solutions have been validated when they are compared to those of some other degenerated problems, which have been widely discussed before. After being reduced to the problem of a semi-infinite antiplane crack in a piezoelectric material or an interface crack in piezoelectric multi-layer materials, the results of the first or second problem can be used as a fundamental solution of other more complicated crack problems by superposition, respectively.

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