本論文包含二部分，第一部份為求解單一壓電材料有限楔形結構在面外負載下之機電場；第二部份為求解雙等楔形角壓電材料結合之有限楔形結構在面外負載下之機電場。利用有限梅林轉換積分轉換法，可解析壓電楔形體內部之機電場，如位移場、電位場、應力場以及電位移場。並由所得之機電場進一步探討各種廣義強度因子以及奇異性階數。
結果顯示，在此面外問題中，奇異性階數只與楔形角度有關，並且在不同的圓週邊界條件下均會有相同的奇異性階數以及角函數。除此之外，受到圓週邊界條件的影響，外加機械負載以及電負載的強弱將使強度因子對楔形長度的變化而有不同的趨勢影響。
為瞭解裂紋的破壞行為，本研究亦利用能量密度因子探討楔形圓週的邊界效應以及楔形長度對於含裂縫壓電體的破壞行為。在結果中發現，當只有機械負載時，能量密度因子對楔形長度的趨勢將根據圓週的彈性場邊界條件做變化。反之，隨著電負載的增加，能量密度因子將根據圓週電場的邊界條件做變化。除此之外，能量密度因子與裂縫尖端的局部圓柱座標無關。因此裂紋將根據尖端附近之破壞韌性的強弱而可能沿著任意角度成長。
本研究可假設雙壓電材料之材料性質相同或是假設楔形長度為無窮大，結果可以退化為單一壓電材料或是無限域壓電楔形結構之機電場。此外，若忽略壓電效應，結果可以退化為彈性體楔形結構問題以驗證本研究的正確性。

This paper presents the general solutions of antiplane electro-mechanical field for two piezoelectric finite wedge problems: (1) a piezoelectric finite wedge subjected to a pair of concentrate forces and free charges; (2) a finite wedge of equal wedge angles bonded by two dissimilar piezoelectric materials. Employing the finite Mellin transforms method, the displacement, electrical potential, stress and electrical displacement fields are derived analytically. In addition, the singularity orders and all generalized intensity factors can also be obtained.
The results show that the singularity orders and angular functions depend on wedge angle under antiplane problem. These quantities are identical for different circular boundary conditions. Besides, the strength of applied force or free charge plays important role on the fracture behavior according to the circular boundary conditions.
After being reduced to the crack problem, the energy density theory is applied to study the effects of the boundary conditions on the circular edge and wedge radius on the fracture behaviors of the cracked piezoelectric medium. The results show that the elastic field condition on circular edge will effect the variations of energy density factor with wedge radius when the antiplane loading is subjected to mechanical loading only. The tendency may be reversed if the applied surface charge increases according to the electric field condition on circular edge. The results also show that the energy density factors are independent of the local coordinate  defined at the crack tip. It means that the crack may extend along any direction depending on the fracture toughness of the materials near the crack tip.
The accuracy of these solutions has been validated when they are compared to those of some other degenerated problems (e.g. piezoelectric infinite wedge or elastic wedge problem).

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