本論文主要目的在於研究功能梯度壓電楔形結構受到面外剪力及面內電負載之電彈場問題。首先將材料性質假設為沿著半徑方向變化的連續函數，藉由梅林轉換及殘值定理的數學方法推導出在三種不同邊界條件A-A，B-B及A-B (flux-flux, potential-potential, flux-potential)下之奇異性階數及電彈場完整的形式及其物理意義。
研究結果發現奇異性階數與非均質材料參數、楔形角及邊界條件等因素有關。當楔形邊界受到均佈剪力及均佈電荷作用下，在滿足特定條件時，奇異性可能由r的指數型式轉變成log(r)之型式。而位移、電位、應力及電位移之解析解可退化成功能梯度楔形、壓電楔形及彈性楔形等問題。

The electro-elastic problems of a functionally graded piezoelectric material wedge under longitudinal shear load and inplane electrical load are studied in this paper. The material properties are assumed as a continuous function along radial direction. After applying Mellin transform and Residues theorem, the singularity orders, the physical quantities in the electro-elastic field are obtained in explicit forms for three different boundary conditions (flux-flux, potential-potential, flux-potential).
The results show that the singularity orders depend strongly on the nonhomogeneous material parameter, the wedge angle and the boundary conditions. When one of the boundary edges is subjected to uniformly distributed shear force and/or electrical displacement starting from the apex of the wedge, the r-type singularity will be shifted to log(r)-type singularity if the special condition is satisfied. The analytical expressions of the displacements, electrical potentials, stresses, and the electrical displacements can be simplified to the degenerated problems such as the functionally graded elastic material wedge problem, the piezoelectric wedge problem, and the elastic wedge problem.

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