本文目的在探討接合半平面之含單一裂縫功能梯度壓電無限條板破壞問題。以材料之極化方向及外加負載簡化壓電材料之本構方程式，並以Fourier積分轉換法將不同邊界問題轉換為奇異積分方程組，再利用Gauss-Chebyshev定理及Chebyshev多項式將其表示為代數聯立方程組，並藉電腦輔助計算應力強度因子及電位移強度因子之數值解。藉由改變裂縫長度、位置及不同材料非均質參數，以觀察前述各項對強度因子之影響。

The fracture problem of a cracked functionally graded piezoelectric layer bonded to a substrate is discussed in this thesis. Due to the poling direction of the piezoelectric materials, applied antiplane shear loading and the inplane electric loading, the constitutive equation is simplified. A system of singular integral equation is derived by using the Fourier integral transform. These equations are then reduced to algebraic simultaneous equations with the aid of Gauss-Chebyshev theorem and Chebyshev polynomials. The numerical solutions of stress and electric displacement intensity factors can be obtained by solving the above equations and the effects of crack length, crack position and different nonhomogeneous parameters upon the intensity factors can be discussed.

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