近十年來，功能梯度材料(FGMs)這種新式材料常常被
來設計現代結構，例如感測器、致動器、智慧結構和絕熱塗層。因為功能梯度材料的材料常數在整個結構上平滑連續地變化，使得由於機械力和熱效應所引起的應力集中現象大大地降低。相對地，結構的可靠度自然就提高了。最近，功能梯度材料的觀念延伸到壓電材料，並且受到耦合的彈力場和電場兩者的作用。這個新式材性就被稱作功能梯度壓電材料(FGMPs)。
本論文研究的是一個FGPMs的半平面上第三型非滲透和滲透裂縫的問題。外加兩種邊界條件，自由邊界和固定邊界。藉由使用傅立葉轉換，問題能夠被減化為奇異積分方程，並且利用高斯-謝畢雪夫積分方程求其數值解。隨後，算出來的應力和電位移強度因子顯示一些有影響的因素，例如裂縫長度、裂縫位置、邊界條件和非均質材料參數。最後結果顯示奇異應力場和電場的形式同於均質壓電裂縫問題的相應形式。裂縫端點處的材料強度較高時， 伴隨著強度因子也較高，例如當β> 0。至於滲透性裂縫，應力和電位移強度因子僅和外加的機械力有關。

In the last decade, new composite materials called functionally graded materials(FGMs)are developed to design the modern structures such as sensors, actuators, smart structures,and the thermal barriers.Since the material properties of FGMs vary smoothly and continuously in the body, stress concentrations due to the mechanical and thermal loads can be reduced significantly. Therefore,the reliability of the structures may be improved. Recently,the concept of FGMs has been extended to piezo- electric materials, which couple the elastic and electric fields.These new materials are called the functionally graded piezoelectric materials(FGPMs).
This study deals with the mode Ⅲ impermeable and permeable crack problems in a half-plane of FGPMs.Traction free-electrical open and clamped-electrical closed conditions are assigned on the boundary surface, respectively. By using the Fourier transform,the field equations are reduced to a system of singular integral equations and solved numerically by Gauss-Chebyshev integration technique.The stress and electrical displacement intensity factors are then calculated to show the influential factors such as the crack length,the crack location, the boundary conditions,and the nonhomogeneous material parameter.The intensity factors are higher at the crack tip with stronger material, i.e.β> 0. For permeable crack,the stress and electrical displacement intensity factors depend only on the external me- chanical load.

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