本文研究功能性梯度壓電材料之裂紋擴展問題，解析無窮域含可滲透擴展裂紋之功能性梯度壓電材料受反平面剪應力的破壞問題。文中利用Yoffe模型與指數型梯度變化之假設，將滿足邊界條件的控制方程式轉為對偶積分方程式，並使用含複指數對偶積分方程法將其化為含餘弦函數的對偶積分方程，進一步轉化為第二類的Fredholm積分方程。最後求得含有限長擴展裂紋之功能性梯度壓電材料承受mode-III均佈載荷的應力強度因子解析解。數值結果計算了不同材料、不同材料梯度與裂紋擴展速度對於應力強度因子之影響，並做詳細的討論。

In this study, the steady-state response of a moving crack in the functional graded piezoelectric materials (FGPM) is investigated. The material parameters are assumed to vary exponentially and Yoffe's model is adopted. The governing equations for FGPM are solved by use of Fourier consine transform. The formulation for the boundary conditions is derived as a system of dual integral equations, which in turn are reduced to Fredholm integral equation of the second kind. The obtained solutions can be reduced to existing solutions in the literature. Numerical results for stress intensity factors are evaluated and discussed in detail.

目錄 ………………………………………………………………… I
圖目錄 …………………………………………………………… 　IV
表目錄 ……………………………………………………………VI
第一章 緒論 …………………………………………………………1
1.1  研究動機 ………………………………………………1
1.2  文獻回顧 ………………………………………………4
1.3  內容簡介 ……………………………………………8
第二章 理論基礎………………………………………9
2.1  功能性梯度壓電材料控制方程與本構方程
………………………………………………………9
2.2  傅立葉餘弦轉換及逆轉換………………………………12
第三章 壓電材料動力破壞之應用…………………………13
3.1  問題描述…………………………………………13
3.2  理論解析…………………………………………14
第四章 數值結果與討論………………………………………30
4.1  高斯積分法………………………………………30
4.2  求解弗萊德積分方程式之數值法……………30
4.3  數值結果比較…………………………………32
第五章 結論與展望…………………………………………37
5.1本文結論…………………………………………37
5.2  本文成果……………………………………………37
5.3  尚待研究的方向………………………………38
參考文獻………………………………………………………………40
附錄一 論文簡要版……………………………………………………62

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