本文利用半雙曲線近似下推導而得的線彈性壓電控制方程式與本構方程式，解析一含有限長裂紋之無窮域壓電材料，於裂紋面上施加反平面應力及平面電位移的簡諧載荷問題。此外，本文亦將此假設應用於靜力問題上，解析一含有限長Yoffe擴展裂紋之壓電材料，於無窮遠處施加反平面應力及平面電位移負載之靜態力問題。本文利用積分轉換法求得含裂紋之壓電材料分別受簡諧載荷與靜力負載時的解析解，並與穩靜態近似下所得到之解作比較。最後針對所求之應力強度因子振幅大小以及相位，做詳細的數值計算與討論。

In this study, the quasi-hyperbolic approximation is used to investigate the dynamic behavior of a crack under the action of anti-plane stresses and in-plane electric displacements in a piezoelectric material. First, the steady-state response of a finite crack subjected to harmonically anti-plane loading and in-plane electric displacement on crack faces is analyzed. Moreover, a moving crack of Yoffe type in piezoelectric materials under remote anti-plane static stresses and in-plane static electric displacements is studied. The stress intensity factors and electric displacement intensity factors are obtained for both problems. Finally, numerical results of the first problem are evaluated and discussed in detail.

目     錄
中文摘要 ………………………………………………………………I
英文摘要 ………………………………………………………………II
目錄 ……………………………………………………………………III
圖目錄 …………………………………………………………………V
第一章 緒論 ……………………………………………………………1
1.1	研究動機 …………………………………………………1
1.2	文獻回顧 …………………………………………………4
1.3	內容介紹 …………………………………………………7
第二章 理論基礎 ……………………………………………………8
 2.1  麥斯威爾方程式 ……………………………………8
 2.2  線彈性壓電控制與本構方程式 ……………………...10
第三章  含裂紋之壓電材料之穩態問題分析 ………………19
3.1	問題描述 ……………………………………………19
3.1	理論解析 ………………………………………………20
3.2	數值計算方法 …………………………………………35
   3.3.1  高斯積分法 ………………………………………35
   3.3.2  L. U.法 …………………………………………36
   3.3.3  數值計算方法應用於求解弗萊德積分方程式 …37
3.4   數值結果與比較 ………………………………………42
第四章  含擴展裂紋之壓電材料受靜態力分析 ……………46
        4.1  理論解析 ……………………………………………46
        4.2  結果討論 ……………………………………………59
  第五章  成果與討論 ……………………………………………60
        5.1  本文結論 ………………………………………………60
        5.2  本文成果 ………………………………………………60
        5.3  尚待研究方向 …………………………………………62
參考文獻 ………………………………………………………………64






















圖 目 錄
圖3-1  含裂紋之壓電材料於不可誘電邊界條件下受簡諧載荷
　　　的結構示意圖 ……………………………………………68
圖3-2 含裂紋之壓電材料分別採用穩靜態近似以及半雙曲線近似
       下， 其應力強度因子的振幅大小關係圖 …………………69
圖3-3  含裂紋之壓電材料分別於採用穩靜態近似以及半雙曲線近似
       下， 其相位關係圖 …………………………………………70
圖3-4  含裂紋之壓電材料採用半雙曲線近似下，於不同平面電位移
       負載所得到的應力強度因子振幅大小關係圖 ……………71
圖3-5  含裂紋之壓電材料採用半雙曲線近似下，於不同平面電位移
       負載所得到的相位關係 ……………………………………72
圖3-6  Chen and Yu (1998) 於不同平面電位移負載所得到的應力強
       度因子振幅大小關係圖 ……………………………………73
圖3-7  Chen and Yu (1998) 於不同平面電位移負載所得到的相位關
       係圖 …………………………………………………………74
圖3-8  一般彈性材料受簡諧載荷時的應力強度因子的振幅大小關係
       圖 ……………………………………………………………75
圖3-9  Loeber and Sih(1968) 一含有限長裂紋之無窮域純彈性材料，受一反平面動力載荷的應力強度因子振幅大小關係…76
圖3-10  含裂紋之壓電材料於半雙曲線近似下，於較大振動頻率時所 
        得到的應力強度因子振幅大小關係圖 ……………………77
圖3-11  含裂紋之壓電材料於半雙曲線近似下，於較大振動頻率時所
        得到的相位關係圖 …………………………………………78
圖3-12 含裂紋之壓電材料分別採用穩靜態近似以及半雙曲線近似
        下，受較大振動頻率時的應力強度因子振幅大小關係
        圖 ……………………………………………………………79
圖4-1  含擴展裂紋之壓電材料於無窮遠處受力示意圖 …80
圖4-2  無裂紋之壓電材料於無窮遠處受力示意圖 ………81
圖4-3  含有限長裂紋之無窮域壓電材料受反平面均佈應力
      及平面電位移負載示意圖 ……………………………82

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