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研究生： 郭修宇
Kuo, Hsiu-yu
論文名稱： 含單一嵌入式裂縫雙接合梯度壓電材料條板問題破壞分析
Mode Ⅲ Fracture Analysis of Two Bonded Functionally Graded Piezoelectric Strips with an Embedded Crack
指導教授： 褚晴暉
Chue, Ching-hwei
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2007
畢業學年度： 95
語文別： 中文
論文頁數： 105
中文關鍵詞： 功能梯度材料 、壓電 、應力強度因子
外文關鍵詞： Piezoelectric, Functionally graded material, Stress intensity factor
相關次數： 點閱：140  下載：2 
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    • 本論文主要目的在於分析探討含有單一嵌入式裂縫雙接合梯度壓電材料條板的破壞問題。依據壓電材料之極化方向及其相關之力電場方程式，運用傅立葉積分轉換法，將此混和邊界值問題化解成一組奇異積分方程式，再藉由Gauss- Chebyshev多項式技術化為代數聯立方程組，以求得應力強度因子與電位移強度因子之數值解。從數值結果分別討論條板邊界條件、非均質材料參數及裂縫位置對強度因子的影響。另外，本文推導所得之力電場解可以簡化至數個文獻上已經發表之案例，藉此證明本論文結果之正確性。

    This thesis deals with the fracture behavior of a functionally graded piezoelectric strip bonded to a functionally graded piezoelectric cracked strip under antiplane shear loads and inplane electrical loads. The materials are gradient along the crack direction which is normal to the bonded surface. After applying Fourier integral transform, the field equations with mixed boundary condition can be transformed into a system of integral equation and then solved numerically by employing the Chebyshev polynomials. The results show the effects of boundary condition, nonhomogeneous parameters and crack geometry on the stress and electrical displacement intensity factors. In additions, the derived electro-elastic field solutions can be reduced to several simple problems and compared well with the results previous studies.

    摘要......................................................i Abstract.................................................ii 誌謝....................................................iii 目錄.....................................................iv 表目錄..................................................vii 圖目錄..................................................vii 符號說明..................................................x 第一章 緒論...............................................1 1-1 前言..................................................1 1-2 文獻回顧..............................................5 1-3 研究目的..............................................7 1-4 本文架構..............................................8 第二章 基本公式推導.......................................9 2-1 壓電材料基本理論..................................9 2-2 壓電材料裂縫面之力電條件.........................14 2-3 含單一嵌入式裂縫雙接合梯度壓電材料條板問題.......18 2-3.1 案例1 (A-A條件).............................26 2-3.2 案例2 (B-B條件).............................35 2-3.3 案例3 (A-B條件).............................39 2-3.4 案例4 (B-A條件).............................43 第三章 數值運算方法......................................47 3-1 第一型奇異積分方程式.............................47 3-2 Gauss-Chebyshev的數值積分法......................49 第四章 結果與討論........................................58 4-1 β = γ = 0.......................................58 4-2 γ = 0 ， β ≠ 0.................................60 4-2.1裂縫位置對於強度因子的影響...................60 4-2.2裂縫與邊界間的距離對於強度因子的影響.........64 4-3 β = 0 ， γ ≠ 0.................................71 4-4 β ≠ γ..........................................74 4-4.1裂縫位置對於強度因子的影響...................74 4-4.2裂縫與邊界間的距離對於強度因子的影響.........81 第五章 結論..............................................88 參考文獻.................................................90 附錄A....................................................93 附錄B....................................................94 附錄C....................................................98 附錄D...................................................101 附錄E...................................................103

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