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系統識別號 U0026-1408201012193000
論文名稱(中文) 完全結合楔形壓電裂紋體之分析
論文名稱(英文) Analysis of Two Perfectly Bonded Piezoelectric Wedges with Crack
校院名稱 成功大學
系所名稱(中) 土木工程學系碩博士班
系所名稱(英) Department of Civil Engineering
學年度 98
學期 2
出版年 99
研究生(中文) 盧貞宇
研究生(英文) Chen-Yu Lu
電子信箱 ninalulala@hotmail.com
學號 N6697106
學位類別 碩士
語文別 中文
論文頁數 51頁
口試委員 指導教授-宋見春
口試委員-許澤善
口試委員-劉鈞耀
中文關鍵字 壓電材料  複合材料  楔形體  裂紋  差排 
英文關鍵字 piezoelectric material  composite materials  wedge-shaped  crack  dislocation 
學科別分類
中文摘要 本文旨在研究楔形體複合壓電材料,內含一裂紋,受到反平面位移及平面電場作用下應力與電位移強度因子問題。此問題之探討,首先引用Liou & Sung(2002)楔形壓電複合材料受一集中螺旋差排之應力與電位移場的結果,對裂紋上的螺旋差排進行積分,在給定施加於裂紋周圍的均佈力與電位移下,建立問題之奇異積分方程式。其次應用數值方法求得此螺旋差排密度之數值解,由螺旋差排密度之數值解進一步求得裂紋尖端處的應力與電位移強度因子。
英文摘要 A crack embedded in two perfectly bonded piezoelectric wedges is analyzed under anti-plane stress and in-plane electric displacement fields applied on the crack faces. Based on the fundamental solutions developed by Liou & Sung(2002) for a screw dislocation interacting with a wedge-shaped piezoelectric bi-material interface, a system of singular integral equations is obtained by distributing the screw dislocation densities on the crack faces. System equation is solved numerically. With the numerically obtained piezoelectric screw dislocation density, the stress and electric displacement intensity factors at the tip of cracks are further computed.
論文目次 摘要 I
Abstract II
誌謝 III
目錄 V
圖目錄 VII
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 本文綱要 4
第二章 基本公式 6
2-1 受反平面位移及平面電場作用之應力複數函數
與電位移複數函數 6
2-2 複合楔形壓電裂紋體受一集中螺旋差排作用之
基本解 10
2-3 平滑曲線之曳引力 15
第三章 問題推演 17
3-1 奇異積分方程組 18
3-2 應力及電位移強度因子 21
第四章 數值方法 23
4-1 奇異積分方程式組之正規化 23
4-2 正規奇異積分方程式組之離散化 25
第五章 結果與討論 30
5-1 兩材料夾角變化對裂紋尖端強度因子影響之探討 32
5-2 裂紋中點距離兩材料交點距離變化對裂紋尖端強
度因子影響之探討 35
第六章 結論 41
參考文獻 43
附錄A 數值方法 46
參考文獻 Berlincourt D.A., Curran D.R., Jaff H., 1964. Piezoelectric and piezomagnetic materials and their function in transducers. Physical Acoustics I-A, W.P.(Ed.), Academic Press, New York.
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Dundurs J., Markenscoff X., 1989. A green's function formulation of anticracks and their interaction with load-induced singularities. Journal of Applied Mechanics, Vol. 56, No. 3, 550-555.
Gerasoulis, A., 1982. The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type. Computers & Mathematics with Applications, Vol. 8, No. 1, 15-22.
Head A.K., 1953. The interaction of dislocations and boundaries. Philosophical Magazine, Vol. 44, No. 348, 92-94.
Jaff B., Cook W.R., Jaff H., 1971. Piezoelectric Ceramics. Academic Press Limited, India.
Liou J.Y., Sung J.C., 2002. The Green’s function for the line source core interacting with a wedge-shaped piezoelectric bi-material interface, private discussion.
Muskhelishvili, N.I., 1953. Some basic problems of the mathematical theory of elasticity. P. Noordhoff, Groningen.
Nye J.F., 1985. Physucal Properties of Crystals. Clarendin Press, Oxford.
Pak, Y.E., 1990a. Crack extension force in a piezoelectric material. Journal of Applied Mechanics, Vol. 57, 647-653.
Pak, Y.E., 1990b. Force on a Piezoelectric Screw Dislocation. Journal of Applied Mechanics, Vol. 57, 863-869.
Sung, J.C., Liou, J.Y., 1995. An internal crack in a half-plane solid with clamped boundary. Computer Method in Applied Mechanics and Engineering, Vol. 121, 361-372.
Xiao Z.M., Chen B.J., Fan H., 2001. An edge dislocation interacting with a wedge-shaped bi-material interface. International Journal of Solids and Structures, Vol. 38, No. 46-47, 8219-8233.
徐仲毅, 2006. 半平面壓電裂紋材料之數值分析. 國立成功大學土木工程研究所碩士論文.
陳財生, 2009. 含剛性絕緣線異質物之壓電裂紋體解析. 國立成功大學土木工程研究所碩士論文.
楊秉順, 2008. 雙層界面完全結合之壓電裂紋體解析. 國立成功大學土木工程研究所博士論文.
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