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研究生:徐穎成
研究生(外文):Ying-cheng Hsu
論文名稱:含單一嵌入式裂縫之功能梯度壓電半無窮平板問題面內破壞分析
論文名稱(外文):In-plane Fracture Analysis of an Embedded Crack in a Functionally Graded Piezoelectric Half-plane
指導教授:褚晴暉褚晴暉引用關係
指導教授(外文):Ching-Hwei Chue
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:102
中文關鍵詞:強度因子面內問題功能梯度壓電材料裂縫
外文關鍵詞:in-plane problemintensity factorsCrackFunctionally graded piezoelectric material
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本論文主要的研究目的在於探討含有單一嵌入式裂縫之功能梯度壓電半無窮平板的破壞問題,在受到面內均勻負載下,求解其應力強度因子以及電位移強度因子,運用壓電力學理論以及Fourier轉換法對此種混合邊界問題求解,可推導出一組奇異積分方程式,再使用Gauss-Chebyshev多項式技術配合破壞力學理論,可得到裂縫尖端之應力與電位移強度因子之數值解。
研究結果顯示,非均質壓電材料其裂縫尖端之無因次化強度因子,會受到裂縫長度、材料非均質參數以及外加機電負載比例的影響,且 Mode I 之無因次化強度因子跟裂縫長度與非均質參數成正比,若結構具有外加電位移負載依其負載的方向、大小,則會改變其結果,另外 Mode II 之無因次化應力強度因子,其數值的正負號會依據,非均質參數、裂縫長度、邊界效應以及外加面內機電負載比例的交互影響而有所改變。
In this thesis, the in-plane fracture problem of an embedded crack within a functionally graded piezoelectric half-plane of is discussed. Using the theory of piezoelectricity and the method of Fourier integral transform to solve the field equations associated with mixed boundary condition, we derive a system of singular integral equations. The stress and electric displacement intensity factors of the crack tip are computed by employing the Gauss-Chebyshev polynomials technique and the theory of fracture mechanics.
The results show that the normalized intensity factors of the crack tip will be affected by the crack length, the non-homogenous parameter and the ratio of mechanical and electrical loading. The Mode I normalized intensity factors are proportional to the crack length and the non-homogenous parameter. If the electrical loading is applied only on the structure, the numerical results of the intensity factors will be changed according to the direction and magnitude of the electrical loading. The sign (positive or negative) of Mode II normalized stress intensity factor depends on the interaction between the crack length, non-homogenous parameter, boundary effect and the ratio of mechanical and electrical loading.
摘要....................................................Ⅰ
Abstract................................................Ⅱ
致謝....................................................Ⅲ
目錄....................................................Ⅴ
表目錄..................................................Ⅶ
圖目錄..................................................Ⅸ
符號說明...............................................XII
第一章 緒論.............................................1
1-1 前言................................................1
1-2 文獻回顧............................................5
1-3 本論文分析問題簡介..................................8
1-4 本文架構............................................9
第二章 分析問題推導....................................10
2-1 壓電材料基本方程式.................................10
2-2 壓電材料裂縫面邊界條件假設.........................15
2-3 含裂縫功能梯度壓電半無窮平板之面內破壞分析.........19
2-3.1求解含裂縫之功能梯度壓電無窮平板...................22
2-3.2求解不含裂縫之功能梯度壓電半無窮平板...............36
2-3.3將子問題疊加求解...................................40
第三章 數值運算方法....................................45
3-1 第一型奇異積分方程式...............................45
3-2 Guass-Chebyshev 的數值積分法.......................48
第四章 結果與討論......................................55
4-1 含裂縫之功能梯度壓電半無窮平板問題.................56
4-2 含裂縫之功能梯度PZT-4半無窮平板受均勻機械負載......61
4-3 含裂縫之功能梯度PZT-4半無窮平板受均勻機械與電負載..69
4-4 電負載對不同材料之含裂縫半無窮平板的強度因子的影響.82
第五章 結論............................................86
參考文獻................................................90
附錄A...................................................94
附錄B...................................................99
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