臺灣博碩士論文加值系統

本文應用微分再生核(DRKP)方法於簡支承多層疊合彈性與壓電材料板之靜力分析。有別於傳統文獻中之再生核方法，直接以近似形狀函數進行微分運算來獲得導函數相應之形狀函數；DRKP方法則以基底函數微分再生條件來決定高階導函數之形狀函數。本文應用廣義Hellinger-Reissner能量穩值原理，經由變分推衍程序獲得三維電彈力學Euler-Lagrange方程式和可能的邊界條件。依據DRKP適點方法，求解簡支承多層疊合彈性或壓電材料板受電場和彈性場外載重作用下的靜力行為。結果顯示DRKP方法是一種十分精準並且快速收歛的無網格方法。

A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional piezoelectricity and the possible boundary conditions are derived. A point collocation method based on the present DRKP approximations is formulated for the static analysis of simply supported, multilayered elastic and piezoelectric plates under electro-mechanical loads. It is shown that the present DRKP method indeed is a fully meshless approach with excellent accuracy and fast convergence rate.

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
第一章 緒論 1
1.1 研究動機 1
1.2 本文內容 3
第二章 廣義Hellinger-Reissner能量穩值原理 5
2.1 基本三維電彈力學方程式 5
2.2 Hellinger-Reissner能量函數 6
2.3 三維電彈力學Euler-Lagrange方程式 9
第三章 微分再生核(DRKP)方法 14
3.1 再生核形狀函數 14
3.2 再生核形狀函數的推導 16
3.3 加權函數 18
第四章 應用問題解析 20
4.1 無因次化 20
4.2 雙傅利葉級數方法展開 21
第五章 數值範例與綜合討論 25
5.1 單層壓電材料板 25
5.2 多層疊合複合材料板 27
5.3 多層疊合壓電材料板 30
第六章 結論 34
參考文獻 35
表5.1 各種壓電材料的彈性係數、壓電係數與介電電容率
等參數值 40
表5.2 單層壓電材料板受側向電位勢之收斂性比較 41
表5.3 多層疊合複合材料板[00/900/00]外表面受正向載重之
收斂性比較 42
表5.4 各種寬厚比之多層疊合複合材料板[00/900/00]外表面
受正向載重收斂性比較 43
表5.5 多層疊合壓電材料板受彈性場外載重作用之收斂性
比較 44
表5.6 多層疊合壓電材料板受電位勢作用之收斂性比較 45
表5.7 多層疊合壓電材料板受電位移作用之收斂性比較 46
圖1.1 複合層板之幾何形狀與正交座標示意圖 47
圖5.1 多層疊合壓電材料板之疊層排序與廣域座標示意圖 48
圖5.2 疊序[00/900/00]複合材料層板受正向載重作用各變數
沿厚度方向之變化圖 49
圖5.3 多層疊合壓電材料板受上下表面正向載重作用各變
數沿厚度方向之變化圖 53
圖5.4 多層疊合壓電材料板受上下表面電位勢作用各變數
沿厚度方向之變化圖 56
圖5.5 多層疊合壓電材料板受上下表面電位移作用各變數
沿厚度方向之變化圖 59
自述 62

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