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系統識別號 U0026-0106201014561400
論文名稱(中文) 應用微分再生核內插函數適點法於功能性梯度壓電材料中空圓柱殼之耦合分析
論文名稱(英文) A DRK Interpolation-Based Collocation Method for the Analysis of Functionally Graded Piezoelectric Hollow Cylinders under Electro-Mechanical Loads
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) 王建鑫
研究生(英文) Jian-Sin Wang
電子信箱 n6697411@mail.ncku.edu.tw
學號 n6697411
學位類別 碩士
語文別 中文
論文頁數 55頁
口試委員 指導教授-吳致平
口試委員-王永明
口試委員-胡宣德
中文關鍵字 DRK內插法  適點法  無網格法  耦合分析  功能性材料  圓柱殼 
英文關鍵字 DRK interpolation  Collocation method  Meshless methods  Coupled analysis  FG  Cylinders 
學科別分類
中文摘要 本文發展以微分再生核內插法(the differential reproducing kernel (DRK) interpolation)為基礎之無網格適點法,應用於三維簡支承功能性壓電材料中空圓柱殼之耦合分析。其功能性中空圓柱殼的材料性質則假設為沿著厚度方向呈指數律分佈。本DRK內插法中,每一個參考點的形狀函數是由具有Kronecker delta性質的原始函數(primitive functions)與滿足再生條件的改善函數(enrichment functions)所組成,可方便於幾何邊界條件之代入,與有限元素法的用法相似。本無網格法的另一創新在於其高階形狀函數的微分可經由一組微分再生條件求得,而非直接對再生核函數作微分。文中對無網格方法應用時相關之關鍵參數,諸如:最佳影響半徑範圍、基底函數的最高階次數以及影響功能性材料中空圓柱殼場變數的材料特性梯度指數等,均有討論,並作出合宜之建議。數值範例的結果顯示,本DRK內插適點法與現有的三維解有相當一致的結果且收歛迅速。
英文摘要 A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependence on this. In the present formulation, the shape function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of the present DRK interpolation, the essential boundary conditions can be readily applied, exactly like the implementation in the finite element method (FEM). An additional innovation of the present meshless method is that the shape functions for derivatives of the reproducing kernel (RK) functions are determined using a set of differential reproducing conditions, rather than differentiating these RK functions. In the implementation of the DRK interpolation-based collocation method presented in this work, several crucial parameters are discussed, such as the optimal support size and highest-order of the basis functions. The influence of the material-property gradient index on the field variables induced in the FG hollow cylinders is also studied.
論文目次 中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1 研究動機 1
1.2 本文內容 3
第二章 三維壓電力學 4
2.1 基本方程式 4
2.2 狀態空間方程式 7
2.3 無因次化 8
第三章 微分再生核內插法 11
3.1 再生核內插函數 11
3.2 再生核內插函數的推導 13
3.3 加權函數 15
第四章 應用問題解析 16
4.1 雙傅立葉級數方法展開 16
4.2 多層疊合壓電材料中空圓柱殼 17
4.3 功能性壓電材料中空圓柱殼 19
第五章 數值範例 21
5.1 單層均質壓電材料中空圓柱殼 21
5.2 多層疊合壓電材料中空圓柱殼 22
5.3 功能性壓電材料中空圓柱殼 23
第六章 結論 25
參考文獻 26
表 30
圖 35
附錄A 52
附錄B 53
附錄C 54
自述 55
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