無網格局部皮得洛夫葛勒金法

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廖偉鈞(Wei-Chun Liao) 查詢紙本館藏

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機械工程學系

論文名稱

無網格局部皮得洛夫葛勒金法
(Meshless Local Petrov-Galerkin Method)

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摘要(中)

摘要
本文主要是在介紹無網格局部皮得洛夫葛勒金法(簡稱MLPG)分析彈性靜力問題，MLPG是利用變動最小平方法(簡稱MLS)來建立形狀函數，MLPG有著需要引入必要邊界條件的問題，根據原本由Atluri等人所提出的MLPG是利用懲罰法來引入必要邊界條件。MLPG是一完全無需有限元素建立的無網格法，也不用設置基底網格。MLPG之加權殘值定理積分式是侷限在一節點之局部的規則形狀區域(一般二維為:矩型、圓形,三維為:立方體、球型)以及邊界中求得。MLPG是較穩定的因為是利用局部加權殘值定理積分式。本文中也包含3項數值算例來分析不同情況下的彈性靜力問題，可以顯示MLPG法在分析彈性靜力時有著相當的效率以及精確度。最後本文也附上了程式可以方便日後對MLPG法之研究。

摘要(英)

ABSTRACT
In this essay, the Meshless Local Petrov-Galerkin (MLPG) method for solving problems in elasto-statics is developed and numerically implemented. Moving least squares approximation is employed for constructing shape functions. There is an issue of imposition of essential boundary conditions. The original MLPG proposed by Atluri et al. uses the penalty method. MLPG does not need any finite element mesh, it is a truly meshless method. The major idea in MLPG is, however, that the implementation of the integral form of the weighted residual method is confined to a very small local subdomain of a node. The MLPG is more sable due to the use of locally weighted residual integration. In this essay, there are three numerical examples to analyze the problem in elasto-statics in different situations. it shows MlPG is quite efficient and accuracy in analyzing the problem in elasto-statics. In the end of this essay, the program to study MLPG is enclosed.

關鍵字(中)

★ 無網格局部皮得洛夫葛勒金法
★ 變動最小平方法

關鍵字(英)

★ meshless local petrov-galerkin method
★ moving least square method

論文目次

目錄
中文摘要.................................................................... I
英文摘要…............................................................... II
目錄........................................................................... III
圖目錄....................................................................... V
表目錄....................................................................... VI
第一章緒論
1.1 前言................................................................... 1
1.2 文獻回顧........................................................... 1
1.3 研究目的........................................................... 4
1.3 本文架構........................................................... 4
第二章變動最小平方法
2.1 前言................................................................... 6
2.2 變動最小平方法基本理論............................... 6
2.2加權函數........................................................... 11
第三章無網格局部皮得洛夫葛勒金法
3.1 前言................................................................... 12
3.2 無網格局部皮得洛夫葛勒金法之推導........... 12
3.3 無網格局部皮得洛夫葛勒金法之程式流程... 20
第四章數值範例
4.1 前言............................................................... 22
4.2 範例1：補丁試驗............................................ 22
4.3 範例2：懸臂梁................................................ 25
4.4 範例3：中間挖一圓孔矩形平板.................... 29
第五章結論與未來發展
5.1 結論................................................................... 32
5.2 未來發展........................................................... 33
參考文獻.......................................................................... 34
附錄.................................................................................. 37

參考文獻

參考文獻
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指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2006-7-12

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