Responsive image
博碩士論文 etd-0113106-172449 詳細資訊
Title page for etd-0113106-172449
論文名稱
Title
CPIM,改進之元素釋放法在工程結構分析之研究
CPIM, an Improved Element Free method for Engineering Application
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
105
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2005-12-23
繳交日期
Date of Submission
2006-01-13
關鍵字
Keywords
影響區域、元素釋放法、移動式最小平方法、節點內插法
Element Free Galerkin Method, Point Interpolation Method, Moving Least Square Method, Influence domain
統計
Statistics
本論文已被瀏覽 5693 次,被下載 1459
The thesis/dissertation has been browsed 5693 times, has been downloaded 1459 times.
中文摘要
中文摘要

本文主旨在改善節點內插法( Point Interpolation Method ,PIM )於元素釋放法( Element Free Galerkin Method ,EFG )的應用。元素釋放法的特色為使用不同節點之間影響區域的交集來建立離散節點的關聯性,只需使用節點資料,完全不需要元素。

EFG建立形狀函數的技巧分為擬合與內插兩類。擬合的方式利用移動式最小平方法(Moving Least Square Method,MLS),MLS-EFG在數值分析上有穩定的效果,但它需使用者自訂較多個數值參數、計算量大且邊界條件不能直接引用;內插的方式稱為節點內插法,使用節點座標資料進行計算,邊界條件可以直接使用且計算量少,但常常出現無解的(Singular)取樣點內插函數係數。

本文嘗試提出配位式節點內插法(Coordination Point Interpolation Method ,CPIM),該法兼具前兩者特色且不需要額外數值參數,利用MLS-EFG影響區域的概念,針對取樣點鄰域,搜尋反矩陣存在的相關有效節點,保證取樣點內插函數的係數存在。經由分析顯示,CPIM有良好的收斂性與精確計算結果,而且計算效益優於MLS-EFG。本文最後並對CPIM提出未來的發展方向與建議。
Abstract
Abstract

To improve the application of Point Interpolation Method (PIM) in Element Free Galerkin Method (EFG) is the aim of this study. The trait of EFG is using overlap of influence domain between different nodes to construct discretization nodes’ connection. EFG just uses nodal data, but not element.

For constructing shape function, EFG has two types of methods, Fitting and Interpolation. Fitting uses Moving Least Square Method (MLS). MLS-EFG has stable effect on numerical analysis; however, users who use it need to choose more numerical parameters and do more computation. Besides, users can not apply boundary conditions directly when using MLS-EFG. Interpolation method applies nodal coordinates to proceed computation, and it called PIM. Boundary conditions could be used directly and less computation is needs while using PIM. However, the coefficient of interpolation function of sample is singular.

This study tries to construct Coordination Point Interpolation Method. It owns advantages of both methods that mentioned above, and extra numerical parameters are not needed. It applies the notion of influence domain of MLS-EFG, then search correlative efficient nodes which are contained in near field of sample. The correlative efficient nodes make up matrix that con cause inverse matrix. In addition, via numerical simulations, it shows that CPIM has excellent convergence and accurate solution, and is better that MLS-EFG.
目次 Table of Contents
目錄
表目錄 ……………………………………………………III
圖目錄 ……………………………………………………IV
符號表 ………………………………………………………V
第一章 緒論 ………………………………………………1
1.1 研究動機 ………………………………………………1
1.2 文獻回顧 ………………………………………………3
1.3 內容大綱 ……………………………………………5
第二章 元素釋放法理論 ……………………………………7
2.1 移動最小平方近似法 ……………………………………7
2.2 節點選取 …………………………………………………11
2.3 權重函數的形式與探討 …………………………………12
2.4 一致性檢驗 ………………………………………………14
第三章 元素釋放法的改善 …………………………………20
3.1 Constrained Moving Least Squares Method(CMLS) …20
3.2 Point Interpolation Method(PIM) ………………………24
3.3 Coordination Point Interpolation Method(CPIM) ……28
第四章 元素釋放法於彈性體力學之應用 ………………32
4.1 彈性體控制方程式 ………………………………………32
4.1.1 廣義虎克定律……………………………………………32
4.1.2 運動方程式 ………………………………………………34
4.2 彈性體方程式使用元素釋放法離散 ……………………35
4.2.1 CPIM對於彈性體控制方程式的離散 …………………38
4.2.2 EFG-MLS對於彈性體控制方程式的離散 ……………40
4.3 元素釋放法分析的流程 …………………………………45
第五章 數值算例 …………………………………………50
5.1 算例一 ……………………………………………………51
5.2 算例二 ……………………………………………………53
5.3 算例三 ……………………………………………………55
第六章 結論與建議 ………………………………………86
6.1 結論 ………………………………………………………86
6.2 未來發展與建議 …………………………………………87
參考文獻 ……………………………………………………89
參考文獻 References
參考文獻

1.Gingold R.A., and J.J. Monaghan, (1977) “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars,” Monthly Notices of the Royal Astronomical Society, Vol. 181, pp. 375~389.

2.Lucy L.B.,(1977) ”Numerical Approach to Testing the Fission Hypothesis,”Astrophysical Journal,Vol. 82, pp. 1013~1024,

3.Nayroles B., G. Touzot, and P. Villon, (1992) “Generalizing the Finite Element Method:Diffuse Approximation and Diffuse Element” Computational Mechanic, Vol. 10, pp. 307~318.

4.Belytschko T., Lu Y.Y., Gu L.,(1994) “Element-Free Galerkin Methods,” International Journal for Numerical Methods in Engineering, Vol. 37, pp.229~256.

5.Belytschko T., Y. Krongauz, M. Flemming, D. Organ and W.K. Liu, (1996) ”Smoothing and Accelerated Computations in the Element-Free Galerkin Methods,” Journal of Computational and Applied Mechanics Vol.74, pp. 111~126.

6.Zhu, T. and S.N. Atluri,(1998) “A Modified Collocation Method and a Penalty Formulation for Enforcing the Essential Boundary Conditions in the Element Free Galerkin Method,” Computational Mechanics, Vol. 21, pp. 211~222.

7.Liu, W. K., S. Jun and Y. F. Zhang, (1995)“Reproducing Kernel Particle Method,” Interational Journal for Numerical Methods in Fluids, Vol. 20, pp.1081~1106.

8.Liu G.R.,and Gu Y.T.,(1999) “A Point Interpolation Method,” in Proc. 4th Asia-Pacific Conference on Computational Mechanics, December, Singapore, pp.1109~1014.

9.Liu G.R. and Gu, Y.T.,(2000) ”Vibration analysis of 2-D Solids by the Local Point Interpolation Method,” in Proc. 1st International Conference on Structural Stability and Dynamic, December 7-9, Taiwan, 411~416.

10.Liu G.R. and Gu Y.T.,(2002) “Comparisons of Two Meshfree Local Point Interpolation Methods for Structural Analyses,” Computational Mechanics, Vol. 29, pp. 107~121.

11.Liu G.R. (2003), Meshfree Methods: Moving Beyond the Finite Element Method, CRC Press LLC, New York.

12.朱崧豪(2001),「無網格法分析彈性靜力問題之研究」,碩士論文,中原大學土木工程學系碩士班。

13.沈國瑞(2002),「無元素分析之積分權值調整法」,博士論文,國立中央大學土木工程學系博士班。

14.朱俊平(2003),「元素釋放法計算加速之研究」,碩士論文,中原大學土木工程學系碩士班。

15.張智星(2000),「MATLAB 程式設計與應用」,清蔚科技出版部,新竹。
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:校內立即公開,校外一年後公開 off campus withheld
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code