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研究生:陳志洋
研究生(外文):Chih-Yang Chen
論文名稱:具數值消散之結構相依外顯式積分法
論文名稱(外文):Structure – Dependent explicit Integration Method with Numerical Dissipation
指導教授:張順益張順益引用關係
口試委員:簡文郁廖文義
口試日期:2012-07-23
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:土木與防災研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:99
中文關鍵詞:無條件穩定數值消散外顯式積分法擬動態試驗
外文關鍵詞:Unconditional StabilityNumerical DissipationExplicit MethodPseudodymamic test
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  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
使用逐步積分法來分析複雜非線性結構的動態反應是非常普遍的,而擁有良好的數值消散特性,更是近年來積分法發展的重點。本文將提出一個新的外顯式積分法來進行擬動態實驗,其擁有外顯式積分法與內隱式積分法的優點,其擁有外顯式積分法的運算效率、無條件穩定與可以抑制高頻振態而不影響低頻振態的數值消散特性,且可以同時克服外顯式積分法與內隱式積分法在擬動態實驗上的個別缺點。本文將經由數值論例與擬動態實驗來詳細探討此新積分法的各種特性 ,尤其是在對於含有高頻振態的擬動態實驗上。

The step-by-step integration is the most frequently adopted way to obtain the dynamic responses of complex nonlinear structure system. The major topic of this study is to develop a new integration method which can have computational efficiency, unconditional stability, and favorable numerical dissipation, which can accurately integrate the low frequency modes while it can effectively filter out the spurious participation of high frequency modes. Some numerical examples and actual pseudodynamic tests were conducted to confirm the numerical properties of the proposed integration method, especially the characteristics of favorable numerical dissipation.

目 錄

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 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究內容概述 3
第二章 數值特性 5
2.1 新逐步積分法簡介 5
2.2 新逐步積分法的數值特性 7
2.2.1 線性系統下研擬參數α的範圍 10
2.2.2 穩定性 11
2.2.3 精準度 12
2.3 多自由度系統計算流程 14
第三章 擴大穩定性的方法 31
3.1 研擬擴大穩定條件的 值 31
3.2 穩定性 32
3.3 精確度 33
第四章 數值論例 47
4.1 論例一 無阻尼線彈性系統 47
4.2 論例二 勁度軟化系統 48
4.3 論例三 勁度硬化系統 49
4.4 論例四 擴大穩定條件勁度硬化系統 50
4.5 論例五 多自由度非線性系統 50
第五章 擬動態試驗 69
5.1 擬動態試驗 69
5.2 擬動態試驗之流程 69
5.3 擬動態試驗之誤差 70
5.4 擬動態試驗的儀器與設備 71
5.5 擬動態試驗結果 71
5.5.1 初始位移試驗 72
5.5.2 地震外力(線性) 73
5.5.2.1 實驗一 73
5.5.2.2 實驗二 74
5.5.3 地震外力(非線性) 75
第六章 結論 96
參考文獻 97



參考文獻

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[2] K. Subbaraj and M. A. Dokainish, "A survey of direct time-integration methods in computational structural dynamics--II. Implicit methods." Computers & Structures vol. 32, no. 6, 1989, pp. 1387-1401.
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[4] T. Belytschko and T. J. R. Hughes, Computational Methods for Transient Analysis, New York:North-Holland, 1983.
[5] H. M. Hilber, "Analysis and design of numerical integration methods in structural dynamic, "Earthquake Engineering Research Center, University of California, Berkeley, CA, 1976, Report no. EERC 76-29.
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[9] K. J. Bathe, Finite element procedures, New Jersey: Prentice hall Englewood Cliffs, 1996.
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[12] E. L. Wilson, "A Computer Program for the Dynamic Stress Analysis of Underground Structures," Division Structural Engineering and Structural Mechanics, University of California, Berkeley, 1968. SESM Report no.68-1,
[13] E. L. Wilson, I. Farhoomand, and K. J. Bathe, "Nonlinear Dynamic Analysis of Complex Structures," Earthquake Engineering and Structural Dynamics, vol. 1, pp. 241-252.
[14] H. M. Hilber, T. J. R. Hughes, and R. L. Taylor. "Improved numerical dissipation for time integration algorithms in structural dynamics," Earthquake engineering & structural dynamics, vol. 5, no. 3, 1977, pp. 283-292.
[15] T. Belytschko, H. J. Yen, and R. Mullen, "Mixed methods for time integration," Computer Methods in Applied Mechanics and Engineering, vol.17-18, 1979, pp. 259-275.
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[17] 張順益,「適用於擬動態試驗之具數值消散特性的外顯式積分法」,中國土木水利工程學刊,第十卷,第三期,1998,第493-503頁。
[18] G. Dahlquist, "A Special Stability Problem for Linear Multistep Methods, " BIT, vol. 3, 1963, pp. 27–43.
[19] R. D. Krieg, "Unconditional Stability in Numerical Time Integration Methods, " Journal of Applied Mechanics, Vol. 40, 1973, pp. 417–421.
[20] S. Y. Chang, "Explicit Pseudodynamic Algorithm with Unconditional Stability," Journal of Engineering Mechanics, ASCE, Vol. 128, No. 9, 2002, pp. 935-947.
[21] K. Takahashi et. al, "Nonlinear Earthquake Response Analysis of Structures by a computer Actuator On-Line System," Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Scince, University of Tokyo, 1975, No.8.


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