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論文中文名稱:新一族無條件穩定外顯式積分法 [以論文名稱查詢館藏系統]
論文英文名稱:A New Family of Unconditionally Stable Explicit Methods [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:工程學院
系所名稱:土木與防災研究所
畢業學年度:98
出版年度:99
中文姓名:王閔正
英文姓名:Min Zheng Wang
研究生學號:97428014
學位類別:碩士
語文別:中文
口試日期:2010-07-02
論文頁數:125
指導教授中文名:張順益
口試委員中文名:尹世洵;吳俊霖
中文關鍵詞:擬動態實驗時間步長外顯式積分法
英文關鍵詞:pseudodynamic testtime stepexplicit method
論文中文摘要:使用具有數值消散特性的逐步積分法已被認為是新發展逐步積分法的重要目標。然而,現今具有數值消散特性的逐步積分法幾乎都是內隱式積分法,而內隱式積分法在擬動態實驗上的應用較為繁複且不易,因而較少被採用。本論文將介紹新一族逐步積分法,此積分法不但具有外顯式與無條件穩定的數值特性,可使積分法的運算效率大幅度提高,同時也擁有數值消散的特性。可用以克服試驗時由於數值誤差或實驗誤差所引起的不正確高頻振態反應。因此新發展的積分法不僅可以應用在一般的動態歷時分析,也是擬動態實驗上克服高頻振動所引起誤差累積傳播效應的有效方式。我們將透過數值釋例及進行實際的擬動態實驗來加以驗證。
論文英文摘要:It is generally recognized that an integration method with favorable numerical dissipation becomes an important motive in developing a novel integration method. Although some dissipative integration methods have been developed, most of them are implicit methods, which generally involve an iteration procedure per time step. Thus, their pseudodynamic implementations are more complicated than those of explicit methods. A new dissipative explicit integration method has been proposed and is presented. This explicit method can have unconditional stability. In addition, it has favorable numerical dissipation, where the low frequency modes can be reliably integrated while the spurious-growth high frequency responses can be suppressed or even eliminated. This explicit method can be applied to solve the general structural dynamic problems both for time history analysis and pseudodynamic testing. Both numerical examples and actual pseudodynamic tests are conducted to confirm the numerical properties obtained from basic analysis.
論文目次:中文摘要 i
英文摘要 ii
誌 謝 iii
目 錄 iv
圖目錄 vi
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 4
第二章 新逐步積分法之數值特性 6
2.1 新逐步積分法簡介 6
2.2 新逐步積分法的數值特性 7
2.2.1 線性系統研擬 的範圍 10
2.2.2 穩定性 11
2.2.3 精確度 12
2.3 多自由度系統的計算流程 14
第三章 新逐步積分法之數值模擬 30
3.1 釋例一 瞬時勁度不變系統 30
3.2 釋例二 瞬時勁度軟化系統 31
3.3 釋例三 瞬時勁度硬化系統 32
3.4 釋例四 多自由度非線性彈簧-質量系統 33
第四章 新逐步積分法之擬動態實驗 54
4.1 擬動態實驗 54
4.2 擬動態實驗的流程 55
4.3 擬動態實驗的誤差傳播特性 55
4.4 試驗儀器與設備 56
4.4.1 試驗裝置 56
4.4.2 控制系統 56
4.4.3 量測系統 57
4.5 實際的擬動態實驗 57
4.5.1 新積分法初始勁度的量測 57
4.5.2 實驗步驟 58
4.6 擬動態實驗結果 59
4.6.1 自由振動 59
4.6.2 簡諧荷重 61
4.6.3 地震外力 62
第五章 擴大穩定條件的簡易方法 88
5.1 擴大穩定條件方法的簡介 88
5.2 數值特性 89
5.2.1廣義穩定與狹義穩定 89
5.2.2 精確度 91
5.3 數值釋例 92
5.3.1 釋例一 瞬時勁度不變系統 92
5.3.2 釋例二 瞬時勁度軟化系統 93
5.3.3 釋例三 瞬時勁度硬化系統 94
第六章 結論與建議 122
參考文獻 123
論文參考文獻:[1] E.L.Wilson, “A Computer Program for the Dynamic Stress Analysis of Underground Structures,” SESM Report No.68-1, Division Structural Engineering and Structural Mechanics, University of California, Berkeley, 1968.
[2] 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, 1973.
[3] G. Dahlquist, “ A Special Stability Problem for Linear Multistep Methods,” BIT, 3, pp. 27–43, 1963.
[4] H.M. Hilber, T.J.R. Hughes, and R.L. Taylor,“Improved Uumerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, Vol.55, pp.283-292, 1977.
[5] H.M. Hilber,“Analysis And Design of Numerical Integration Methods in Structural Dynamics.”EERC Report No.76-29. Earthquake Engineering Research Center, University of California, Berkeley, CA, 1976.
[6] J.C.Houbolt,“A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft,”Journal of the Aeronautical Sciences, Vol.17, pp.540-550, 1950.
[7] J.Chang and G.M.Hulbert,“A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation:The Generalized- Method.”Journal of Applied Mechanics, Transactions of the ASME, Vol.60, pp.371-375, 1993.
[8] M.W. Dobbs,“Comments on ‘Stability and Accuracy Analysis of Direct Integration Methods,’by Bathe and Wilson,”Earthquake Engineering and Structural Dynamics,Vol.2,pp.295-299, 1974.
[9] N.M. Newmark,“A method of Computation for Structural Dynamics.”Journal of Engineering Mechanics Division,ASCE,Vol.85,pp.67-94, 1959.
[10] O.C. Zienkiewicz, The Finite Element Method, McGraw-Hill, Book Co(UK)Ltd., Third Edition.,1977.
[11] P.B. Shing, and S.A. Mahin,“ Elimination of Spurious Higher-mode Response in Pseudodynamic Test,” Earthquake Engineering and Structural Dynamics, Vol.15.pp.425-445, 1987.
[12] P.B.Shing and S.A.Mahin,“Elimination of Spurious Higher-Mode Response in Pseudodynamic Tests.“Earthquake Engineering and Structural Dynamics,Vol.15, pp.425-445,1987.
[13] P.B. Shing and S.A. Mahin,“Experimental Error Propagation in Pseudodynamic Testing”Report No.UCB/EERC-83/12, Earthquake Engineering Research Center, University of California at Berkeley, June, 1983.
[14] R.D. Krieg, “ Unconditional Stability in Numerical Time Integration Methods,” Journal of Applied Mechanics, Vol. 40, pp. 417–421, 1973.
[15] R.W. Clough and J. Penzien, Dynamics of Structures, New York:McGraw-Hill,1993.
[16] S.Y. Chang,“Improved Numerical Dissipation for Explicit Method in Psudodynamic Test,”Earthquake Engineering and Structural Dynamics, Vol. 26, No3,pp.917-929,1997.
[17] S.Y.Chang,“Explicit Pseudodynamic Algorithe with Unconditional Stability,” Journal of Engineering Mechanics, ASCE, Vol.128, No.9, pp.935-947, 2002.
[18] S.Y.Chang,“A Series of Engergy Conserving Algorithms for Structural Dynamics,”Journal of the Chinese Institute of Engineers, Vol.19, No.2, pp.219-230, 1996.
[19] S.Y. Chang and W.I. Liao,“An Unconditionally Stable Explicit Method for Structural Dynamics,”Journal of Earthquake Engineering,Vol.9, No.3, pp.349-370, 2005.
[20] S.Y. Chang,“Improved Explicit Method for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, Vol.133, No.7, pp.748-760, 2007.
[21] T. Belytschko and T.J.R. Hughes, Computational Methods for Transient Analysis,New York:North-Holland,1983.
[22] T. Belytschko, and D.F. Schoeberle,“On the Unconditional Stability of An Implicit Algorithm for Nonlinear Structural Dynamics,”Journal of Applied Mechanics,Vol.17,pp.865-869, 1975.
[23] T.J.R. Hughes, The Finite Element Methods, Prentice-Hall, Inc., Englewood Cliffs, N.J.,1987.
[24] Takanashi, K., et al.,“Nonlinear Earthquake Response Analysis of Structure by a Computer-Actuator On-Line System”, Bull. Of Earthquake Resistant Structure Research Center, Institute of Industrial Science, University of Tokyo, No.8, 1975.
[25] 張順益,“無條件穩定外顯式積分法之發展”,中國土木水利工程學刊,第十三卷,第一期,第61~70頁,中華民國九十年四月。
[26] 張順益,“擬動態實驗”,中華民國工程學會,結構工程,第十一卷,第四期,第79~84頁,中華民國八十五年十二月。
[27] 張順益,“擬動態實驗之發展概況”,科學發展月刊,第二十七卷,第一期,第29~37頁,中華民國八十八年一月。
[28] 張順益,“擬動態試驗在地震工程上之應用”,土木技術,四月號,第十四期,第51~59頁,中華民國八十八年四月。
論文全文使用權限:同意授權於2010-08-24起公開