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論文中文名稱:適用於一般結構動力問題與擬動態試驗之具數值消散能力的外顯式積分法 [以論文名稱查詢館藏系統]
論文英文名稱:A New Explicit Method with Numerical Dissipation for Structural Dynamics
and Pseudodynamic Tests [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:工程科技研究所
畢業學年度:99
出版年度:100
中文姓名:許琦偉
英文姓名:Chi-Wei Hsu
研究生學號:95679037
學位類別:博士
語文別:中文
口試日期:2011-07-08
論文頁數:188
指導教授中文名:張順益
口試委員中文名:呂良正;黃炯憲;鍾立來;尹世洵;楊元森
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
英文關鍵詞:Unconditional StabilityNumerical DissipationExplicit MethodPseudodymamic tests
論文中文摘要:由理論分析來求解複雜非線性結構的動態反應是十分困難的事,最常見的方法就是使用逐步積分法。發展擁有數值消散能力的逐步積分法,更是近幾十年積分法發展的重點,因為數值消散特性的逐步積分法已被認為是擬動態試驗上克服因高頻振態所引起誤差累積傳播效應最有效的方式。然而,逐步積分法分成內隱式與外顯式,外顯式運算簡潔有效率,但有穩定條件;內隱式沒有穩定條件,但每一步計算較繁瑣,而且目前擁有數值消散的積分法大多為內隱式。
本文提出一個新的外顯式逐步積分法,擁有外顯式積分法的運算效率、二階精確度、無條件穩定與可控制且只會抑制高頻振態而不影響低頻振態的數值消散特性。此新積分法不止適用於一般數值分析,而且也十分適用於擬動態試驗上,用以克服試驗時由於數值誤差或試驗誤差所引起不正確的高頻振態反應。最後本文將經由數例、擬動態試驗與分析來驗證新積分法的優異數值特性。
論文英文摘要:Analyzing dynamic responses of complex nonlinear structure systems through theoretical calculation is extremely difficult and the step-by-step integration method is the most frequently adopted way to conduct this analysis. Numerous efforts have recently been made for developing integration algorithm with controllable numerical dissipation in the high-frequency response domain, because it has been recognized that numerical dissipation is an effective way for suppressing the spurious high-frequency modes. Integration algorithms are generally divided into “explicit methods” and “implicit methods.” Explicit methods are computationally efficient, but not unconditionally stable; implicit methods, however, can be unconditionally stable, but their implementation in a computer program is more complex. In general, most integration methods with numerical dissipation are implicit methods.
The present study proposes a new explicit integration method which possesses computational efficiency of explicit methods, two order accuracy, unconditional stability, and controllable numerical dissipation that focuses on high-frequency responses but has no impact on low-frequency responses. This method is suitable not only for numerical analyses, but also for pseudodynamic tests due to the existence of numerical dissipation for eliminating the spurious high-frequency response. Furthermore, the study, based on numerical examples, pseudodynamic tests and analyses, supports advantageous numerical characteristics of the new explicit method proposed.
論文目次:目 錄

摘 要 i
Abstract ii
誌 謝 iv
目 錄 vi
圖目錄 ix
表目錄 xiii
第一章 緒 論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 研究方法 4
1.4 論文組織與架構 5
第二章 逐步積分法與結構相依外顯式積分法 8
2.1 逐步積分法 8
2.1.1 差分方程式 8
2.1.2  內穩式積分法概述 9
2.1.3 外顯式積分法 12
2.1.4  Chang外顯式積分法 (Chang Explicit Method) 14
2.1.5  HHT-α內隱式積分法 (HHT-α Method) 17
2.2 結構相依外顯式積分法 18
2.2.1 結構相依外顯式積分法發展 18
2.2.2 結構相依外顯式積分法TypeⅠ與TypeⅡ 21
第三章 結構相依外顯式積分法數值特性 23
3.1 SEM -Ⅰ與SEM -Ⅱ的數值特性 23
3.1.1 瞬時非線性程度與放大矩陣 23
3.1.2 廣義穩定、狹義穩定與數值參數 值 26
3.1.3 頻譜半徑 30
3.1.4 相對週期誤差與數值阻尼 40
3.1.5 改良穩定性的方法 46
3.2 結構相依外顯式積分法積分流程 61
3.2.1 積分流程一 61
3.2.2 積分流程二 66
3.2.3 特例探討-不可逆的質量矩陣 69
第四章 數值模擬 72
4.1 初始位移問題 72
4.2 彈塑性問題 77
4.3 瞬時勁度軟化問題 81
4.4 瞬時勁度硬化問題 86
4.5 擴大穩定性的改良方法驗證 90
4.6 不可逆質量矩陣問題 94
4.7 二階精確度驗證 97
4.8 大自由度非線性彈簧質量系統運算時間比較 103
4.9 Drain-2DX 數例 107
第五章 擬動態試驗設置與試驗結果 116
5.1 擬動態試驗 116
5.1.1 擬動態試驗流程 117
5.1.2 擬動態試驗的儀器與設備 118
5.1.3 擬動態試驗的誤差 118
5.2 擬動態試驗界面發展 122
5.2.1 擬動態試驗界面發展原則 122
5.2.2 PID控制 123
5.2.3 校正、荷重計讀取、位移控制、一次性位移控制與外力歸零任務單元 125
5.2.4 離散位移制動與單步擬動態試驗任務單元 130
5.2.5 初始勁度量測 133
5.2.6 擬動態試驗任務流程 134
5.3 擬動態試驗結果 137
5.3.1 初始位移問題 137
5.3.2 小變位地震外力 143
5.3.3 大變位地震外力 147
第六章 結論與建議 151
6.1 結論 151
6.2 建議 152
參考文獻 153
附錄 158
論文參考文獻:參考文獻

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