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論文中文名稱:具數值消散之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 Family of Unconditionally Stable Explicit Method with Numerical Dissipation [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:李盈陞
英文姓名:Ying-Sheng Li
研究生學號:97428020
學位類別:碩士
語文別:中文
口試日期:2010-07-02
論文頁數:142
指導教授中文名:張順益
指導教授英文名:Shuen-Yi Chang
口試委員中文名:尹世洵;簡文郁
口試委員英文名:Shih-Hsun Yin;Wen-Yu Chien
中文關鍵詞:無條件穩定外顯式積分法擬動態試驗
英文關鍵詞:unconditional stabilityexplicit methodpseudodynamic tests
論文中文摘要:逐步積分法為結構動態歷時分析所廣泛使用的方法,而具數值消散特性的積分法被認為是逐步積分法發展的重要方向。具數值消散特性的積分法幾乎都是內隱式積分法,內隱式積分法雖然可具有無條件穩定的特色,但其計算效率卻不如外顯式積分法,且外顯式積分法仍是擬動態試驗上較廣為採用的方式。本文將介紹新一族具數值消散特性的無條件穩定外顯式積分法,此積分法具有無條件穩定的特色使其可不考慮穩定條件而適用於一般結構動力問題的求解,且在運算效率上亦可大幅提高。在擬動態試驗上,新發展的逐步積分法更可藉由數值消散特性來抑制數值誤差與實驗誤差所產生的不正確高頻振態反應,成為克服因高頻振態引起誤差傳播與累積之有效方式。在本研究中將透過不同的數值釋例,以及進行實際的擬動態試驗來加以探討和驗證。
論文英文摘要:For the solution of structural dynamic problems, step-by-step integration methods are widely used and the methods that have numerical dissipation are considered to be important in the development of a new integration method. Although implicit methods can generally have unconditional stability, explicit methods generally preferred over implicit methods since they involve no iteration procedure or extra hardware in the pseudodynamic testing. This paper will propose a new family of unconditionally stable explicit method with numerical dissipation, which is bested to solving general structural dynamic problems. Due to the explicitness of each time step, this integration method can be implemented as simply as a general explicit method. In addition, the spurious participation of high frequency responses can be effectively eliminated in performing a pseudodynamic test since it has desired numerical dissipation. Numerical characteristics of this method in the solution of linear and nonlinear systems are analytically explored and analytical results are further confirmed through the numerically simulations and the actual pseudo-dynamic testing.
論文目次:目 錄

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 3
1.3研究內容概述 5
第二章 新逐步積分法之數值特性 7
2.1 新逐步積分法簡介 7
2.2 新逐步積分法的數值特性 9
2.2.1線性系統下研擬參數 的範圍 13
2.2.2穩定性 15
2.2.3精確度 15
2.3多自由度系統計算流程 19
第三章 數值釋例 38
3.1 釋例一 勁度線彈性系統 38
3.2 釋例二 瞬時勁度軟化系統 40
3.3 釋例三 瞬時勁度硬化系統 41
3.4 釋例四 多自由度非線性彈簧—質量系統 42
第四章 擬動態試驗 63
4.1 擬動態試驗 63
4.2 擬動態試驗的流程 64
4.3 擬動態試驗誤差的來源 64
4.4 擬動態試驗儀器與設備 65
4.4.1 試驗裝置 65
4.4.2 控制系統與量測系統 66
4.5 實際的擬動態試驗 66
4.5.1 新逐步積分法初始勁度的量測 67
4.5.2 試驗步驟 68
4.6 試驗結果 69
4.6.1 初始位移問題 69
4.6.2 簡諧荷重 71
4.6.3 地震外力 73
第五章 擴大穩定範圍的方法 101
5.1 擴大穩定範圍之建議方法 101
5.2 新逐步積分法的數值特性 101
5.2.1 研擬擴大穩定條件的σ值 102
5.2.2 精確度 105
5.3 數值釋例 106
5.3.1 釋例一 勁度線彈性系統 107
5.3.2 釋例二 勁度軟化系統 108
5.3.3 釋例三 勁度硬化系統 109
第六章 結論 138
參考文獻 139
論文參考文獻:參考文獻

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論文全文使用權限:同意授權於2011-08-24起公開