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論文中文名稱:具數值阻尼且為結構相依之逐步積分法的發展 [以論文名稱查詢館藏系統]
論文英文名稱:Development of Structure-Dependent Integration 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:99
出版年度:100
中文姓名:蔡欣芸
英文姓名:Shin-Yun Tsai
研究生學號:98428017
學位類別:碩士
語文別:中文
口試日期:2011-07-14
論文頁數:112
指導教授中文名:張順益
口試委員中文名:楊元森;吳俊霖
中文關鍵詞:逐步積分法無條件穩定擬動態實驗
英文關鍵詞:step-by-step integration methodunconditional stabilitypseudodynamic tests
論文中文摘要:具數值消散特性的積分法已被認定是逐步積分法的重要發展目標,但目前盛行的幾乎都是內隱式積分法。內隱式積分法雖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。且內隱式積分法因計算繁複,應用在擬動態實驗上也較不易。本文將介紹新一族具數值消散特性的無條件外顯式積分法,既具有內隱式積分法的無條件穩定優點,亦有外顯式積分法的運算速度,可大幅提高運算效率。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,成為抑制誤差傳播的有效方式。本文將以線性及非線性的數值論例證實新積分法的數值消散能力,並應用在擬動態實驗上,證明新積分法具有消除因實驗位移控制誤差帶來的不正確高頻反應。
論文英文摘要:For the solution of structure dynamic problems, the integration method with 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, witch is basted to solving general structural dynamic problems. Due to the explicitness of each time step, this family method involves no nonlinear iteration and thus it is very suitable for both time history analysis and pseudodynamic testing. In addition, many computational efforts can be saved in a time history analysis since there is no nonlinear iteration involved per time step. Both numerical examples and actual pseudodynamic tests are employed to confirm the superiority of the proposed new family method.
論文目次:中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
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 4
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 6
2.2.1 線性系統下研擬參數ρ的範圍 9
2.2.2 穩定性 10
2.2.3 精確度 11
2.3 多自由度系統計算流程 14
2.4 擴大穩定範圍的方法 16
2.4.1 擴大穩定範圍方法的數值特性 16
2.4.1.1 穩定性 17
2.4.1.2 精確度 18
第三章 數值模擬 42
3.1 論例一 線彈性系統 42
3.2 論例二 勁度軟化系統 43
3.3 論例三 勁度硬化系統 44
3.4 論例四 多自由度非線性系統 44
3.5 擴大穩定條件的數值論例 46
3.5.1 論例五 線彈性系統 46
3.5.2 論例六 勁度軟化系統 47
3.5.3 論例七 勁度硬化系統 47
第四章 擬動態試驗 76
4.1 擬動態試驗 76
4.2 擬動態試驗流程 76
4.3 擬動態試驗誤差的來源 77
4.4 擬動態試驗儀器與設備 77
4.4.1 試驗裝置 77
4.4.2 控制系統 78
4.4.3 量測系統 79
4.5 實際進行擬動態試驗 79
4.5.1 新逐步積分法初始勁度的量測 79
4.5.2 試驗步驟 80
4.6 試驗結果 81
4.6.1 線性系統 81
4.6.1.1 自由振動問題 81
4.6.1.2 地震外力 83
4.6.2 非線性系統 83
第五章 結論與建議 110
參考文獻 111
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論文全文使用權限:同意授權於2011-08-23起公開