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論文中文名稱:具數值消散能力且不需疊代之積分法 [以論文名稱查詢館藏系統]
論文英文名稱:A Family of Non-iterative Integration Method with Desired 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:101
出版年度:102
中文姓名:林士偉
英文姓名:Shih-Wei lin
研究生學號:100428082
學位類別:碩士
語文別:中文
口試日期:2013-06-20
論文頁數:111
指導教授中文名:張順益
口試委員中文名:簡文郁;吳俊霖
中文關鍵詞:外顯式積分法無條件穩定數值消散擬動態試驗
英文關鍵詞:Explicit MethodUnconditional StabilityNumerical DissipationPseudodynamic test
論文中文摘要:以逐步積分法來分析結構動力的問題已經非常的普遍,而具有數值消散特性的逐步積分法更是近年來發展的重要目標。本論文將介紹一個新的逐步積分法,此積分法將具有外顯式積分法的運算效率,以及內隱式積分法的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,同時克服外顯式與內隱式積分法之間的缺點。不論是數值消散特性或是運算效率的比較,本論文將以自由振動與強迫振動在線性及非線性的數值論例中加以驗證與討論。最後將應用於擬動態試驗上,證明本積分法在含有高頻振態的擬動態試驗上依然具有良好的數值消散特性及積分的正確性。
論文英文摘要:A family of integration methods has been developed for structural dynamics and earthquake engineering. In general, it has unconditional stability and second order accuracy. In addition, it can possess the favorable numerical dissipation properties that can be continuously controlled. In particular, it can have zero damping. This numerical damping is helpful to suppress or even eliminate the spurious growth of high frequency modes while the low frequency modes are almost unaffected. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it is very computationally efficient when compared to a general second-order accurate integration method, such as the constant average acceleration method.
Numerical properties of the proposed family method are obtained through the basic analysis and are confirmed by numerical examples. In addition, its application to pseudodynamic testing is also implemented and a series of actual pseudodynamic tests are performed to confirm the feasibility and superiority of the proposed family method.
論文目次:中 文 摘 要 i
英 文 摘 要 ii
致 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 4
第二章 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α的範圍 13
2.2.2 穩定性 16
2.2.3 精準度 17
2.3 多自由度系統計算流程 19
第三章 擴大穩定範圍 37
3.1 擴大穩定範圍的方法 37
3.2 研擬擴大穩定條件的σ值 38
3.3 穩定性 40
3.4 精確度 40
第四章 數值論例 55
4.1 線彈性系統 55
4.2 勁度軟化系統 56
4.3 勁度硬化系統 57
4.4 擴大穩定勁度硬化系統 58
4.5 多自由度非線性系統 58
第五章 擬動態試驗 79
5.1 擬動態試驗 79
5.2 擬動態試驗流程 79
5.3 擬動態試驗的誤差 80
5.4 擬動態試驗的儀器與設備 81
5.4.1 試體裝置 81
5.4.2 施力控制系統 81
5.4.3 量測系統 82
5.5 擬動態試驗結果 82
5.5.1 初始勁度的量測 82
5.5.2 初始位移試驗 83
5.5.3 初始位移試驗(非線性) 84
5.5.4 地震外力(線性) 85
5.5.5 地震外力(非線性) 86
第六章 結論 107
參考文獻 109
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論文全文使用權限:同意授權於2016-08-13起公開