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論文中文名稱:張氏積分法在結構動力學上的應用 [以論文名稱查詢館藏系統]
論文英文名稱:Application of Chang explicit method to Structural Dynamics [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:102
出版年度:103
中文姓名:彭泓淇
英文姓名:Hung-Chi Peng
研究生學號:101428014
學位類別:碩士
語文別:中文
口試日期:2014-06-25
論文頁數:156
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:無條件穩定外顯式積分法OpenSees
英文關鍵詞:Explicit MethodUnconditional StabilityOpenSees
論文中文摘要:逐步積分法為動態歷時分析所廣泛運用的方法,而逐步積分法又分為內隱式積分法與外顯式積分法,前者雖具有無條件穩定的特色,但計算過程複雜繁瑣導致效率不佳,後者雖然每一步的計算非常的簡單與省時,卻往往為了滿足穩定條件的限制而被迫採用非常小的積分時間步長來進行逐步積分,因而需要較大的積分總步數,因此一個理想的積分法希望具有無條件穩定且計算簡單省時的優點,本文所採用的張氏積分法就有此特性。OpenSees是一個以C++編譯而成的有限元素軟體,為了探討張氏積分法的實用性以及計算效率上的優越性,特別將張氏積分法撰寫成C++的程式碼加入OpenSees當中,並且透過OpenSees建立各種不同結構型式的分析模型來進行動態歷時分析。除了張氏積分法以外,也利用等平均加速度積分法與Newmark外顯式積分法來進行動態歷時分析,並將分析所得結果相互比較,以證實張氏積分法能廣泛應用於求解各種不同線性及非線性的結構動力問題。同時,也可驗證張氏積分法的數值特性。最後則利用每次動力分析所使用的CPU時間比較,來進一步證實此積分法的計算效率。
論文英文摘要:Step-by-step methods are widely used in the solution of dynamic problems, and they are classified as implicit and explicit methods. Implicit methods can have unconditional stability, however, the involvement of an iteration procedure lead to computationally inefficiency. Although the calculation of each time step of explicit method is simple, it can only have conditional stability and thus a small time step may be required to meet stability conditions. Therefore, an ideal integration method would like to have explicit formulation and unconditional stability simultaneously. Since Chang explicit method can integrate these two properties together, it is adopted in this study. OpenSees is a finite element software, where the code was written by C++ language. In order to study the feasibility and computational efficiency of Chang explicit method, its computing procedure is implemented into OpenSees for the dynamic analysis. Consequently, many structural dynamic problems are solved by Chang explicit method. The structural systems considered herein may be linear elastic or nonlinear. In addition, the structural nonlinearity includes both material nonlinearity and geometric nonlinearity. Both the Newmark explicit method and the constant average acceleration method are also used to solve all the structural dynamic problems for comparisons. As a result, the feasibility of using Chang explicit method to perform any dynamic analysis is verified. In addition, it is evident from the comparison of CPU time for each dynamic analysis that Chang explicit method is computationally efficient in the solution of an inertial type problem when compared to the Newmark explicit method and the constant average acceleration method.
論文目次:中文摘要 i
英文摘要 iii
誌謝 v
目錄 vii
圖目錄 xi
表目錄 xvii
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 3
第二章 數值特性 5
2.1 張氏積分法簡介 5
2.2張氏積分法的數值特性 6
2.2.1 穩定性 10
2.2.2 精確度 11
2.3 多自由度系統計算流程 13
第三章 數值分析軟體介紹 19
3.1 OpenSees及TCL簡述 19
3.2 OpenSees之概述 19
3.2.1 ModelBuilder輸入內容 20
3.2.2 Analysis輸入內容 21
3.3 OpenSees 程式架構 22
3.4 OpenSees整體分析流程 23
3.4.1 newStep() 25
3.4.2 solveCurrentStep() 26
3.4.3 commit() 26
3.5 OpenSees在Windows系統上的編譯設定 29
3.6 OpenSees Navigator 30
3.6.1 OpenSees Navigator簡介 30
3.6.2 OpenSees Navigator設定 30
第四章 OpenSees新增張氏積分法類別 51
4.1張氏積分法程式中計算流程 51
4.2 張氏積分法程式設計與更改 56
4.2.1 ChangExplicit04.h新增宣告 56
4.2.2 ChangExplicit04.cpp新增定義 57
4.2.3 ChangExplicit04.cpp新增程式內容 59
第五章分析論例 73
5.1 鋼筋混凝土系統分析 73
5.2 簡單桁架系統分析 75
5.3帶隔震底座的框架系統分析 76
5.4剛性樓板系統分析 78
5.4.1 考慮 效應之剛性樓板結構系統 80
5.5 線性、軟化及硬化之分析 82
5.6殼元素系統分析 82
5.7 L型板殼系統分析 83
5.8 基礎橋梁結構分析 85
5.9 實體元素系統分析 86
第六章 結論與建議 137
參考文獻 139
附錄
A ChangExplicit.h 143
B ChangExplicit.cpp 145
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論文全文使用權限:同意授權於2014-08-06起公開