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論文中文名稱:直接—迭代混合法於結構非線性歷時分析之應用 [以論文名稱查詢館藏系統]
論文英文名稱:Application of Direct-Iterative Hybrid Solution in Structural Nonlinear Time History Analysis [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:土木工程系土木與防災碩士班
畢業學年度:105
畢業學期:第一學期
中文姓名:林佳章
英文姓名:Lin, Jia-Zhang
研究生學號:103428079
學位類別:碩士
語文別:中文
口試日期:2017/01/17
論文頁數:48
指導教授中文名:楊元森
口試委員中文名:王偉仲;謝東儒
中文關鍵詞:結構非線性歷時分析預處理直接—迭代混合法
英文關鍵詞:Structural Nonlinear Time History AnalysispreconditionerDirect-Iterative Hybrid Solution
論文中文摘要:大型而複雜結構物的非線性歷時分析通常需要龐大運算量。耐震設計係以使結構物能夠達到「小震不壞、中震可修、大震不倒」的耐震設計為基本精神,但要驗證大震不倒不容易實現。世界各主要地震帶國家的耐震性能設計法逐漸要求更清楚地檢視結構物在受各種地震力作用下的耐震能力及損害能符合設計要求。目前普遍最嚴謹的方法是進行非線性歷時分析。而非線性歷時分析的冗長運算時間阻礙了在工程上的普及性。以本研究的測試案例分析曾達數週之久。
本研究檢視非線性歷時分析的運算流程,針對流程中最耗時的求解聯立方程作改良。我們結合直接法和迭代法優點的混合法來取代結構分析一般常使用的直接法。本研究採用的混合法之核心思想是將直接法分解的三角矩陣作為迭代法的預處理矩陣(preconditioning matrix),使下一次求解使用迭代法能夠快速收斂,進而使求解聯立方程的運算時間大幅縮減。本論文並以數個測試案例輔以說明直接—迭代混合法加速運算的效率,其加速運算時間最高可達7.76倍。
論文英文摘要:Nonlinear time history analysis in large complex structures typically needs impractically huge computational resources. A general philosophy of the seismic design is to make structures damage free under minor earthquakes, repairable under moderate earthquakes, and with collapse prevention under extreme earthquakes. The developing performance based seismic design generally requests engineers to check seismic capability of structures under extreme earthquakes, where the nonlinear time history analysis is one of the best manners to satisfy the requirement. However, it is difficult to check the collapse prevention in practical applications due to many difficulties including the huge computationally time and cost for nonlinear time history analysis. The computation time in our tests case can up to several weeks, which is much longer than most practical engineers can accept. This work examined the process of nonlinear time history analysis aiming to improve the most expensive runtime routine: solving linear equation. Based on OpenSees platform, this work investigated a direct-iterative hybrid solution and compared it with a direct solver. The main idea is to use triangular matrices which are factorized by a direct solver as a preconditioner to better facilitate the iterative method to converge quickly in the next time step. This work also used several cases to test the improvement of the direct-iterative hybrid solution. A speedup of up to 7.76 was observed in the tests.
論文目次:摘 要 i
ABSTRACT ii
誌 謝 iv
目 錄 v
表目錄 vii
圖目錄 ix
第一章 緒 論 1
1.1 研究背景 1
1.2 研究動機與目的 1
1.3論文架構 1
第二章 結構非線性歷時分析 3
2.1 有限元素分析 3
2.2稀疏矩陣壓縮格式 5
2.3 非線性歷時分析之數學式 6
2.3.1 Newmark 積分法 8
2.3.2 系統方程式 9
2.3.3求解聯立方程 11
2.4非線性歷時分析流程 12
第三章 直接—迭代混合法 14
3.1迭代法預處理 14
3.1.1 LU預處理 14
3.2直接—迭代混合法概念 15
3.3直接—迭代混合法流程 16
3.4 程式庫簡介 17
3.4.1 有限元素分析程式OpenSees 17
3.4.2 直接法求解器UMFPACK 17
3.4.3 迭代法求解器PARALUTION 17
3.5 直接─迭代混合法實作 18
3.5.1 PARALUTION增加UMFPACK預處理介面 18
3.5.2 OpenSees增加混合法求解器 21
第四章 模型測試 24
4.1 地震歷時資料 24
4.2測試環境 25
4.3 測試模型NINESTORY 26
4.3.1 模型資訊 26
4.3.2 測試結果 27
4.4 測試模型37STORY 30
4.4.1 模型資訊 31
4.4.2 測試結果 32
4.5 測試模型M3S 35
4.5.1 模型資訊 35
4.5.2測試結果 36
4.6 測試模型M6S4 38
4.6.1 模型資訊 39
4.6.2 測試結果 39
4.7 模型加速比 41
4.7.1閥值測試 41
第五章 結論與建議 44
參考文獻 45
附 錄 直接—迭代混合法主要程式碼 47
論文參考文獻:1. Sparse Matrix Compression Formats, Web address:http://www.cs.colostate.edu/~mcrob/toolbox/c++/sparseMatrix/sparse_matrix_compression.html. Accessed in 2016.
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11. Matlab, Web address:https://www.mathworks.com/products/matlab.html. Accessed in 2016.
12. P. Labs. Paralution, Web address:http://www.paralution.com/. Accessed in 2016.
13. OpenMP.org, Web address:http://openmp.org/. Accessed in 2016.
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21. Yang, Y. S., Wang, W., & Lin, J. Z. (2017). "Direct-iterative Hybrid Solution in Nonlinear Dynamic Structural Analysis," Computer-Aided Civil and Infrastructure Engineering. (Accepted)
論文全文使用權限:同意授權於2017-02-07起公開