強震中橋梁極限破壞三維分析

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姓名

蘇俊全(Chun-Chuan Su) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

強震中橋梁極限破壞三維分析
(Numerical Simulation on Ultimate Stage of Bridges under Earthquakes by 3D Vector Form Intrinsic Finite Element Method)

相關論文

★ 隔震橋梁含防落裝置與阻尼器之非線性動力反應分析研究	★ 橋梁碰撞效應研究
★ 應用位移設計法於雙層隔震橋之研究	★ 具坡度橋面橋梁碰撞效應研究
★ 橋梁極限破壞分析與耐震性能研究	★ 應用多項式摩擦單擺支承之隔震橋梁研究
★ 橋梁含多重防落裝置之極限狀態動力分析	★ 隔震橋梁之最佳化結構控制
★ 跨越斷層橋梁之極限動力分析	★ 塑鉸極限破壞數值模型開發
★ 橋梁直接基礎搖擺之極限分析	★ 考量斷層錯動與塑鉸破壞之橋梁極限分析
★ Impact response and shear fragmentation of RC buildings during progressive collapse	★ 應用多項式滾動支承之隔震橋梁研究
★ Numerical Simulation of Bridges with Inclined	★ 橋梁三維極限破壞分析

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摘要(中)

依據過去地震經驗發現橋梁常遭受嚴重之損害，而橋梁支承裝置、橋柱之損壞與落橋所造成的損失更為嚴重，為模擬橋梁於強震中極限破壞情形，本研究利用向量式有限元素(Vector Form Intrinsic Finite Element) 之空間梁元素建立橋梁數值分析模型，模擬含防止落橋裝置之不同支承型式橋梁於大地震時極限狀態的反應。向量式有限元為一新近發展之結構分析方法，相較於傳統有限元素方法，向量式有限元之空間梁元素對於有大變形、大旋轉、大變位或剛體運動之問題，能以更簡易之運算處理。
為此，本研究開發新元素與新分析功能於空間向量式有限元素法，新元素包含線性彈簧元素(Linear Spring)、雙線性彈簧元素(Bilinear Spring)、具可開孔塑性彈簧元素(Gap or Hook Plastic Spring)；新分析功能包含平面滑動摩擦分析、位移控制地表運動及構件斷裂模擬等，經由算例與有限元素方法(SAP2000)相較，證實所發展之新元素與新分析方法之正確性。過去VFIFE使用中央差分法處理雷利阻尼相關問題時會有數值發散現象，所以本文改採用隱式Newmark-β直接積分求解運動方程式，研提增量迭代計算程序，求得下一步時間之位移、速度與加速度反應，同時計算構件回復力與阻力內力，成功引入雷利阻尼分析(Rayleigh Damping Analysis)於空間向量式有限元素法。最後本研究再依此建立橋梁三維數值分析模型，輸入水平雙向地表位移紀錄，分析探討防止落橋裝置與支承、橋墩柱間受近斷層地震下極限狀態之互制關係。

摘要(英)

In the past extreme earthquake, observed from the damaged bridges, bearing failure, column failure and deck unseating caused a more serious loss. Therefore, it is full of curiosity that how large earthquake will cause a bridge to collapse and how the ultimate state will be. The Vector Form Intrinsic Finite Element (VFIFE), a new computational method developed by Ting et al. (2004), is adopted in this study. The formulation of VFIFE type 3D frame element includes a new description of the kinematics that can handle large rotation and large deformation, and includes a set of deformation coordinates for each time increment used to describe the shape functions and internal nodal forces.
Some kinds of new 3D VFIFE elements and analysis methods are herein developed for analyzing the target bridges. Through numerical simulation of examples and comparison with the Finite Element analysis (SAP2000), the developed elements and analysis methods are verified to be feasible and accurate. In the past, VFIFE was used Central Different Method to be analysis method, there are numerical disperses when to solve the Rayleigh damping analysis. Implicit time integration method (Newmark-β) is adopted in 3D VFIFE. Incremental formulation of the equation of motion is used to do iteration and to solve the response at next time step (i+1) including the displacement, velocity and acceleration. Furthermore, this calculation is also used to calculate the internal resultant force and the internal damping force exerted by the elements surrounding the particle. Finally, this study analyzes the ultimate situation of bridges through 3D numerical analysis and input two directions of horizontal ground motions to investigate the extreme functions of the bearings, columns and unseating prevention devices. Then predict the collapse situation of target bridges.

關鍵字(中)

★ 動力分析
★ 橋梁
★ 防止落橋裝置
★ 空間向量式有限元
★ 極限狀態
★ Newmark-β直接積分法

關鍵字(英)

★ ultimate state
★ bridge
★ 3D VFIFE
★ Newmark-β method

論文目次

目錄
摘要…………………………………………………………………….I
Abstract………….……………………………………………………….II
致謝………………………………………………………………….III
目錄..…………………………………………………..….…………..IV
表目錄………………………………………………..…………..…VII
圖目錄………………………………………………..…….………VIII
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 論文架構………………………………………..……………7
第二章空間向量式有限元素法…….………..…………..……………..9
2.1 結構離散模式…………………………………………………10
2.2 質點運動方程式……………………………………..………..10
2.3 運動軌跡離散化………………………………………………13
2.4梁元素變形與內力計算…………………..…………………15
2.4.1 空間梁元素之移動基礎架構.………………..…….….….17
2.4.2節點位移與梁元素變形..…..……………………..…….….23
2.4.3 內力計算…………….……….………………..……….….27
第三章採用隱式直接積分法之向量式有限元素分析…..………..…41
3.1 隱式Newmark-β直接積分計算程序…….….………………41
3.2 雷利阻尼分析………………………………………………….46
3.2.1 空間勁度比例阻尼力計算…….………………………...51
3.3 數值算例………………………………………………..……..57
3.4 小結……………………………………………………..……..58
第四章特殊元素分析與橋梁極限狀態模擬…………………..……..68
4.1 特殊元素………………………………………………………68
4.1.1 線性彈簧元素元素……………………………………..…71
4.1.2 雙線性彈簧元素………………………………………..…73
4.1.3 具可開塑性孔彈簧元素………………………………..…73
4.2 地表位移輸入法……………………………...……………….75
4.3 橋梁極限狀態模擬……………………………………………77
4.3.1 支承破壞模擬………………………………………..……78
4.3.2 平面滑動摩擦分析……………………………..…………79
4.3.3 構件斷裂模擬……..…………………………..…………84
4.4 數值算例……………………………………...……………….86
4.4.1 雙線性彈簧元素………………………………..……….86
4.4.2 具可開孔塑性彈簧元素…….....………………..……….87
4.4.3 地表位移輸入法……………………………….………….88
4.4.4 平面滑動摩擦分析………………….…………….…….89
4.5 小結…………………………………………...……………….90
第五章橋梁實例分析與參數研究…………………………………106
5.1 目標橋梁型式………………………………………………107
5.2 數值分析模型…………………….………………………..…107
5.2.1 上部結構模擬……………….…………..……………...107
5.2.2 下部結構模擬……………….…………..……………...109
5.2.3 支承系統模擬……………….…………..……………...112
5.2.4 防止落橋裝置模擬……………….…………..…...……114
5.3 參數研究……………………………………………………...116
5.3.1 動力歷時分析結果…………………………………….116
5.4 小結…………………………………………………………...125
第六章結論與未來展望…………………………………….………..161
6.1 結論……………………………………………………...…161
6.2 未來展望……………………………………………………..164
參考文獻…………………………………………………….……….165
附圖………..………………………………………………….……….168

參考文獻

參考文獻
[1] Ting, E. C., Shih, C. and Wang, Y. K. (2004), "Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and a Plane Frame Element," Journal of Mechanics, Vol.20, No.2, pp. 113-122.
[2] Ting, E. C., Shih, C. and Wang, Y. K. (2004), "Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements," Journal of Mechanics, Vol.20, No.2, pp. 123-132.
[3] Shih C., Wang, Y. K. and Ting, E. C. (2004), "Fundamentals of a Vector Form Intrinsic Finite Element: Part III. Convected Material Frames and Examples," Journal of Mechanics, Vol.20, No.2, pp. 133-143.
[4] Wang, C. Y., Wang, R. Z., Kang, L. C. and Ting, E. C. (2004), "Elastic-Plastic Large Deformation Analysis of 2D Frame Structure," Proceedings of the 21st International Congress of Theoretical and Applied Mechanics (IUTAM), SM1S-10270, Warsaw, Poland, August 15-21.
[5] Wu, T. Y., Wang, R. Z. and Wang, C. Y. (2006), "Large Deflection Analysis of Flexible Planar Frames," Journal of the Chinese Institute of Engineers, Vol. 29, No. 4, pp. 593-606.
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[7] 莊清鏘、陳詩宏、王仲宇 (2006)，〝向量式有限元於結構被動控制之應用〞，固體與結構之工程計算－2006近代工程計算論壇，第O1-O25頁。
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[9] 施柔依 (2010)，「向量式有限元運用於中車軌橋互制數值模擬分析」，國立中央大學土木工程學研究所碩士論文，指導教授：王仲宇。
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[13] 陳開天 (2010)，「橋梁碰撞效應研究」，國立中央大學土木工程學研究所碩士論文，指導教授：李姿瑩。
[14] 汪栢靈 (2010)，「橋梁極限破壞分析與耐震性能研究」，國立中央大學土木工程學研究所碩士論文，指導教授：李姿瑩。
[15] Gakuho Watanabe, Kazuhiko Kawashima (2004), "Numerical Simulation of Pounding of Bridge Decks," 13th World Conference on Earthquake Engineering.

指導教授

李姿瑩(Tzu-Ying Lee)

審核日期

2011-7-26

推文