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

蘇俊全(Chun-Chuan Su)

指導教授 ： 李姿瑩

國立中央大學/工學院/土木工程學系/碩士(2011年)

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

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

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.