橋梁非線性行為之向量式有限元分析法

Analysis of the Nonlinear Behavior of Bridge by the Vector Form Intrinsic Finite Element Method

陳世凱(Shih-kai Chen)

指導教授 ： 王仲宇

國立中央大學/工學院/土木工程學系/博士(2011年)

摘要

本論文以向量式有限元(Vector Form Intrinsic Finite Element，VFIFE，V-5)做為三維橋梁結構非線性行為分析之基本理論，發展橋梁相關功能模組。橋梁支承方面，透過LS-DYNA軟體的超彈性材料模型來分析橡膠材料與支承墊的力學試驗，並建構非線性彈簧元素來計算橡膠支承的遲滯行為。橋梁非線性静力分析方面，提出一個由動量運動方程式為基礎的快速静力收斂方法，經由適當的起始條件假設來處理質點的運動方程式。最後利用C#程式語言來撰寫前、後處理的使用者界面(GUI)，包裝以向量式有限元為主的橋梁非線性計算核心程式，並以OpenGL繪圖函式完成模型之繪製。利用本文所開發的橋梁性能分析軟體，可進行含支承系統橋梁受地震力作用下的非線性動力分析，觀察支承在地震力作用下的非線性遲滯迴圈行為，而透過快速静力收斂方法可有效提升向量式有限元在處理静力問題上效率，最後圖像使用者界面可以兼顧使用者在用使橋梁分析程式過程中的方便性與實用性。

關鍵字

橋梁 ； 地震 ； 非線性 ； 橡膠支承墊 ； 前處理 ； 後處理 ； 向量式有限元

並列摘要

This thesis used the VFIFE (Vector Form Intrinsic Finite Element, V-5) method with some proposed functional modules as the basic theory to analyze the nonlinear behavior of three-dimensional bridge structure. In the part of the nonlinear module of bridge bearing, the LS-DYNA software''s hyper-elastic material model was used to study the rubber bearing’s mechanical testing and develop a nonlinear spring elements to calculate the hysteresis behavior of rubber bearing. In the part of nonlinear static analysis of the bridge, a new algorithm based on the momentum equation of motion to efficiently slove the static problem Finally, the pre-processers and post-processer’s graphic user interface (GUI) with the VFIFE program is developed for packaging the nonlinear bridge’s solving kernel, and using OpenGL library to perform the function of graphic and plot the model on the screen. By the computation program of bridge developed in this thesis, the nonlinear analysis of bridge including the rubber bearing system under seismic excitation can be conducted to understand the behavior of the bearing’s hysterious loop. And by the fast static analysis algorithm, the efficiency of sloving static problems can be greatly improved in the VFIFE method. Furthermore, the graphic user interface can help users to have the convenience and accuracy in the process of analysis.

並列關鍵字

rubber bearing ； nonlinear ； seismic ； bridge ； pre-processer ； post-processer ； VFIFE

參考文獻

13. 陳世凱，2004，「向量式有限元素法於空間桁架之應用」，中原大學土木工程學系碩士論文，台灣。

34. 張國鎮, 陳皇嘉(2005),”裝設橡膠支承墊於橋梁縮尺模型之試驗與分析”,國科會計劃編號:NSC-93-2625-Z-002-026。

5. DYTRAN, MSC Software Corporation, Inc., http://www.mscsoftware.com/.

7. Ting, E.C., Shi C. and Wang, Y.K., “Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a planar frame element”, Journal of Mechanics, Vol. 20, pp.113-122 (2004).

8. Ting, E.C., Shi C. and Wang, Y.K., “Fundamentals of a vector form intrinsic finite element: Part II. Plane solid element”, Journal of Mechanics, Vol. 20, pp.123-132 (2004).