向量式有限元素法於懸索結構的找形分析

Shape Finding of Suspend Cable Structures Using Vector Form Intrinsic Finite Element Method

孫東磊(Dong-Lei Sun)

指導教授 ： 莊清鏘

中原大學/工學院/土木工程研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800268

摘要

懸索結構是由鋼索組成的柔性結構，具有自重小、跨距大、造型各異的特性。需要施加預拉力才具有承載能力，張拉過程伴有剛體位移與材料變形。因為“柔”，即使很小的應力改變，也會帶來很大的變形,具有強烈的幾何非線性效應。因此不適用傳統結構力學微小變形的假設。若使用經典有限元素法分析通常需要進行反覆迭代求解，有時會出現整體勁度矩陣奇異的情況，難以處理。此外，結構構件最大張力出現在施加預拉力階段，而非工作狀態。因此需要對其初始形態進行分析，以求取滿足初始預拉力下的初始幾何分佈狀況。
本文利用向量式有限元素法，對懸索結構進行初形分析及其工作狀態下的荷載分析。靜力模擬時引入運動阻尼概念，以更快達到靜力解。同時，使用懸鏈線元素進行力學推導也將予以介紹，作為柔性索進行分析時的一種選擇。

關鍵字

向量式有限元 ； 找形分析 ； 運動阻尼 ； 懸鏈元 ； 運動歷時

並列摘要

Suspended cable structures are flexible structures. It has the characteristics of light weight, large spanning and variable modeling. Pre-tension applying is required to possess bearing capacity. It has a rigid body motion and material deformation in the process of tensioning. Because of its “flexibility”, even a small variation of stress, great deformation still will be caused, has strong geometric nonlinear effect. Therefore, the assumption of small deformation in traditional structural mechanics is not applicable. Repeated iterations are needed if classic finite element methods were used, sometimes the situation of the singular global stiffness matrix will occur, which is difficult to process. In addition, the maximum tension of structural members occurs at the stage of applying pretension, rather than working state. So it is necessary to analyze its initial state in order to solve the initial geometric distribution which satisfies the initial pretension.
In this paper, the Vector Form Intrinsic Finite Element Method is used to analyze the initial condition of the suspended cable structure, and the load analysis in working state. In order to obtain the static solution when simulating the static problem, the concept of kinetic damping is introduced. Furthermore, using the catenary element for mechanics derivation also will be introduced, as a choice of flexible cable analysis.

並列關鍵字

VFIFE ； Shape Finding ； Kinetic Damping ； Catenary Element ； Motion Time History

參考文獻

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