向量式有限元素法於馬鞍型索網結構的找形研究

Study on Form-Finding of Saddle Shape Cable Net Structures Using Vector Form Intrinsic Finite Element Method

莊清鏘(Ching-Chiang Chuang)；孫東磊(Dong-Lei Sun)；吳俊霖(Chiun-Lin Wu)

索網結構 ； 向量式有限元素法 ； 找形 ； 運動阻尼 ； cable net structure ； vector form intrinsic finite element method ； form finding ； kinetic damping

先進工程學刊

16卷2期（2021 / 07 / 01）

43 - 49

繁體中文

索網結構為纜索組成的柔性結構，有自重輕、跨距大及造型豐富等特點。不同於傳統剛性結構，預拉力施加前，索網結構不具承載力和固定形狀，其結構勁度、形狀和預拉力大小、分佈方式有關；加載前需先求結構初形。索網結構的初形分析係在滿足力平衡及邊界條件的前提下，求取纜索結構的初始幾何和初始預拉力分佈，常見的是，其中一個量已知，另一個量待求，並判斷結構是否張成及是否已達到足夠勁度。本研究在假設索網結構預拉力已知的前提下，用向量式有限元素法求滿足力平衡及邊界條件的初始幾何，同時和文獻案例比較，說明向量式有限元素法進行索網結構找形的可信性和可行性。

The cable net is a flexible structure that has the characteristics of light weight, large span, and rich geometric shapes. Unlike the conventional rigid structure, the cable net can only reach its design geometric shape and starts to show load carrying capacity if the pre-tensioning forces are properly applied. As such, its structural stiffness and geometric shape highly depend on the magnitudes of its pre-tensioning forces and how these forces are distributed over the net. Its initial geometric shape must be first determined before a structural engineer can start to apply the service load to the cable net structure. Form finding analysis for a cable net is to find either the initial geometric shape or the initial distribution of the pre-tensioning forces with one of which is known but the other becomes unknown to meet the physics of force equilibrium under a specified boundary condition. This is to ensure that the cable net structure has reached its stable geometric shape and owns adequate structural stiffness. In concluding, the study employs the vector form intrinsic finite element method to conduct form finding analyses using illustrative examples. The results are then compared with exact solutions and those obtained from another conventional method in the literature to illustrate the credibility and feasibility of the vector form intrinsic finite element method used for form finding.

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