一種計算鏈結構的新方法

Abstract

鏈結構對於薄殼結構的找型具有相當高的應用價值；透過控制邊界條件及桿件的安排可以產生出許多不同幾何外觀的薄殼形式。由於應用此方法所得之薄殼的彎曲力矩極低，因此可大幅提升材料效率。 不穩定鏈結構最終之穩定態一定必須透過對節點位移多次之迭代計算才能得到。本研究之每次迭代中某節點位移的計算方法是將連結於該節點所有桿件之另一端視為固定端來計算，而該位移量還必須折半才能使迭代計算收斂。 利用上述計算方法具有桿件剛性與迭代數約成正比的特性，本研究發展出以桿件剛性低之系統模擬桿件剛性高之系統的方法。該法可以大幅節省原方法所需之迭代數。由於桁架結構與索結構也同為鏈結構之一種，所以本計算方法也同時適用於上述兩種結構。經驗證，在小位移與大位移的運算範疇，本法與商用結構分析軟體SAP 2000所得之計算結果皆一致。 一般鏈結構之初始狀態各桿件之長度需要符合桿件原長，但是符合此條件之初始狀態並不容易求得。本方法可在桿件初始長度與桿件原長並不相符的條件下展開迭代計算，因此可將初始狀態之各節點置於同一平面。這特性對於特定幾何形狀之基地的薄殼找型具有一定的利用價值。

Link structures could be highly useful to the form finding of shell structures. With boundary conditions controlling and elements management, link structures could generate many types of shells with different geometric appearances. Such shells also have great advantage in material efficiency because of extremely low bending moments of witch. The final stable state of the unstable link structures must be found by the iteration of the joints’ positions. In this research, the displacement of the particular joint in one iteration will be calculated under the specification that the other ends of the elements connected to the joint are taken as fixed points. And the displacements acquired above need also to be reduced by half to make sure the iteration convergent. Since the element’s stiffness of the system is directly proportional to the iteration number, we can develop a time saving method by adopting the system with low-stiffness elements to simulate the system with high-stiffness elements. The method developed here can be used to calculate truss structures and cable structures, because these two structures are also in the category of the link structures. We will show how this method and that of SAP2000, the commercial software of structural analysis, have the results in common for both small displacements cases and large displacement cases. Generally, every element’s length of one link structure’s initial state must be equal to their original length. However, it is not easy to determine the joints’ positions of such kind of initial state. Our iteration method could be run under such condition as every element’s length of the initial state is not equal to their original length. Thus, we could make an initial state with all the joints’ positions in one plane. And this property will be very useful to the shells’ form finding of the site with particular geometric shape.