悬索桥结构分析中的索-鞍座单元

为在悬索桥结构的有限元分析中真实、简洁、高效地模拟索鞍,本文建立了一类新的单元。新单元包括索段的一端固定在与其接触部分为单一半径圆弧的索鞍上,另一端分别位于索鞍两侧的两节点“左索-鞍座单元”和“右索-鞍座单元”,以及索段两端点分别位于索鞍两侧,中间一点固定于鞍座上的三节点“索-鞍座单元”,后者的鞍槽可为两不同半径圆弧的组合。根据要求的成桥状态几何参数确定结构的无应力状态时,可利用前二者进行悬索桥的单跨分析。新单元通过自动调整索与鞍座的脱离点而处于平衡状态,从而简化了计算。单元算法的推导基于有限元分析的基本原理和弹性悬链线的精确解,并利用了处于平衡状态时索与鞍座之间的内力关系。新单元可象常规单元一样直接用于成桥状态或施工过程中悬索桥结构的有限元分析。设计的算例验证了新单元的正确性,并举例说明了新单元在悬索桥结构分析中的应用。

Cable-saddle element in finite element analysis of suspension bridge

In order to model the cable saddles in finite element analysis of suspension bridge more realistically and effectively,one class of new elements was developed.They include two-node left cable-saddle element,right cable-saddle element and three node cable-saddle element.Each of the first two elements has one cable end fixed on the saddle,where the contact part is an arc with uniform radius,and the other end on each side respectively,they are effective in single cable span analysis to determine the unstrained state of the suspension bridge according to the designed geometric parameters.The last new element has one cable end on each side,and other one point fixed on the saddle,whose longitudinal curve can be composed of two arcs with different radii.They simplify computations by automatically adjusting the cable departing points to maintain equilibrium state.The derivation was based on the foundational principles of finite element analysis and the analytical solutions of elastic catenary,the forces relation between cable and saddle at equilibrium state was used.These new elements can be incorporated into conventional finite element analysis schemes.The designed examples proved their correctness,and one practical example shows the applications of the new elements in structural analysis of suspension bridge.