用于悬索桥非线性分析的鞍座-索单元

SADDLE-CABLE ELEMENTS FOR NONLINEAR ANALYSIS OF SUSPENSION BRIDGES

悬索桥是跨越能力最大的一种桥型,鞍座是使主缆转向的一个重要构件,直接约束着主缆的变形。然而,鞍座及其顶推的模拟一直是悬索桥非线性分析时的一个难点,现有方法存在一定的不足之处。为此,本文提出了一种基于弹性悬索精确解的二节点新单元———鞍座-索单元,这种单元隐含了主缆与鞍座相切及主缆无应力长度保持不变这两个重要条件,同时将鞍座及其顶推的模拟融为一体,提出了基于NewtonRaphson法的状态求解方法,并推导了其切线刚度矩阵和等效节点力。计算表明,状态求解方法精确而有效,切线刚度矩阵推导正确。采用这种单元,既可使悬索桥非线性分析的计算模型更接近实际结构,也能显著提高计算精度和计算速度,并且具有很好的通用性。

Suspension bridges can allow the largest spans in all types of bridges,and a saddle is an important member of suspension bridges,which allows change of direction of the cables and constrains their deformation.Modeling of the saddle and its jacking is a difficult problem for nonlinear analysis of suspension bridges,and the methods presented in the literature have some drawbacks.A new type of two-node element, saddle-cable element,based on exact analytical expressions for the elastic catenary,is proposed.This element contains two important conditions about the cable and saddle:the cable is always tangent to the saddle and the unstressed cable length remains constant,and it can be employed to model the saddle and its jacking conveniently.An algorithm based on the Newton-Raphson method is also proposed to determine the complete geometry of the element and its equivalent nodal forces,while an explicit tangent stiffness matrix is derived. The reliability and efficiency of the formulations are demonstrated by an example. Using this element in the nonlinear analysis of a suspension bridge can make the calculation more realistic,and improve the precision and speed of the calculation.Further more,the proposed element can be employed to model all types of saddles.