索结构几何非线性分析的悬链线索单元法

A Catenary Cable Element for the Nonlinear Analysis of Cable Structures

基于索的基本假定和悬链线平衡方程,通过对沿索曲线均布荷载作用下的索段分析,得到了索端力和索的几何线形之间的对应关系;进一步通过索单元的柔性迭代分析,获得了内力改变和位移增量之间的关系,进而得到索单元的刚度矩阵和节点力,从而建立起了空间悬链线索单元的几何非线性有限元分析方法.经典算例结果证明了空间悬链线索单元的正确性,同时具有较高的精度,可为大跨度悬索桥、斜拉桥以及张拉结构等几何非线性较强的结构精确分析提供强有力的计算工具.

Based on the basic assumption and catenary formulation of cable structure, the corresponding relationship between end forces and the geometrical shape of the cable structure was obtained through the analysis of the cable element with uniform load along the cable curve. And the flexible iteration analysis of the cable structure was performed to obtain the relationship between the inner force change and the displacement increment of the cable structure. As a result, the stiffness matrix and the nodal force vector of the cable element were developed. Moreover, the spatial catenary cable element for the geometrical nonlinear finite element method was established. The results of numerical examples have shown that the spatial catenary cable element is accurate, and can be used in the precise analysis of the geometrical nonlinear structures, such as long-span suspension bridges, cable-stayed bridges, and tensile structures.