一种考虑初始垂度影响的非线性索单元

本文首先运用Mathematic的符号运算功能，通过解偏微分方程给出了不等高单索的显式解析解，然后把该解析解应用于索微元的应变计算中，在此基础上用虚功原理推导了考虑初始垂度影响的两节点非线性索单元，并给出了索单元的单刚矩阵的具体形式，通过与两节点直线索单元的单铡矩阵的形式的比较，明确了该曲线非线性索单元的修正项，并给出了垂度影响因子的变化曲线。比较直观的给出了垂度对索单元刚度各项的影响程度。该非线性索单元既有多节点索单元精度高的特点，又有节点少，刚度元素较易求解以及有限元列式简洁等特点。本文通过两个数值算例表明，本文的非线性索单元是正确的，也表明了所编制的非线性计算程序是正确和可靠的。

A Kind of New Nonlinear Cable Element Considering the Influence of Initial Sag

In this paper the authors firstly solved the differential equation of the cable mini-element and presented the analytical solution for the inequility-height single cable by using the symbolic functions of Mathematic. And then the analytic solution is used in the strain computing of the mini-element of cable. On the base of the analytic solution and by using virtual work principle, the authors gave out a two-node nonlinear cable element and presented the stiffness matrix form. By comparing with the two-node straight line cable element, the correct item and the influence factor figure of the matrix was presented by a changing curve, which directly give out the influence result of cable sag. This cable element has the characters not only high computing precision comparing with multi-node cable element but also with few nodes and tidy expression for the stiffness matrix. The cable element presented in this paper is proved by two numerical examples. And also it is proved that the nonlinear program in this paper is right and reliable.