悬索结构平衡及振动非线性有限元分析

采用五节点索单元，提出了悬索结构平衡及自由振动非线性分析的一种新的有限元方法，将索元变形后的位置用修正的ａｇｒａｎｇｉａｎ坐标的四次多项式来表示，并在索元变形后的位置上由虚功原理建立了非线性有际元基本方程，所的非线性有限元分析方法可充分考虑拉索的几何非线性特性的影响，并给悬索结构的线形结构的找形及振动分析带来方便，此外，对单索结构的平衡及自振特性进行了计算分析。

Nonlinear Finite Element Method for Equilibrium and Natural Frequencies of Cable Structures

By use of five node cable element,a new finite element method for nonlinear analysis of equilibrium and natural frequencies of cable structures is presented in this paper.The deformed geometry of the element is defined as polynomial of four terms in terms of updated Lagrangian coordinates.All geometric nonlinearities are retained,and elastic deformation is taken into consideration.The method can be easily applied to the analysis of form finding if the unstressed length of cables is given.The problems of static deflection and natural frequency for small oscillation about the nonlinear equilibrium position are investigated for single span cables.