车辐式结构找形分析的逐点去约束法

Constraints removal method for form-finding problem of spoke structures

车辐式结构是一种双层索系的柔性结构,需要通过找形分析确定结构的初始预应力态.与索膜、索网结构等柔性结构不同,车辐式结构的找形分析不是用给定的预应力值寻找结构位形,而是从给定的位形出发求解可能存在的预应力分布情况.目前已有的找形方法有平衡矩阵理论、力密度法、动力松弛法、非线性有限元法等.除了非线性有限元法外,其他方法都难以直接通过通用有限元软件进行找形分析.本文在平衡矩阵理论的基础上,将车辐式结构整体找形问题转化为针对每个节点处3个索杆单元的计算.通过使每个节点在预应力作用下达到设计位形,求出结构初始应力态的预应力分布.这种方法不但能够直接用于有限元软件的计算,还能够判定结构的初始应力态是否存在.

Spoke structures are kind of double-layer cable structures, whose initial stress state is achieved through formfinding process. Form-finding problems of spoke structures is needed for finding the distribution of the pre-stress according to the designed configuration which is different from cable-membrane structures or cable-net structures, whose formfinding problem is to get the shape of the membrane or cable-net under particular pre-stress. Except for the nonlinear finite element method, other methods such as equilibrium matrix theory, force density method, dynamic relaxation method can not be used directly in the general finite element software. Based on the equilibrium matrix theory, this paper transforms the integrated form-finding problem of spoke structures to the calculation of an one-point-three-element substructure, as constraints removal method. This method can not only be used directly in general finite element software, but also in judging whether the initial stress state exists or not.