基于悬链线元的索穹顶形状精确确定方法

Accurate Form-Finding Method for Cable Dome Based on Catenary Element

针对目前索穹顶结构研究中其形状确定方面所存在的不足,提出了基于悬链线元逆迭代的精确修正技术,可以精确求得预张力;使其能在考虑索杆自重的情况下,在给定的初始几何位置上严格平衡.由于刚度矩阵形成和已知索的预张力情况求解索原长是运用悬链线元进行结构分析时需要解决的两个先决问题,首先根据目前文献中处理这两个问题的不足,提出了具有大范围收敛性的刚度迭代技术和不需迭代的索原长高精度求解方法;在此基础上引进逆迭代方法,建立了基于悬链线元的逆迭代形状精确确定方法.最后编制程序对算例进行验证,结果表明这一方法精度极高,且收敛速度快,收敛性好.

In this paper, an iterative algorithm in form-finding of cable dome structures is proposed to determine precisely the prestress of the cable dome and the original length of the cables which are definitely balanced in the initial geometrical condition with the effect of self-weight taken into account. The most important issues in analyzing cable structures by using eatenary elements are how to effidently calculate the element stiffness matrix and the original length of cables. In this study, a globally convergent method is proposed first to calculate the element stiffness matrix and a direct method to obtain the original cable length is then employed. These methods can solve the inadequacy of the iterate algorithms presented in the literature. Based on these methods this paper finally presents a form-finding method by using eatenary elements. The results obtained from a benchmark problem demonstrate that the form-finding method proposed in this paper is efficient and accurate.