基于几何位移计算理论的索杆结构成形分析

Shape-Forming Analysis for Cable-Member Structures Based on Geometric-Displacement Computation Theory

为求解索杆体系在成形过程中存在的几何位移,系统地研究了几何位移计算理论.分别根据余能原理和虚功原理,导出了发生几何位移时系统的变形协调方程和等价不平衡方程,构成了几何位移求解的理论基础;归纳了求解几何位移的3类约束条件:松弛条件,定量约束条件,定向约束条件.几何位移的求解可归结为根据系统等价不平衡方程不断修正几何位移模态、使之满足系统变形协调条件和约束条件的迭代过程.算例分析表明,所研究的理论可准确计算出系统形态变化中的几何位移,实现对索杆体系的成形分析.

In order to analyze geometric displacement during shape-forming process of cablemember structures, the theory of geometric-displacement computation is studied. The systemdisplacement harmonic term and equivalent unbalanced equation are deduced based on the complementary energy principle and virtual work principle, respectively. Three types of constraint terms for computation of geometric displacement are concluded, including slack term, fixingquantity term and fixing-direction term. The solution of geometric displacement can be summarized as an iterative computation of geometric-displacement modes based on the equivalent unbalanced equation obeying the system deformable harmonic term and constraint terms. The examples show the theory is able to correctly evaluate geometric displacement for morphologically varying systems, and to successfully simulate the shape-forming process of cable-member structures.