索网结构欧拉坐标找形法

Shape Optimization of Cable Net by Euler Coordinates Form-finding Method

摘要:

基于无弯矩假定，以节点坐标为待求参数，提出了一种适用于索网结构找形的数值算法——欧拉坐标找形法，并建立了欧拉空间坐标系。以轴力与杆长为未知参数，再根据杆单元的力学特性和平衡条件，直接建立结构节点坐标和轴力的平衡迭代矩阵。实例验证结果表明，欧拉坐标找形法能够适应各种类型的索网结构优化问题，鲁棒性好，收敛较为稳定。

Abstract:

Based on the assumption of no bending moment， taking the node coordinates as the parameters to be determined， a numerical algorithm suitable for the form-finding of cable-net，i.e.，Euler coordinates form-finding method， was proposed to establish the Euler space coordinate system. Taking the axial force and rod length as unknown parameters， the equilibrium iteration matrix of the structural node coordinates and axial force was directly established according to the mechanical properties and balance conditions of the rod element. A case study shows that the Euler coordinates form-finding method can adapt to various types of cable net structure optimization， with good robustness and stable convergence.