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

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.

Key words:cable net;shape optimization;Euler coordinates form-finding method;geometrical minimum way net