The Kinematic Analysis Of Load-bearing Mechanisms Consisting Of Cable And Bar Elements

Based on the background of the problems such as construction of cable-strut tensile structures and jacking process of Panta Dome, these systems are abstracted to be load-bearing mechanisms consisting of cables and bar elements, and the theoretical kinematic analysis of the mechanism is focused in this paper. The main work includes:(1) A kinematic path analysis method for the pin-bar mechanism is presented based on the finite element method. The basic kinematic equations of the load-bearing pin-bar mechanism are established and the elongations of the driving bars are taken as the control parameters. The arc-length method is employed so the kinematic path can be traced automatically.(2) The kinematic configuration stability criterion is introduced into the kinematic analysis of the load-bearing pin-bar mechanism. The minimal eigenvalue of the tangent stiffness matrix is employed to determinate the stability of the equilibrium configuration on the kinematic path. The method for pinpointing the singular point on the kinematic path based on the Newton method is presented. The bifurcation conditions of the singular point are explained theoretically. In order to trace the bifurcation paths, the disturbing force depend on the zero space vector of the tangent stiffness matrix is introduced.(3) The arc-length method is introduced into the traditional dynamic relaxation method, and a modified method for the load-bearing cable-bar mechanism kinematic analysis is presented. The high computational efficiency of the dynamic relaxation method is preserved, and the automatic path tracing can be realized combined with the arc-length method. More importantly, the bifurcation path can be traced by introducing the initial disturbing velocity depended on the zero space vector of the tangent stiffness matrix into the modified method.(4) The construction process of the novel crescent-shaped cable-strut tensile structure is analyzed based on a practical application. Numerical simulation of the recommended construction process is carried out by the proposed method, and the characteristics of the structure during the construction are analyzed. Based on the1:15experimental model of the tensile structure, the hoisting experiment of the construction process is conducted to verify the recommended construction scheme. The results of the experiment are compared with the numerical simulation and the proposed method is verified.