Studies On Geometrical Stability Of Pin-bar Assemblies Considering Member Removal And Multi-equilibrium Configurations Of Pin-bar Mechanisms

The geometrical stability and the equilibrium configurations analyzing are both the basic thoery-problems of the constructing-process simulation of cable-strut structures and the motion-tracing of deployed structures. This thesis treats spatial pin-bar assemblies as its object. On the basis of structural stability theory, this thesis layes heavy stress on the effect factors and judgment criterion of structural geometric stability, and multi-equilibrium configurations of pin-bar mechanisms as also.Based on analysing the common enegy criterion and the components of tangent stiffness matrix, this thesis anatomyes the effect factors of bar-assembly stability: the geometry and topology of the system, the member stiffness and the equilibrium inner force. As this thesis indicates, the conventional kinematic analysis is virtual a stability problem when the assembly is unforced. This thesis also discusses the effect of inner force on the mechanisms stability.The zero stiffness member in a assembly can be considered as the removal of this member. Furthermore, this thesis carries out some discussions about the geometrical stability of the pin-bar assemblies after removing some bars. The efficient criterion of the necessary bar is developed. Moreover, against some problems such as topological optimization, which need to repeating the members optimization, this thesis puts forward a simplified method. The mothods are much time-saving than the common methods.Considering the form-finding problem of the bar assemblies as a nonlinear programming problem, a new idea of form-finding is brought. Taking the nodal non-equalibrium forces as the objective functions and the coordinate of the free node as the design variables, we can use the genic algorithm to solve it and obtain multi-equalibrium configurations. This method is testified feasible to solve this problem through the form-finding analysis of a simple mechanism.