Study On Numerical Method For DAEs Of Dynamics Of Flexible Multibody System In Deployable Antenna

Study on large scale space deployable antenna is one of the research focuses of national defence technology at present. Large in size, light in weight and high in flexibility, this type of antenna has flexible or rigid- flexible mix structures. Dynamic analysis and simulation based on the dynamics theory of flexible multibody system of deploying process of large scale space deployable antenna is an important precondition for controlling antenna deployment. And dynamic equations of deployable antenna are differential algebraic equations (DAEs), which belong to stiff equations and are also called ill-conditioned equations. Therefore, their numerical solutions are not always stable, and do not satisfy all the constraint equations, which bottleneck the rapid development of dynamics of flexible multibody system. The purpose of the study on numerical method of DAEs is to find a method with stabilization, high precision and fast computing speed to supply the information such as displacement and driving force to deploying control module.This thesis firstly deals with the theory of flexible multibody dynamics, modeling method, symbolic computation and its application in modeling, and the essence and analyzing method of dynamic stiffening of flexible body. Secondly, the introduction of basic concepts of stiff equation and stable region and a summary of the methods suitable for solving DAEs are made. And the mathematic principles, advantages and disadvantages, and applied range of those methods are also expounded and analyzed. Through comparison and analysis, default direct correction method belonging to augmented method is chosen as simulation method. The application of this method is illustrated with an example of double flexible connecting rods model. Finally, the flow chart of the system, design of numerical simulation module, and program interface are explained and the resolutions of key parts of simulation design are given. This thesis is of great theoretical significance in guiding the subsequent research on dynamic analysis of deployable antenna.