There is an increasing number of discontinuous dynamics problems, such as contact and impact, in the engineering field. The known modelling theories and methods, which are used to solve the continuous dynamics of flexible multibody systems, are not able to solve those problems or to solve those problems perfectly. In this paper, an appending constraint method was proposed to solve the contact/impact dynamics of flexible multibody system based on the idea of topology variable. The impact experiment of flexible bars was designed to verify the validity of the proposed method. At last, a multi-variable method was proposed to solve the multi-scale problems of time and space when the global simulation of the discontinuous dynamics of flexible multibody systems was carried out, and the computational efficiency of the global simulation of the discontinuous dynamics of flexible multibody systems was improved by using this method.