基于李群局部标架的多柔体系统动力学建模与计算

The main content of the dynamics of flexible multibody systems focuses on the dynamic modeling, computation and control of complex systems composed of flexible components, which are subjected to the relative overall motion and connected by kinematical constraints. Compared with the computational structural mechanics, the multibody dynamics issues have high geometrically nonlinear, which is not only deduced by the large rotation caused from the large deformation of flexible components, but also is deduced by the overall rigid body motion. Under the concept of the local frame of Lie group (LFLG), the topic that how to develop a new modeling and computational method for flexible multibody dynamics is discussed. The major studies of this paper include the following aspects: the modelling methods of beam elements and plate/shell elements based on the LFLG, the long-time integration algorithm for the flexible multibody systems including collision problems, the parallel algorithm for multibody systems based on the domain decomposition method, and several numerical examples to verify the feasibility of the proposed method. The unique feature of the new method can eliminate the geometrically nonlinear of the overall rigid motion for flexible components. Therefore, the generalized inertial forces and internal forces as well as their Jacobian matrices are invariable under the arbitrary rigid body motion. The proposed method can motivate the integration of the modeling method of the flexible multibody dynamics and the computational structural dynamics with large deformation components and is expected to promote the development of the next-generation software of multibody system dynamics.