Multiscale Multibody Dynamics

Abstract

The multibody systemMultibody system (Bauchau in Flexible multibody dynamics. Springer, Dordrecht, 2011 [1]) can be regarded as a collection of rigid and flexible bodies connected by mechanical joints. According to the definition of Cosserat continuum (Rubin in Cosserat theories: shells, rods and points. Springer, Dordrecht, 2000 [2]), it can be concluded that the rigid body or flexible bodies, such as beams, plates and shells, are exactly the Cosserat continuum with dimensions varying from zero to three. Obviously, all these Cosserat continua with different geometric sizes could be arbitrarily combined each other into a complicated multibody system with multiscale dimensions. By considering the deformations of material directors under the assumption of scale separation, this chapter decouples the original Cosserat continuum into a global macroscopic model and a local microscopic model. The microscopic model is valid only for static problem, and the application of Gaussian elimination makes it possible to solve the macro problem first and then the local micro problem. In view of the fact that multiscale modeling affords an efficient approach for detailed analysis of micro-structures at the speed of quickly global analysis, six different multiscale models, covering three-dimensional Cosserat continuum, shell and beam together with modal superelement, are developed, which are specially used for the numerical simulations of multiscale multibody systems.