Model order reduction for dynamic simulation of a flexible multibody system via absolute nodal coordinate formulation

The Absolute Nodal Coordinate Formulation (ANCF) can be used to model a flexible multibody system subject to both overall motions and large deformations. With an increasing number of finite elements of ANCF to mesh flexible bodies, however, the computation cost will become extremely high. To improve the computational efficiency of ANCF for a large-scaled flexible multibody system, a systematic method is proposed in this study for the model order reduction based on the proper orthogonal decomposition and the Galerkin projection. At first, an approach for the selection of reduced constraint equations is proposed to deal with the singularity of the coefficient matrix of the Reduced-Order Model (ROM). Then, the computation of the reduced stiffness matrix and generalized force vector of the ROM are parallelized via the OpenMP directives. Afterwards, two parametric approaches are presented to make the ROM be adaptive to the change of system parameters. One is the interpolation approach of reduced-order basis vectors on a manifold to obtain the parametric ROM, and the other is the fast-to-slow ROM approach via the reduced-order basis vectors extracted from the fast dynamic responses to simulate slow dynamic responses. Finally, four numerical examples are given to validate the efficacy of the proposed method for the dynamic simulations of both rigid and flexible multibody systems.