Computational Schemes for Flexible, Nonlinear Multi-Body Systems

This paper deals with the development of computational schemes for the dynamic analysis of flexible, nonlinear multi-body systems. The focus of the investigation is on the derivation of unconditionally stable time integration schemes for these types of problem. At first, schemes based on Galerkin and time discontinuous Galerkin approximations applied to the equations of motion written in the symmetric hyperbolic form are proposed. Though useful, these schemes require casting the equations of motion in the symmetric hyperbolic form, which is not always possible for multi-body applications. Next, unconditionally stable schemes are proposed that do not rely on the symmetric hyperbolic form. Both energy preserving and energy decaying schemes are derived that both provide unconditionally stable schemes for nonlinear multi-body systems. The formulation of beam and flexible joint elements, as well as of the kinematic constraints associated with universal and revolute joints. An automated time step selection procedure is also developed based on an energy related error measure that provides both local and global error levels. Several examples of simulation of realistic multi-body systems are presented which illustrate the efficiency and accuracy of the proposed schemes, and demonstrate the need for unconditional stability and high frequency numerical dissipation.