Separate Time Integration Based on the Hilber, Hughes, Taylor Scheme for Flexible Bodies With a Large Number of Modes

In the current development of flexible multibody dynamics, the efficient and accurate consideration of distributed and nonlinear forces is an active area of research. Examples are, forces due to body-body contact or due to elastohydrodynamics (EHD). This leads to many additional modes for representing the local deformations in the areas on which those forces act. Recent publications show that these can be several hundred to several thousand additional modes. A conventional, monolithic numerical time integration scheme would lead to unacceptable computing times. This paper presents a method for an efficient time integration of such systems. The core idea is to treat the equations associated with modes representing local deformations separately. Using the Newmark formulas, a fixed point iteration is proposed for these separated equations, which can always be stabilized with decreasing step size. The concluding examples underline this property, as well as the fact that the proposed method massively outperforms the conventional, monolithic time integration with increasing number of modes.