Model reduction for efficient time-integration of spatial flexible multibody models

A reduction method is proposed for efficient time-integration of compliant mechanism models that undergo large deflections. Of particular importance for the modelling of this class of mechanisms is the accurate description of geometric non-linearities, as stiffness characteristics can change significantly during deflection. A finite element-based flexible multibody approach is used to describe the compliant mechanism in terms of independent generalized coordinates. The modelling of large deflections requires a sufficient number of finite elements to ensure that deformations remain small in a co-rotational context. Increasing the number of elements, increases, besides the number of degrees of freedom, the largest eigenfrequency in the model. This reduces the allowable step size for explicit time-integrator methods. The proposed reduction method aims to suppress the high frequency vibrational modes which are not important for the desired simulation results, while retaining the geometric non-linearities in the reduced model. For this purpose we add constraint relations between the independent generalized coordinates. These constraint relations can be linear or non-linear. Both cases are investigated in this paper and are implemented as a fixed and an interpolated basis method, respectively. The effectiveness of the two methods is demonstrated by a simulation of a compliant straight guidance in a gravity field that undergoes large deflection. Both methods can yield accurate results with a significant increase in computational efficiency