Mixed timestepping schemes for nonsmooth mechanics with high frequency damping

TL;DR

This paper introduces a mixed timestepping scheme for nonsmooth multibody systems with impacts and friction, combining impulsive corrections with existing integration methods to improve accuracy and consistency.

Contribution

It develops an automatic impulsive correction framework integrated with generalized-$\alpha$, Bathe, and ED-$\alpha$ methods for better nonsmooth dynamics simulation.

Findings

The scheme improves trajectory accuracy after impacts.

It maintains consistency with impact and friction laws.

Comparative analysis shows advantages over traditional methods.

Abstract

This work deals with the integration of nonsmooth flexible multibody systems with impacts and dry friction. We develop a framework which improves a non-impulsive trajectory of state variables by impulsive correction after each time-step if necessary. This correction is automatic and is evaluated on the same kinematic level as the piecewise non-impulsive trajectory. The resulting overall mixed timestepping scheme is consistent with respect to impacts and friction as well as benefits from advantages of the base integration schemes used to calculate the approximation inside the time-step. Therefore, we compare the generalized-$\alpha$ method, the Bathe method and the ED-$\alpha$ method.