A time-stepping method for multibody systems involving frictional impacts and phases with persistent contact

Abstract

This work complements and continues efforts towards developing a complete numerical integration method for multibody dynamic systems with frictional impacts. Specifically, the new method is a time-stepping scheme, which is applicable to mechanical systems subject to a set of bilateral and a single unilateral motion constraint. During an impact free phase of the motion, a suitable augmented Lagrangian methodology is applied. When an impact is detected during a time step, the post-impact state is determined by employing a special process, which addresses properly the inherent numerical stiffness associated with the impact events. The basic contribution of the present study is the extension to cover cases where the contact between the interacting bodies is possible to exist for a finite period of time after an impact. This phenomenon occurs frequently in machines and mechanisms and is known as persistent contact. First, a complete strategy is developed for establishing a general numerical procedure for capturing and treating both activation of contact and loss of contact between two bodies. Then, the accuracy and efficiency of this procedure is tested and demonstrated by applying it to a selected set of mechanical examples.