A Newmark-type integrator for flexible systems considering nonsmooth unilateral constraints

Mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints. Inspired by the HHT time integration method for smooth flexible multibody dynamics, this paper presents a Newmark-type integrator, denoted by nonsmooth HHT method, to include the nonsmooth property of unilateral constraints. Through numerical examples accounting for both rigid and flexible body models, a
bunch of methods are compared with the unilateral constraints on both velocity level and position level. Results show that the presented nonsmooth HHT method benefits from the accuracy and stability property of the classical HHT method with controllable numerical damping. In particular, when it comes to the analysis of flexible systems, the nonsmooth HHT method shows much better accuracy property than that of the other methods, including the Moreau–Jean time-stepping method and the fully implicit Newmark methods.