63975 MODELING AND ANALYSIS OF CONTACT PHENOMENA IN MULTIBODY SYSTEMS USING A LINEAR COMPLEMENTARITY FORMULATION(Contact, Impact, and Friction)

Abstract

The dynamic modeling and analysis of rigid multibody systems that experience contact-impact events is presented and discussed in this study. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. The generalized contact kinematics is formulated in terms of gap functions and normal and tangential relative velocities. The dynamics of rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the normal and tangential directions. In the present work, the unilateral constraints are described by a set-valued force law of the type of Signorini's condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb's law for dry friction. Then, the resulting contact-impact problem is formulated and solved as a linear complementarity problem, which is embedded in the Moreau's time-stepping method. This method is considered here mainly due to its simplicity and robustness. The effectiveness of the methodologies presented in this study is demonstrated throughout the dynamic simulation of a planar multibody system.