Nonsmooth Generalized-α Scheme for the Simulation of Multibody Systems

Abstract

We present a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels. Thus, it significantly differs from penalty techniques since no penetration is allowed. The numerical scheme is obtained in two main steps. Firstly, a splitting method is used to isolate the contributions of impacts, which shall be integrated with only first-order accuracy, from smooth contributions which can be integrated using a higher order scheme. Secondly, following the idea of Gear, Gupta and Leimkuhler, the equations of motion are reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels. After time discretization, the equations of motion involve two complementarity conditions and it can be solved at each time step using a monolithic semismooth Newton method. The numerical behavior of the proposed method is studied and compared to other approaches for a number of numerical examples. It is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies (1).
REFERENCES
[1] O. Bruls, V. Acary, A. Cardona, Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-_ scheme. Computer Methods in Applied Mechanics and Engineering, http://dx.doi.org/10.1016/j.cma.2014.07.025. (2014).