The numerical simulation of friction constrained motions (II): Multiple degrees of freedom models

In a previous article (Ref. [R. Glowinski, L.J. Shiau, Y.M. Kuo, G. Nasser, The numerical simulation of friction constrained motions (I): One degree of freedom models, Applied Mathematics Letters 17 (2004) 801-807]) the authors discussed the application of operator-splitting methods to the time-discretization of those mathematical relations describing the behavior of elasto-dynamical systems with friction, focusing on one-degree of freedom models. The main goal of the present article is to generalize the methodology discussed in Ref. [R. Glowinski, L.J. Shiau, Y.M. Kuo, G. Nasser, The numerical simulation of friction constrained motions (I): One degree of freedom models, Applied Mathematics Letters 17 (2004) 801-807]; there are no conceptual difficulties in doing so, the main issue being the computation of a vector-valued multiplier modeling the friction forces (or part of them). An iterative method allowing the computation of this multiplier will be discussed and the results of numerical experiments will be presented.