A relaxed coupling method for algebraically constrained mechanical systems

A coupling method is presented that aims at computing the dynamics of constrained mechanical systems connected by algebraic constraints. A relaxed coupling method is proposed, where each subsystem is reformulated as a set of ODEs and solved with an iteration process. The method is straightforward to implement, also for parallelization. The core idea is to eliminate the Lagrange multipliers of the DAEs that describe the constraint dynamics of each subsystem using a proper constraint stabilization technique. A linear combination of the constraint equations at position and velocity level is enforced, to prevent the occurrence of numerical drifting. The associated stabilization parameter is chosen in relation to the time step size. The effectiveness of the proposed approach is verified by solving a three-dimensional problem with rigid and flexible bodies. The results show that the method is effective in co-simulating algebraically constrained mechanical systems.