Assessment of simultaneous and nested conservative augmented Lagrangian schemes for constrained multibody dynamics

Two alternative schemes used for the solution of multibody systems are reported and compared between them to evaluate their performance. Within the context of kinematic constraints imposed via augmented Lagrangian technique, one scheme proposes a simultaneous iterative solution for the computation of the Lagrangian multipliers and the nonlinear Newton-Raphson iterations. The second scheme uses a more classical Uzawa approach to compute the Lagrangian multipliers, and the nonlinear iterations are nested into the multiplier update loop. The performance of the methodology is tested by solving numerical experiments: simple, double, triple, and 10 bars pendulums with revolute joints. Moreover, 2D and 3D analyses are performed. The computed results using both the simultaneous iterative, and the nested iterative techniques, are reported to evaluate: kinematic responses, energy conservation, constraints verification, and iterations reduction.