Comparison of index-3, index-2 and index-1 DAE solvers for nonsmooth multibody systems with unilateral and bilateral constraints

Mounia Haddouni 1, 2, * Vincent Acary 1, * Jean-Daniel Beley 2
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This work is devoted to the study of some numerical solvers for the numerical time integration of nonsmooth multibody systems with unilateral or bilateral constraints. In the framework of event-detecting time-stepping schemes (a.k.a. event- driven schemes), an index-3 Differential Algebraic Equation (DAE) has to be solved between two events with a constant number of bilateral constraints. In this paper, we compare several solvers for index-1, index-2 and index-3 DAEs in the specific context of unilateral contact and impact. These solvers will be compared in terms of drift of the constraints which is an important feature when we have to update the index sets of the active unilateral constraints. Their implementation and efficiency with fixed and adaptive time-step strategies will also be reviewed. Finally, we discuss the way they handle cases when the constraints are not sufficiently differentiable, which is of utmost importance for practical applications.
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Mounia Haddouni, Vincent Acary, Jean-Daniel Beley. Comparison of index-3, index-2 and index-1 DAE solvers for nonsmooth multibody systems with unilateral and bilateral constraints. Multibody Dynamics 2013, Eccomas, Jul 2013, Zagreb, Croatia. ⟨hal-00821314⟩

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