Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts

Vincent Acary 1
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 : The article is devoted to the study of higher order time integration methods for multibody systems with unilateral constraints. After a brief presentation of the mathematical modelling of nonsmooth multibody systems, several estimates on the local error of consistency of the Moreau time-stepping scheme are given. Based on these estimates, an attempt at an adaptive time-step strategy is presented with academic examples. Finally, higher order event--capturing methods are designed by coupling implicit Runge-Kutta schemes and Moreau's time-stepping scheme.
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Applied Numerical Mathematics, Elsevier, 2012, Selected Papers from NUMDIFF-12, 62 (10), pp.1259-1275. 〈10.1016/j.apnum.2012.06.026〉
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Vincent Acary. Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts. Applied Numerical Mathematics, Elsevier, 2012, Selected Papers from NUMDIFF-12, 62 (10), pp.1259-1275. 〈10.1016/j.apnum.2012.06.026〉. 〈inria-00476398〉

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