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

Authors:
Vincent Acary
Affiliations:
INRIA Grenoble Rhône-Alpes, Inovallée de Montbonnot, 655, Avenue de lEurope. 38334 Saint Ismier Cedex, France
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 6
Cited 1

Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas

Mathematics of Computation
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A perturbation analysis for the dynamical simulation of mechanical multibody systems

NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
Rigid-Body Dynamics with Friction and Impact

SIAM Review
A Numerical Scheme for Impact Problems I: The One-Dimensional Case

SIAM Journal on Numerical Analysis
A Numerical Scheme for Impact Problems II: The Multidimensional Case

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Original article: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlook

Mathematics and Computers in Simulation

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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 modeling 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.