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

DOI10.1016/j.apnum.2012.06.026zbMath1351.70005OpenAlexW2134333398MaRDI QIDQ450884

Vincent Acary

Publication date: 26 September 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00476398/file/VAHO.pdf

zbMATH Keywords

unilateral constraintserror estimatesmultibody systemsimpactorder of accuracynonsmooth mechanicsadaptive time-step strategyMoreau's sweeping processnumerical integration scheme

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) (n)-body problems (70F10) Dynamics of multibody systems (70E55)

Related Items

Simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized-\(\alpha\) scheme, An explicit time-integrator with singular mass for non-smooth dynamics, A nonsmooth generalized-αscheme for flexible multibody systems with unilateral constraints, A nonsmooth modified symplectic integration scheme for frictional contact dynamics of rigid-flexible multibody systems, A new heterogeneous asynchronous explicit-implicit time integrator for nonsmooth dynamics, On preserving dissipativity properties of linear complementarity dynamical systems with the \(\theta\)-method, Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: definition and outlook, Half-explicit timestepping schemes on velocity level based on time-discontinuous Galerkin methods, Nonsmooth spatial frictional contact dynamics of multibody systems, A framework of time integration methods for nonsmooth systems with unilateral constraints, An improved implicit method for mechanical systems with set-valued friction, A nonsmooth contact dynamic algorithm based on the symplectic method for multibody system analysis with unilateral constraints, A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction
• A sweeping process approach to inelastic contact problems with general inertia operators
• Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems
• Numerics of unilateral contacts and friction. Modeling and numerical time integration in non-smooth dynamics
• Automatic integration of Euler-Lagrange equations with constraints
• One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
• A unified variational model for the dynamics of perfect unilateral constraints
• Nonsmooth mechanics. Models, dynamics and control.
• Convergence of a time-stepping scheme for rigid-body dynamics and resolution of Painlevé's problem
• The dynamics of discrete mechanical systems with perfect unilateral constraints
• A perturbation analysis for the dynamical simulation of mechanical multibody systems
• Numerical aspects of the sweeping process
• Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics
• Simulation techniques for applied dynamics. Proceedings of the advanced school, CISM, Udine, Italy, September 17--21, 2007
• Comparison of several numerical methods for mechanical systems with impacts
• Solving Ordinary Differential Equations I
• Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics
• Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas
• A class of nonlinear differential equations of second order in time
• Approximation en graphe d'une évolution discontinue
• A Numerical Scheme for Impact Problems I: The One-Dimensional Case
• A Numerical Scheme for Impact Problems II: The Multidimensional Case
• Rigid-Body Dynamics with Friction and Impact
• Numerical methods for simulation in applied dynamics