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References (9)
-
J. Moreau (1988)
Unilateral Contact and Dry Friction in Finite Freedom Dynamics -
J. Marsden, Matthew West (2001)
Discrete mechanics and variational integratorsActa Numerica, 10
-
R. Leine, N. Wouw (2008)
Stability and Convergence of Mechanical Systems with Unilateral ConstraintsApplied and Computational Mechanics, 36
-
R. Leine, D. Campen, C. Glocker (2003)
Nonlinear Dynamics and Modeling of Various Wooden Toys with Impact and FrictionJournal of Vibration and Control, 9
-
G. Capobianco, Simon Eugster (2016)
A Moreau‐type Variational IntegratorPAMM, 16
-
E. Hairer, C. Lubich, G. Wanner (2004)
Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations -
Christian Studer (2009)
Numerics of Unilateral Contacts and Friction -
T. Schindler, Vincent Acary (2014)
Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: Definition and outlookMath. Comput. Simul., 95
-
Vincent Acary (2014)
Energy conservation and dissipation properties of time‐integration methods for nonsmooth elastodynamics with contactZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 96
- Publisher
- Wiley
- Copyright
- Copyright © 2017 Wiley Subscription Services, Inc., A Wiley Company
- ISSN
- 1617-7061
- eISSN
- 1617-7061
- DOI
- 10.1002/pamm.201710041
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we derive and compare three integrators for nonsmooth mechanical systems by discretizing the principle of virtual action with finite elements in time. The weak as well as the strong variational form of the principle are discretized using a piecewise linear shape function and different quadrature rules. After introducing a suitable constitutive law for the contact forces arising in the discretized system, this approach leads to the well established time‐stepping scheme of Moreau [1], the variational Moreau‐type scheme derived in [3] and another related scheme, which we call the symmetric Moreau‐type scheme. It is shown using a benchmark system that the symmetric and the variatonal Moreau‐type schemes, in contrast to Moreau's scheme, show an excellent longterm energy behavior. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Journal
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Dec 1, 2017