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A Moreau‐type Variational Integrator
Author(s) -
Capobianco Giuseppe,
R. Eugster Simon
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610453
Subject(s) - discretization , integrator , variational integrator , scheme (mathematics) , mathematics , action (physics) , type (biology) , variational principle , control theory (sociology) , finite element method , mathematical analysis , computer science , physics , control (management) , artificial intelligence , computer network , ecology , bandwidth (computing) , quantum mechanics , biology , thermodynamics
In this paper we derive a variational integrator for nonsmooth mechanical systems by discretizing the principle of virtual action with finite elements in time. After the discretization with local finite elements, the constitutive laws for the contact forces are introduced as in Moreau's time stepping scheme. This derivation shows exemplary how variational integrators for systems with frictional unilateral constraints can be derived. The long‐time energy behavior of the presented scheme is compared with the behavior of Moreau's stepping scheme on an example system. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)