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Mechanical integrators for constrained dynamics of geometrically exact beams
Author(s) -
Leyendecker S.,
Betsch P.,
Steinmann P.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410153
Subject(s) - discretization , hamiltonian (control theory) , holonomic , invariant (physics) , hamiltonian system , nonlinear system , classical mechanics , finite element method , integrator , holonomic constraints , hamiltonian mechanics , beam (structure) , physics , mathematics , mathematical analysis , mathematical physics , mathematical optimization , quantum mechanics , phase space , voltage , thermodynamics , optics
The finite element formulation for nonlinear beams in terms of directors, providing a framework for the objective description of their dynamics, is considered. Geometrically exact beams are analyzed as Hamiltonian systems subject to holonomic constraints with a Hamiltonian being invariant under the action of SO(3). The formulation of the Hamiltonian systems in terms of the invariants of SO(3) is perfectly suited for a temporal discretization which leads to energy‐momentum conserving integration. In this connection the influence of alternative procedures for the treatment of the constraints is investigated for the example of a beam with concentrated masses. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)