An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1

Rods

authored by: P. M. Pimenta, E. M.B. Campello, Peter Wriggers
Abstract: A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computational mechanics
Volume: 42
Pages: 715-732
No. of pages: 18
ISSN: 0178-7675
Publication date: 02.04.2008
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Sustainable Development Goals: SDG 7 - Affordable and Clean Energy
Electronic version(s): https://doi.org/10.1007/s00466-008-0271-5 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{7a2e6f55c3e54d6c8a5861fd1a9e4d1f,
title = "An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods",
abstract = "A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.",
keywords = "Energy conservation, Momentum conservation, Nonlinear dynamics, Rods, Time integration",
author = "Pimenta, {P. M.} and Campello, {E. M.B.} and Peter Wriggers",
year = "2008",
month = apr,
day = "2",
doi = "10.1007/s00466-008-0271-5",
language = "English",
volume = "42",
pages = "715--732",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "5",
}