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

Rods

verfasst von
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.

Organisationseinheit(en)
Institut für Kontinuumsmechanik
Externe Organisation(en)
Universidade de Sao Paulo
Typ
Artikel
Journal
Computational mechanics
Band
42
Seiten
715-732
Anzahl der Seiten
18
ISSN
0178-7675
Publikationsdatum
02.04.2008
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
Ziele für nachhaltige Entwicklung
SDG 7 – Erschwingliche und saubere Energie
Elektronische Version(en)
https://doi.org/10.1007/s00466-008-0271-5 (Zugang: Unbekannt)