A new conservative/dissipative time integration scheme for nonlinear mechanical systems

verfasst von

Cristian Guillermo Gebhardt, Ignacio Romero, Raimund Rolfes

Abstract

We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our approach relies on a collection of linearly constrained quadratic programs defining high order correction terms that modify, in the minimum possible way, the classical midpoint rule so as to guarantee the strict energy conservation/dissipation properties. The solution of these programs provides explicit formulas for the algorithmic forces and velocities which can be easily incorporated into existing implementations. Similarities and differences between our approach and well-established methods are discussed as well. The approach, suitable for reduced-order models, finite element models, or multibody systems, is tested and its capabilities are illustrated by means of several examples.

Organisationseinheit(en)

Institut für Statik und Dynamik

Externe Organisation(en)

IMDEA Materials Institute
Universidad Politécnica de Madrid (UPM)

Typ

Artikel

Journal

Computational mechanics

Band

65

Seiten

405-427

Anzahl der Seiten

23

ISSN

0178-7675

Publikationsdatum

02.2020

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://arxiv.org/abs/1903.08728 (Zugang: Offen)
https://doi.org/10.1007/s00466-019-01775-3 (Zugang: Geschlossen)