On the design of energy-momentum integration schemes for arbitrary continuum formulations. Applications to classical and chaotic motion of shells

verfasst von

Carlo Sansour, Peter Wriggers, Jamal Sansour

Abstract

The construction of energy-momentum methods depends heavily on three kinds of non-linearities:(1) the geometric (non-linearity of the strain-displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric nonlinearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law.

Organisationseinheit(en)

Institut für Baumechanik und Numerische Mechanik

Externe Organisation(en)

University of Adelaide

Typ

Artikel

Journal

International Journal for Numerical Methods in Engineering

Band

60

Seiten

2419-2440

Anzahl der Seiten

22

ISSN

0029-5981

Publikationsdatum

21.08.2004

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Numerische Mathematik, Ingenieurwesen (insg.), Angewandte Mathematik

Ziele für nachhaltige Entwicklung

SDG 7 – Erschwingliche und saubere Energie

Elektronische Version(en)

https://doi.org/10.1002/nme.931 (Zugang: Unbekannt)