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

authored by: 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.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): University of Adelaide
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 60
Pages: 2419-2440
No. of pages: 22
ISSN: 0029-5981
Publication date: 21.08.2004
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Sustainable Development Goals: SDG 7 - Affordable and Clean Energy
Electronic version(s): https://doi.org/10.1002/nme.931 (Access: Unknown)