An energy-momentum integration scheme and enhanced strain finite elements for the non-linear dynamics of shells

authored by: Carlo Sansour, Werner Wagner, Peter Wriggers, Jamal Sansour
Abstract: The paper is concerned with a dynamic formulation of shells and the development of a corresponding robust energy-momentum integration scheme within the framework of enhanced finite elements. Energy-momentum schemes preserve, by design, specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the system and the applied forces allow to. In a previous work, an energy-momentum scheme was developed by the authors which enjoys the feature of being applicable to any shell theory whatever the non-linearity in the strain-displacement relations may be. The method goes beyond a formulation by Simo and Tarnow which applies only when the non-linearity is of quadratic nature. In this paper, we build up on previous work and extend the formulation to encompass enhanced strain finite elements frequently used in structural analysis. The shell formulation used is characterized by seven degrees of freedom and the non-linearity in the strain-displacement relations is of cubic nature. Various examples of non-linear shell dynamics including free large overall motion and non-linear vibrations in conjunction with cases of dynamic stability are considered.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): Karlsruhe Institute of Technology (KIT)
Type: Article
Journal: International Journal of Non-Linear Mechanics
Volume: 37
Pages: 951-966
No. of pages: 16
ISSN: 0020-7462
Publication date: 30.12.2001
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/S0020-7462(01)00108-1 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{cfb04e2175b843e49d70a4550cc2fe84,
title = "An energy-momentum integration scheme and enhanced strain finite elements for the non-linear dynamics of shells",
abstract = "The paper is concerned with a dynamic formulation of shells and the development of a corresponding robust energy-momentum integration scheme within the framework of enhanced finite elements. Energy-momentum schemes preserve, by design, specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the system and the applied forces allow to. In a previous work, an energy-momentum scheme was developed by the authors which enjoys the feature of being applicable to any shell theory whatever the non-linearity in the strain-displacement relations may be. The method goes beyond a formulation by Simo and Tarnow which applies only when the non-linearity is of quadratic nature. In this paper, we build up on previous work and extend the formulation to encompass enhanced strain finite elements frequently used in structural analysis. The shell formulation used is characterized by seven degrees of freedom and the non-linearity in the strain-displacement relations is of cubic nature. Various examples of non-linear shell dynamics including free large overall motion and non-linear vibrations in conjunction with cases of dynamic stability are considered.",
author = "Carlo Sansour and Werner Wagner and Peter Wriggers and Jamal Sansour",
year = "2001",
month = dec,
day = "30",
doi = "10.1016/S0020-7462(01)00108-1",
language = "English",
volume = "37",
pages = "951--966",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Ltd.",
number = "4-5",
}