A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids. Applications to shells

authored by: C. Sansour, Peter Wriggers, J. Sansour
Abstract: In this paper we introduce the finite element version of the so-called post-processed Galerkin method into the field of solid mechanics and apply the new technique to the dynamics of shells. The proposed post-processed method provides low-cost means to lift low-dimensional solutions to high-dimensional solutions. It is the very fact that the kinematical fields are improved to higher orders which makes the method of great interest. Our shell theory is geometrically exact in the sense that all non-linearities are included in the formulation. For time integration an energy/momentum scheme is used to enhance integration stability. Two hierarchical enhanced finite elements are formulated, on the basis of which a specific post-processed method is then developed. With the help of some examples of non-linear shell vibrations, a critical examination and validation of the post-processed method is carried out.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): University of Adelaide
Type: Article
Journal: Computational mechanics
Volume: 32
Pages: 104-114
No. of pages: 11
ISSN: 0178-7675
Publication date: 09.2003
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-003-0465-9 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{296aaec082d147e89661b9c0ee74fc4a,
title = "A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids. Applications to shells",
abstract = "In this paper we introduce the finite element version of the so-called post-processed Galerkin method into the field of solid mechanics and apply the new technique to the dynamics of shells. The proposed post-processed method provides low-cost means to lift low-dimensional solutions to high-dimensional solutions. It is the very fact that the kinematical fields are improved to higher orders which makes the method of great interest. Our shell theory is geometrically exact in the sense that all non-linearities are included in the formulation. For time integration an energy/momentum scheme is used to enhance integration stability. Two hierarchical enhanced finite elements are formulated, on the basis of which a specific post-processed method is then developed. With the help of some examples of non-linear shell vibrations, a critical examination and validation of the post-processed method is carried out.",
keywords = "Finite elements, Hierarchical, Non-linear dynamics, Post-processed Galerkin, Redūktion methods",
author = "C. Sansour and Peter Wriggers and J. Sansour",
year = "2003",
month = sep,
doi = "10.1007/s00466-003-0465-9",
language = "English",
volume = "32",
pages = "104--114",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "1-2",
}