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Computational Mechanics
Erschienen in: Computational Mechanics 1/2015

01.07.2015 | Original Paper

Tangential differential calculus and the finite element modeling of a large deformation elastic membrane problem

verfasst von: Peter Hansbo, Mats G. Larson, Fredrik Larsson

Erschienen in: Computational Mechanics | Ausgabe 1/2015

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Abstract

We develop a finite element method for a large deformation membrane elasticity problem on meshed curved surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also applied to form finding problems.
Vorheriger Artikel On parallelization of the loop over elements in FEAP
Nächster Artikel Surface effects on shape and topology optimization of nanostructures

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Fußnoten
1
Henceforth, we use the notation \(\{\bullet \}\) to indicate an implicit function.
 
2
Note that the first Piola Kirchhoff stress tensor is a two-point tensor with “legs” in both current and reference configurations.
 
3
For illustration, we here give the explicit component forms in the orhogonal \(XYZ\) and \(\xi \eta \zeta \) systems, respectively.
 
4
Note that \(\varvec{L}_{NN}\) is of second order.
 
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Metadaten
Titel
Tangential differential calculus and the finite element modeling of a large deformation elastic membrane problem
verfasst von
Peter Hansbo
Mats G. Larson
Fredrik Larsson
Publikationsdatum
01.07.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 1/2015
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-015-1158-x

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