NURBS-based geometries

A mapping approach for virtual serendipity elements

authored by: Peter Wriggers, Blaž Hudobivnik, Fadi Aldakheel
Abstract: A NURBS-based serendipity virtual element method for general (arbitrary) element shapes is outlined in this work. The low-order VEM ansatz function is now extended towards higher-order formulation. In comparison with the already existing serendipity VEM, a general mapping scheme is developed within this contribution allowing to deviate from the assumption of straight edges of virtual elements. A number of numerical examples illustrates the robustness and accuracy of the new mapping methodology. The results are very promising and underline the advantages of the formulations for dealing with arbitrary geometries.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 378
ISSN: 0045-7825
Publication date: 01.05.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2021.113732 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{16ff9491942a4000ab04ae8ea23126ec,
title = "NURBS-based geometries: A mapping approach for virtual serendipity elements",
abstract = "A NURBS-based serendipity virtual element method for general (arbitrary) element shapes is outlined in this work. The low-order VEM ansatz function is now extended towards higher-order formulation. In comparison with the already existing serendipity VEM, a general mapping scheme is developed within this contribution allowing to deviate from the assumption of straight edges of virtual elements. A number of numerical examples illustrates the robustness and accuracy of the new mapping methodology. The results are very promising and underline the advantages of the formulations for dealing with arbitrary geometries.",
keywords = "Bezier splines, Higher-order formulations, Isoparametric maps, Serendipity elements, Virtual element method (VEM)",
author = "Peter Wriggers and Bla{\v z} Hudobivnik and Fadi Aldakheel",
note = "Funding Information: The first author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the collaborative research center CRC 1153 while the third author acknowledges support for this research by the DFG–Priority Program SPP 2020 under the project WR 19/58-2.",
year = "2021",
month = may,
day = "1",
doi = "10.1016/j.cma.2021.113732",
language = "English",
volume = "378",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}