On triangular virtual elements for Kirchhoff–Love shells

authored by: T. P. Wu, P. M. Pimenta, P. Wriggers
Abstract: We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Archive of applied mechanics
Volume: 94
Pages: 2371-2404
No. of pages: 34
ISSN: 0939-1533
Publication date: 09.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanical Engineering
Electronic version(s): https://doi.org/10.1007/s00419-024-02591-9 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{53eea15640c142f88229400024b6731b,
title = "On triangular virtual elements for Kirchhoff–Love shells",
abstract = "We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works.",
keywords = "Elasticity, Kirchhoff–Love, Linearity, Shells, Virtual element method",
author = "Wu, {T. P.} and Pimenta, {P. M.} and P. Wriggers",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",
year = "2024",
month = sep,
doi = "10.1007/s00419-024-02591-9",
language = "English",
volume = "94",
pages = "2371--2404",
journal = "Archive of applied mechanics",
issn = "0939-1533",
publisher = "Springer Verlag",
number = "9",
}