A locking free virtual element formulation for Timoshenko beams

authored by: P. Wriggers
Abstract: The virtual element method (VEM) provides new ways of deriving discretization for problems in structural and solid mechanics, starting with the contribution by Beirão da Veiga et al. (2013) for elastic solids. Interestingly, the virtual element method allows also to revisit the construction of different elements which have the same shape as finite elements. This is even true for one-dimensional structures like trusses and beams. Here we study a virtual element development of the Timoshenko beam which surprisingly leads to a straight forward formulation of locking free and in the linear range even exact Timoshenko beam elements. These elements can be easily incorporated into classical finite element codes since they have the same number of unknowns as finite elements for beams. The formulation allows to compute nonlinear structural problems undergoing large deflections and rotations using the formulation provided in Reissner (1972).
Organisation(s): Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 417
ISSN: 0045-7825
Publication date: 15.12.2023
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.2023.116234 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{ddff1be7d15c4ccbb23d122b1d2293ec,
title = "A locking free virtual element formulation for Timoshenko beams",
abstract = "The virtual element method (VEM) provides new ways of deriving discretization for problems in structural and solid mechanics, starting with the contribution by Beir{\~a}o da Veiga et al. (2013) for elastic solids. Interestingly, the virtual element method allows also to revisit the construction of different elements which have the same shape as finite elements. This is even true for one-dimensional structures like trusses and beams. Here we study a virtual element development of the Timoshenko beam which surprisingly leads to a straight forward formulation of locking free and in the linear range even exact Timoshenko beam elements. These elements can be easily incorporated into classical finite element codes since they have the same number of unknowns as finite elements for beams. The formulation allows to compute nonlinear structural problems undergoing large deflections and rotations using the formulation provided in Reissner (1972).",
keywords = "Higher order ansatz, Large deflections, Large rotations, Timoshenko beams, Virtual Element Method (VEM)",
author = "P. Wriggers",
year = "2023",
month = dec,
day = "15",
doi = "10.1016/j.cma.2023.116234",
language = "English",
volume = "417",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}