Details
| Original language | English |
|---|---|
| Article number | 116234 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 417 |
| Early online date | 22 Jul 2023 |
| Publication status | Published - 15 Dec 2023 |
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).
Keywords
- Higher order ansatz, Large deflections, Large rotations, Timoshenko beams, Virtual Element Method (VEM)
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computer Methods in Applied Mechanics and Engineering, Vol. 417, 116234, 15.12.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A locking free virtual element formulation for Timoshenko beams
AU - Wriggers, P.
PY - 2023/12/15
Y1 - 2023/12/15
N2 - 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).
AB - 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).
KW - Higher order ansatz
KW - Large deflections
KW - Large rotations
KW - Timoshenko beams
KW - Virtual Element Method (VEM)
UR - http://www.scopus.com/inward/record.url?scp=85166192594&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116234
DO - 10.1016/j.cma.2023.116234
M3 - Article
AN - SCOPUS:85166192594
VL - 417
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116234
ER -