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, Physics and Astronomy(all), Computer Science Applications

Electronic version(s)

https://doi.org/10.1016/j.cma.2023.116234 (Access: Closed)