A locking free virtual element formulation for Timoshenko beams

The virtual element method (VEM) provides new ways of deriving discretization for problems in structural and solid mechanics, starting with the contribution by Beirao 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). (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

The virtual element method (VEM) is a new discretization method for problems in structural and solid mechanics. It allows the construction of different elements with the same shape as finite elements. This study shows the potential application of VEM in the development of Timoshenko beams, providing an accurate element formulation.