Virtual element formulation for trusses and beams

The virtual element method (VEM) was developed not too long ago, starting with the paper Beirao da Veiga et al. (2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements in solid mechanics, however, has so far not been applied to one dimensional structures like trusses and beams. In this project, several VEM elements suitable for trusses and beams are derived. It could be shown that the virtual element methodology produces elements that are equivalent to well know finite elements but also elements that are different, especially for higher order ansatz functions, like 2nd and 3rd order for the truss and 4th order for the beam. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same nodal degrees of freedom as finite beam elements. Furthermore, the formulation allows to compute nonlinear structural problems undergoing large deflections and rotations.