A novel virtual element formulation for geometrically exact three-dimensional beams

Discretization techniques for large-displacement analyses of shear-deformable 3D beams should ideally introduce a minimal number of unknowns with a clear physical interpretation and that should possibly be approximated through polynomials of generic degree. Moreover, numerical formulations should be objective, locking-free and singularity-free for arbitrarily large rotations. In this context, the Virtual Element (VE) method offers significant potential that remains to be fully explored. In this work, we propose a novel VE formulation that enables the construction of new nonlinear 3D beam elements of arbitrary polynomial interpolation order. The proposed formulation introduces displacements and rotations at the element endpoints as the only unknowns, even in the case of high-order interpolation functions, as the additional internal degrees of freedom are statically condensed at the element level. The consistency, robustness, and accuracy of this new formulation are assessed through a series of well-established benchmark tests. Numerical results confirm that the developed 3D beam virtual elements are computationally efficient, locking-free, and highly accurate, particularly when high-order ansatz functions are used.