beamFoam: A Cell-Centred Finite Volume Solver for Nonlinear Geometrically-Exact Beams in OpenFOAM

Abstract

This paper presents a new cell-centred finite volume beam solver, beamFoam, for simulating slender structures undergoing large deformations and rotations. The solver is based on the geometrically exact nonlinear Simo–Reissner beam theory and can represent tension, bending, shear, and torsion. Although the underlying model is 1-D, the formulation resolves 3-D kinematics, enabling accurate prediction of spatial deformations and rotations. The paper outlines the governing equations, spatial and temporal discretisation, and code implementation, together with guidelines for simulation setup. The solver’s accuracy and efficiency are demonstrated through three benchmark cases. A 3-D cantilever column under finite deformation shows close agreement with a continuum 3-D solver from the \texttt{solids4Foam} toolbox, while achieving improved accuracy on coarse meshes and significantly reduced computational cost. Additional quasi-static and dynamic tests illustrate the implementation of boundary conditions, stability of time-integration schemes, and mesh convergence behaviour. These results establish beamFoam as an efficient and accurate beam solver within OpenFOAM represent a first significant step towards fluid–structure interaction simulations of slender structures.