  This paper presents a novel total Lagrangian cell-centred finite volume
formulation of geometrically exact beams with arbitrary initial curvature
undergoing large displacements and finite rotations. The choice of rotation
parametrisation, the mathematical formulation of the beam kinematics, conjugate
strain measures and the linearisation of the strong form of governing equations
is described. The finite volume based discretisation of the computational
domain and the governing equations for each computational volume are presented.
The discretised integral form of the equilibrium equations are solved using a
block-coupled Newton-Raphson solution procedure. The efficacy of the proposed
methodology is presented by comparing the simulated numerical results with
classic benchmark test cases available in the literature. The objectivity of
strain measures for the current formulation and mesh convergence studies for
both initially straight and curved beam configurations are also discussed.
