A cell-centred finite volume formulation of geometrically-exact Simo-Reissner beams with arbitrary initial curvatures

TL;DR

This paper introduces a new finite volume method for geometrically exact beams with initial curvature, capable of handling large displacements and rotations, validated against benchmark tests.

Contribution

It develops a total Lagrangian cell-centred finite volume formulation for beams with arbitrary initial curvature, including novel discretisation and solution strategies.

Findings

Accurate simulation of large displacements and rotations.

Mesh convergence demonstrated for straight and curved beams.

Validated against classical benchmark cases.

Abstract

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.