Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 123, Issue 17, Pages 3950-3973Publisher
WILEY
DOI: 10.1002/nme.6994
Keywords
block-coupled; finite volume method; geometrically exact beam; Newton-Raphson; total Lagrangian
Funding
- Bekaert
- Irish Research Council [IRCLA/2017/45]
- Science Foundation Ireland [16/RC/3872, RC2302_2]
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This article introduces a novel finite volume formulation for geometrically exact beams undergoing large displacements and finite rotations, and demonstrates its effectiveness through various tests.
This article presents a novel total Lagrangian cell-centered finite volume formulation of geometrically exact beams with arbitrary initial curvatures undergoing large displacements and finite rotations. The choice of rotation parameterization, the mathematical formulation of the beam kinematics, conjugate strain measures, and the linearization of the strong form of governing equations are described. The finite volume based discretization of the computational domain and the governing equations for each computational volume are presented. The discretized integral form of the equilibrium equations is 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.
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