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A cell‐centered finite volume formulation of geometrically exact Simo–Reissner beams with arbitrary initial curvatures
Author(s) -
Bali Seevani,
Tuković Željko,
Cardiff Philip,
Ivanković Alojz,
Pakrashi Vikram
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6994
Subject(s) - mathematics , discretization , finite element method , linearization , finite volume method , mathematical analysis , geometry , nonlinear system , physics , mechanics , quantum mechanics , thermodynamics
Abstract 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.