A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations

By Ignacio Romero. 2008

139 citations recorded by the source corpus.

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other.

Subfields: Control and Systems Engineering, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4ec415e34eb991b6c7b9d983f7ac303baa90b882

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In Control and Systems Engineering

In Mechanics of Materials

In Numerical Analysis

Citations in the corpus

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams (2016, methodology): “Within the FE method framework, comparisons of different geometrically nonlinear beam formulations in terms of locking are discussed in [64] and a locking-free hybrid formulation is presented in [65].”
Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods (2009, background): “More recently, the multibody system dynamics researches based on ANCF have still also been carried out by many authors in different contexts [22–24].”
Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates (2014, result): “The director interpolation has originally been employed in the finite element discretization of the Simo-Reissner beam theory in Romero & Armero [7] and Betsch & Steinmann [8, 9].”
Comparison of the absolute nodal coordinate and geometrically exact formulations for beams (2014, background): “Romero concluded that the absolute nodal coordinate formulation is more computationally intensive than the geometrically exact formulations.”