2004
DOI: 10.1007/s00466-004-0559-z
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Abstract: The finite element formulation of geometrically exact rod models depends crucially on the interpolation of the rotation field from the nodes to the integration points where the internal forces and tangent stiffness are evaluated. Since the rotational group is a nonlinear space, standard (isoparametric) interpolation of these degrees of freedom does not guarantee the orthogonality of the interpolated field hence, more sophisticated interpolation strategies have to be devised. We review and classify the rotation… Show more

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Cited by 134 publications
(111 citation statements)
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References 28 publications
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“…The reason for that is, that the main focus in FE is accuracy, not computational efficiency. The general problem in geometrically nonlinear FE is the proper interpolation of the finite rotations [38] such that objectivity of the strain measures is maintained, i. e. invariance under rigid body motions. This results in extremely technical and sophisticated models with expensive right hand side functions and Jacobians.…”
Section: Introductionmentioning
confidence: 99%
“…The reason for that is, that the main focus in FE is accuracy, not computational efficiency. The general problem in geometrically nonlinear FE is the proper interpolation of the finite rotations [38] such that objectivity of the strain measures is maintained, i. e. invariance under rigid body motions. This results in extremely technical and sophisticated models with expensive right hand side functions and Jacobians.…”
Section: Introductionmentioning
confidence: 99%
“…the works presented by (Cardona and Geradin, 1988), (Simo and Vu-Quoc, 1991), (Pimenta and Yojo, 1993), (Simo et al, 1995), Ibrahimbegovic and Mikdad, 2000;Ibrahimbegovic and Knopf-Lenoir, 2003), (Saje et al, 1998), Jelenic and Crisfield, 1999), (Planinc and Saje, 1999), Atluri, 1988, 1989;Atluri, 1996, 1998;Atluri et al, 2001), (Betsch and Steinmann, 2002), (Zupan and Saje, 2003b), (Kapania and Li, 2003b,a), (Romero, 2004), (Mata et al, 2007), (Makinen, 2007), (Lens and Cardona, 2008), (Ghosh and Roy, 2008) and (Pimenta et al, 2008).…”
Section: The Geometrically Exact Three-dimensional Beam Theorymentioning
confidence: 96%
“…The reason for that is, that the main focus in FE is accuracy, not computational efficiency. A very hard problem in geometrically nonlinear FE is the proper interpolation of finite rotations such that objectivity of the strain measures is maintained [14,31]. (Rigid body motions must not cause additional strains.)…”
Section: Discrete Geometrically Exact Rodsmentioning
confidence: 99%
“…The basic difficulty for a proper discrete curvature definition is to interpolate rotations in a proper, objective way at acceptable numerical costs. For thorough discussions on that topic, we refer to [31]. Approaches that use Cayley transformation instead of interpolation are as well possible [24].…”
Section: Discrete Geometrically Exact Rodsmentioning
confidence: 99%