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

Romero, Ignacio

doi:10.1007/s11044-008-9105-7

Cited by 99 publications

(51 citation statements)

References 36 publications

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“…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]. Both papers confirm that the standard geometrically exact two-node displacement-based finite element formulation leads to severe locking, unless a one-point Gaussian integration rule is used.…”

Section: Locking Studymentioning

confidence: 88%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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Highlights• Isogeometric collocation is extended to geometrically exact beams.• Consistent linearization of the strong form of the governing equations is derived.• Incremental rotations are parametrized through Eulerian rotation vectors.• Numerical tests show efficiency and high accuracy. AbstractWe extend the isogeometric collocation method to the geometrically nonlinear beams. An exact kinematic formulation, able to represent three-dimensional displacements and rotations without any restriction in magnitude, is presented without the introduction of the moving frame concept. A displacement-based formulation is adopted. Full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold. Incremental rotations are parametrized through Eulerian rotation vectors and configuration updates are performed by means of the exponential map. Numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy.

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Section: Locking Studymentioning

confidence: 88%

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Marino

2016

Computer Methods in Applied Mechanics and Engineering

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“…4.3). We refer othwise to the article of Romero (2008) for a comparison of the geometrically exact and ANCF approaches to nonlinear rods. Mata et al (2008) model the inelastic constitutive behaviour of composite beam structures under dynamic loading, using a Cosserat model as kinematical basis.…”

Section: Related Work On Viscoelastic Rodsmentioning

confidence: 99%

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

2013

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Abstract. We present the derivation of a simple viscous damping model of Kelvin-Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of the Kelvin-Voigt model and illustrate its behaviour for large bending deformations with a numerical example.

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“…The main difference between this element and the classical nonlinear beam formulation is the use of gradients instead of rotational degrees of freedom. The element's performance was analyzed in [16,35] and compared with the classical formulation in [38]. The second element is a non-linear two-node bar.…”

Section: Finite Element Formulationmentioning

confidence: 99%

A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

Tur¹,

Garcia²,

Baeza³

et al. 2014

Engineering Structures

101

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ElsevierTur Valiente, M.; García, E.; Baeza González, LM.; Fuenmayor Fernández, FJ. (2014) AbstractIn this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which take into account axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, height of the contact wire, etc. The main result of the shape-finding problem is the computation of the length of droppers. A comparison of the results obtained for reference catenaries in the bibliography is also included.

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

Cited by 99 publications

References 36 publications

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

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