Rigid and flexible joint modelling in multibody dynamics using finite elements

Cardona, Alberto; Géradin, Michel; Doan, Dinh-Thien-Vuong

doi:10.1016/0045-7825(91)90050-g

Cited by 53 publications

(22 citation statements)

References 3 publications

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“…It is interesting to note that the results obtained using 40 elements are almost identical. This example shows that the solution obtained with the absolute nodal co-ordinate formulation is consistent with the law of physics even though this is a problem of large deformations simulated using a relatively small number of elements (12).…”

Section: Free Falling Pendulummentioning

confidence: 63%

Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation

Berzeri

Shabana

2000

Journal of Sound and Vibration

306

125

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Section: Free Falling Pendulummentioning

confidence: 63%

Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation

Berzeri

Shabana

2000

Journal of Sound and Vibration

306

125

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“…By identifying the configuration space underlying the geometrically exact beam theory as nonlinear, differentiable manifold with Lie group structure and by pointing out important algorithmic consequences resulting from the nonadditivity and non-commutativity of the associated group elements, the original work by Simo [132] and the subse-quent work by Simo and Vu-Quoc [134] laid the foundation for abundant research work on this topic in the following years. The static beam theory [132,134] has been extended to dynamics by Cardona and Geradin [34,35] and by Simo and Vu-Quoc [135]. The contributions of Kondoh et al [88], Dvorkin et al [50] as well as Iura and Atluri [78] can be regarded as further pioneering works in this field.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory

Meier

Popp

Wall

2017

Arch Computat Methods Eng

157

183

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The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C 1 -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages such as lower spatial discretization error level, improved performance of time integration schemes as well as linear and nonlinear solvers or smooth geometry representation as compared to shear-deformable Simo-Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.

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“…Currently, the only available class is the derived class Jacobian, for the calculation of the constraint Jacobian matrices required in the Lagrange multipliers technique that we have chosen to use to couple the algebraic constraint equations with the differential equations of motion of the (Cardona et al, 1991) (Ibrahimbegovic et al, 2000). The incorporation of the constraints via the Lagrange multiplier technique is straightforward, as the inertially-based degrees of freedom of the beam components, which embody both the rigid and deformation motions, are kinematically of the same sense as the physical coordinates of rigid body components.…”

Section: Figure 11 Joint Class Definitionmentioning

confidence: 99%

Object-oriented programming and multibody systems

Kromer¹,

Dufossé

Michel³

2003

Revue Européenne des Éléments Finis

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This paper contains a description of the design of a finite element program dedicated to multibody systems analysis that implements the concepts of object-oriented programming. The principal feature of the mechanical formalism used in this work is to provide a unified framework for both rigid and flexible bodies. We will show that the objectoriented programming greatly simplifies the implementation of other formalisms concerning polyarticulated systems, thus conferring high flexibility and adaptability to the developed software.RÉSUMÉ. Cet article décrit l'architecture orientée objet d'un code de calcul par éléments finis dédié à l'analyse des systèmes multicorps. Le formalisme mécanique mis en oeuvre est caractérisé par le traitement unifié des segments rigides et flexibles. Il est montré que la programmation orientée objet simplifie grandement l'introduction d'autres formalismes relatifs aux systèmes polyarticulés, conférant ainsi une flexibilité et une adaptabilité accrues au logiciel développé.

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Rigid and flexible joint modelling in multibody dynamics using finite elements

Cited by 53 publications

References 3 publications

Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation

Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation

Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory

Object-oriented programming and multibody systems

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