Finite Element Modeling Concepts in Multibody Dynamics

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

doi:10.1007/978-94-011-1166-9_8

Cited by 39 publications

(18 citation statements)

References 8 publications

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“…To solve the quadratic system R(u) = 0 with the ANM, use of the free online package ManLab [6] has been made. Several standard examples of the literature for which an analytical solution is known [1] [2], as well as examples featuring a more intricate bifurcation diagram have been run. On figure 3, the postbuckling of a clamped-clamped beam is illustrated.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…They have been widely studied during the last decades but are still of interest for research, mainly because of the difficulty to describe 3D rotations. Indeed, they are not unique and among the main parametrizations existing, most of the papers have been focusing on rotational vector-like formulation, highlighting the use of only 3 parameters [1]. However, it has been proved that at least 4 parameters are necessary to avoid any singularities.…”

Section: Introductionmentioning

confidence: 99%

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A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

Cottanceau

Thomas

Véron

et al. 2018

Finite Elements in Analysis and Design

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Summary A flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, requiring quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.

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Section: Results and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

Cottanceau

Thomas

Véron

et al. 2018

Finite Elements in Analysis and Design

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show abstract

“…The finite element model of a flexible multibody dynamics can be categorized broadly into two approaches-the incremental finite element modeling [3,4] and the floating frame of reference formulation (FFRF) [5][6][7][8]. In the former approach, the shape function can only describe a small (infinitesimal) rotation and a convected coordinate system is used in order to deal with the finite rigid body motion.…”

Section: Introductionmentioning

confidence: 99%

Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

Rosyid

El‐Khasawneh

2020

Applied Sciences

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This paper presents the implementation of the floating frame of reference formulation to model the flexible multibody dynamics of a nonsymmetric planar 3PRR parallel manipulator. All of the links, including the moving platform, of the manipulator under study are assumed flexible whereas the joints are assumed rigid. Using the Euler-Bernoulli beam, the flexibility of the links is modeled by using the Rayleigh-Ritz and finite element approximations. In both approximations, fixed-free boundary conditions are applied to the elastic coordinates of the links. These boundary conditions enable the evaluation of the elastic displacement at a link tip coincident with the end-effector of the manipulator which is of interest in the high precision robotics application. Both the approximations were compared by applying two different types of loads to the manipulator. It is shown that the elastic displacements obtained by using both the approximations have an agreement with a slight difference in the magnitude. In addition, the sensitivity analysis shows that the rigidity of the manipulator is much affected by the in-plane depth of the manipulator links’ cross section.

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“…Several families of methods may be distinguished in what has been called exible multibody dynamics: the ÿnite segment method, illustrated in Reference [3], in which the deformable body is assumed to consist of a set of rigid bodies connected by spring and=or dampers; the large rotation vectors formulations, further explained in Reference [4] which deÿne the element nodal co-ordinates with respect to the global co-ordinate system; the moving frame approach, clearly described in Reference [5], characterized by the use of a local reference frame for each exible body, where elastic deformations with respect to an undeformed conÿguration are expressed; and the absolute nodal co-ordinate formulation, developed by Shabana [6], which employs absolute displacements and global slopes as the element co-ordinates, in order to avoid inÿnitesimal rotations and the subsequent linearization they produce.…”

Section: Introductionmentioning

confidence: 99%

A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non‐linear FEA code

Cuadrado

Gutiérrez

Naya

et al. 2001

Numerical Meth Engineering

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SUMMARYTo perform the mechanical design of a machine through computer-aided techniques, at least three main di erent products should be used: a CAD software, to model the parts of the machine; a MBS program, to analyse the kinematics and dynamics of the whole system; and a FEA code, to determine the level of stress and strain su ered by each component. If it is true that CAD software is usually well connected with the two other tools, the same does not happen in what respects to FEA-MBS interfaces. Moreover, since both the large-amplitude motion and the elastic deformation are coupled, they cannot be solved separately, and the usual practice consisting of ÿrst analysing the machine motion assuming rigid bodies, and then calculating stresses under the loads previously generated, is just an approximation. In order to provide mechanical designers with a tool which makes easier and shorter the design-cycle, this paper presents a comparison between the two options that are currently available to address the mentioned problem: a dynamic MBS formulation which simultaneously solves motion and performs stress analysis by considering exible bodies; and a non-linear module of a FEA code, which takes into account large displacements and ÿnite rotations. The comparison is carried out in terms of accuracy and e ciency through four examples. The results lead to the conclusion that, for similar accuracy, the ÿrst method is largely more e cient. Therefore, the interest of developing MBS commercial codes which integrate motion calculation and stress analysis through the mentioned approach is envisioned, as long as they would provide faster solutions.

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Finite Element Modeling Concepts in Multibody Dynamics

Cited by 39 publications

References 8 publications

A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables

Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

A comparison in terms of accuracy and efficiency between a MBS dynamic formulation with stress analysis and a non‐linear FEA code

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