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Research Papers

Variational Integrators and Energy-Momentum Schemes for Flexible Multibody Dynamics

[+] Author and Article Information
Peter Betsch, Christian Hesch, Nicolas Sänger, Stefan Uhlar

Chair of Computational Mechanics, Department of Mechanical Engineering, University of Siegen, Paul-Bonatz-Strasse 9-11, D-57076 Siegen Germany

J. Comput. Nonlinear Dynam 5(3), 031001 (May 14, 2010) (11 pages) doi:10.1115/1.4001388 History: Received March 16, 2009; Revised August 27, 2009; Published May 14, 2010; Online May 14, 2010

This work contains a comparison between variational integrators and energy-momentum schemes for flexible multibody dynamics. In this connection, a specific “rotationless” formulation of flexible multibody dynamics is employed. Flexible components such as continuum bodies and geometrically exact beams and shells are discretized in space by using nonlinear finite element methods. The motion of the resulting discrete systems are governed by a uniform set of differential-algebraic equations (DAEs). This makes possible the application and comparison of previously developed structure-preserving methods for the numerical integration of the DAEs. In particular, we apply a specific variational integrator and an energy-momentum scheme. The performance of both integrators is assessed in the context of three representative numerical examples.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The semidiscrete shell with nodal coordinates (φA,dA)∊R3×S2

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Figure 2

Shell intersections: two smooth shell components (left) are joined together modeling a folded shell (right)

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Figure 3

Schematic of the rotary crane

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Figure 4

Rotary crane: total energy calculated with the EM integrator and the VI

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Figure 5

Rotary crane: J3 and J2 components of the total angular momentum (Δt=0.01)

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Figure 6

Rotary crane: distance u(t) between the trolley and the crane axis of rotation (Δt=0.01)

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Figure 7

Rotary crane: relative configuration error of the load mass

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Figure 8

Rotary crane: snapshots of the motion

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Figure 9

Initial mesh configuration of the L-shaped block

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Figure 10

L-shaped block: time history of the external pressure

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Figure 11

L-shaped block: snapshots of the motion at t∊{0,2.5,5,7.5,10}

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Figure 12

L-shaped block: time history of the total energy (EM)

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Figure 13

L-shaped block: time history of the component J2 of the angular momentum (EM)

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Figure 14

L-shaped block: time history of the total energy (VI)

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Figure 15

L-shaped block: time history of the total energy (Δt=0.05)

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Figure 16

L-shaped block: time history of the component J2 of the angular momentum (VI)

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Figure 17

L-shaped block: time history of the component J2 of the angular momentum (Δt=0.05)

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Figure 18

L-shaped block: time history of the total energy (EM)

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Figure 19

L-shaped block: time history of the total energy (VI)

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Figure 20

Three intersecting plates: initial configuration and external loading

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Figure 21

Three intersecting plates: sequence of deformed configurations for t∊{0,1,2,3,4}

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Figure 22

Three intersecting plates (Δt=2.5×10−4): the magnified area shows the results of both the VI and EM schemes

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Figure 23

Three intersecting plates: result of the VI (solid curves) and EM schemes (dashed curves) for different step sizes

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Figure 24

Three intersecting plates (EM): total angular momentum Δt=1.0×10−2

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Figure 25

Three intersecting plates (VI): total angular momentum Δt=2.5×10−4

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