On the consistent formulation of torques in a rotationless framework for multibody dynamics

Betsch, Peter; Sänger, Nicolas

doi:10.1016/j.compstruc.2012.10.005

Cited by 10 publications

(8 citation statements)

References 22 publications

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“…The present approach can be viewed as generalization of the method proposed in [24]. In this work, the director-based formulation of rigid body dynamics is treated.…”

Section: Discussionmentioning

confidence: 99%

“…There, the discretization in time generally destroys the orthonormality of the director frame, which is inherently connected to the kinematic assumption of rigidity. It is shown in [24] that the lack of orthonormality of the director frame distorts the application of external torques and thus destroys the balance of angular momentum. This deficiency of the discrete rigid body formulation can be resolved by properly distinguishing between covariant and contravariant directors in much the same way as in the present work.…”

Section: Discussionmentioning

confidence: 99%

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Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

Eugster

Hesch

Betsch

et al. 2013

Numerical Meth Engineering

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In the present work, a new director-based finite element formulation for geometrically exact beams is proposed. The new beam finite element exhibits drastically improved numerical performance when compared with the previously developed director-based formulations. This improvement is accomplished by adjusting the underlying variational beam formulation to the specific features of the director interpolation. In particular, the present approach does not rely on the assumption of an orthonormal director frame. The excellent performance of the new approach is illustrated with representative numerical examples. CopyrightIn this section, we treat the theory of the geometrically exact beam, also known as the special Cosserat beam, introduced by [2] and [1]. The theory is developed by restricting the kinematics of the three-dimensional continuum to a beam-like kinematic. By inserting the reduced kinematics DIRECTOR-BASED BEAM FINITE ELEMENTS IN SKEW COORDINATES 115with the surface element d 2 Â D dÂ 1 dÂ 2 . For the sake of clarity, the contributions due to external forces and inertia are developed in compact form in the Appendix.

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“…The present approach can be viewed as generalization of the method proposed in [24]. In this work, the director-based formulation of rigid body dynamics is treated.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

Eugster

Hesch

Betsch

et al. 2013

Numerical Meth Engineering

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“…The control extension of EM schemes yields EM consistent schemes which are capable of exactly reproducing the balance laws for energy and angular momentum in the discrete setting. We refer to Betsch and Sänger [32] for further investigations in this direction. Concerning the discrete version of the density cost function, we choose…”

Section: Energy-momentum Schemesmentioning

confidence: 99%

Conservation of generalized momentum maps in mechanical optimal control problems with symmetry

Betsch

Becker

2016

Numerical Meth Engineering

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In this paper, a structure-preserving direct method for the optimal control of mechanical systems is developed. The new method accommodates a large class of one-step integrators for the underlying state equations. The state equations under consideration govern the motion of affine Hamiltonian control systems. If the optimal control problem has symmetry, associated generalized momentum maps are conserved along an optimal path. This is in accordance with an extension of Noether's theorem to the realm of optimal control problems. In the present work, we focus on optimal control problems with rotational symmetries. The newly proposed direct approach is capable of exactly conserving generalized momentum maps associated with rotational symmetries of the optimal control problem. This is true for a variety of one-step integrators used for the discretization of the state equations. Examples are the one-step theta method, a partitioned variant of the theta method, and energy-momentum (EM) consistent integrators. Numerical investigations confirm the theoretical findings. 153On the other hand, the infinitesimal version of the discrete symmetry condition (32) can be derived in analogy to (20) and is given byThe term mechanical integrator has originally been coined by Marsden [33] in the context of conservative mechanical systems with symmetry.

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“…In the context of geometrically exact shell theory [11][12][13][14][15][16][17][18], some authors [12,19] follow an approach where interpolation of the director field (initially perpendicular to the mid surface of the shell) is preferred over interpolation of rotations. Nonetheless, it is ultimately rotations and not the director field which are part of the unknowns of the problem.…”

Section: Introductionmentioning

confidence: 99%

A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory

Ortigosa

Gil

2017

Computer Methods in Applied Mechanics and Engineering

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On the consistent formulation of torques in a rotationless framework for multibody dynamics

Cited by 10 publications

References 22 publications

Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

Director‐based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

Conservation of generalized momentum maps in mechanical optimal control problems with symmetry

A computational framework for incompressible electromechanics based on convex multi-variable strain energies for geometrically exact shell theory

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