Energy-momentum conserving integration of multibody dynamics

Betsch, Peter; Uhlar, Stefan

doi:10.1007/s11044-007-9043-9

Cited by 60 publications

(67 citation statements)

References 36 publications

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“…In general domain decomposition problems, the slave nodes do (37) where N(n) is the normal to the tangent plane spanned by A 1 (n) and A 2 (n) given by…”

Section: Reformulation Of the Nts Constraintsmentioning

confidence: 99%

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Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration

Hesch

Betsch

2009

Numerical Meth Engineering

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SUMMARYThe present work deals with transient large-deformation domain decomposition problems. The tying of dissimilar meshed grids is performed by applying the mortar method. In this connection, a reformulation of the original linear mortar constraints is proposed, which retains frame-indifference for arbitrary discretizations of the interface. Furthermore, a specific coordinate augmentation technique is proposed to make possible the design of an energy-momentum scheme. Numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy-momentum scheme for three-dimensional problems.

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“…In general domain decomposition problems, the slave nodes do (37) where N(n) is the normal to the tangent plane spanned by A 1 (n) and A 2 (n) given by…”

Section: Reformulation Of the Nts Constraintsmentioning

confidence: 99%

“…To this end, we apply a specific coordinate augmentation technique originally 340 C. HESCH AND P. BETSCH introduced by Betsch and Uhlar [37] in the context of multibody dynamics for the description of joint-coordinates and conjugate joint-forces.…”

Section: Augmented Coordinatesmentioning

confidence: 99%

Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration

Hesch

Betsch

2009

Numerical Meth Engineering

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“…Moreover, their use in Multibody System Dynamics has also increased during the last years Goicolea, 2000, 2005;Betsch and Uhlar, 2007), in this case motivated by their excellent performance integrating systems with constraints.…”

Section: Introductionmentioning

confidence: 99%

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

Orden

Romero

2012

European Journal of Mechanics - A/Solids

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A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermovisco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermodynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

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“…Thus the DAEs provide a uniform framework for flexible multibody systems. Moreover, the DAEs turn out to be beneficial to the design of energy-momentum schemes [3][4][5]. Indeed our shell formulation can be shown to be equivalent to the previous work by Simo & Tarnow [6].…”

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confidence: 69%

Geometrically exact shells in a flexible multibody framework

Sänger

Betsch

2008

Proc Appl Math and Mech

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The present work deals with the extension of contemporary finite element methods for nonlinear structural dynamics to the realm of flexible multibody dynamics. In particular, we aim at the incorporation of geometrically exact shell formulations into a multibody framework. Geometrically exact shell formulations are capable of dealing with finite deformation problems. In particular we focus on (i) a finite element discretization in space which inherits the frameindifference of the nonlinear strain measures from the underlying continuous shell formulation, and (ii) a discretization in time which leads to an energy and momentum conserving scheme or an energy decaying variant thereof. In nonlinear structural dynamics energy-momentum schemes have proven to be well-suited for the stable numerical integration of large deformation problems.We show that semi-discrete formulations emanating from the finite element discretization of geometrically exact shell theories can be regarded as discrete mechanical systems subject to holonomic constraints. Accordingly, the corresponding equations of motion can be written as differential-algebraic equations (DAEs) with index three. In particular, this viewpoint fits perfectly well into the framework of a rotationless description of rigid bodies [1] and geometrically exact beams [2]. Thus the DAEs provide a uniform framework for flexible multibody systems. Moreover, the DAEs turn out to be beneficial to the design of energy-momentum schemes [3][4][5]. Indeed our shell formulation can be shown to be equivalent to the previous work by Simo & Tarnow [6]. The newly established DAE framework facilitates the use of geometrically exact shells in flexible multibody dynamics. Representative numerical examples will demonstrate the capability of the proposed methodology. KeywordsNonlinear finite element methods, nonlinear structural dynamics, differentialalgebraic equations References[1] P. Betsch and P. Steinmann. Constrained integration of rigid body dynamics.

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Energy-momentum conserving integration of multibody dynamics

Cited by 60 publications

References 36 publications

Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration

Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

Geometrically exact shells in a flexible multibody framework

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