The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics
Leyendecker S, Betsch P, Steinmann P (2008)
Publication Type: Journal article
Publication year: 2008
Journal
Publisher: Springer Verlag (Germany)
Book Volume: Volume 19
Pages Range: 45-72
Journal Issue: 1-2
DOI: 10.1007/s11044-007-9056-4
Abstract
In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367-391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy-momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method. © 2007 Springer Science+Business Media B.V.
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APA:
Leyendecker, S., Betsch, P., & Steinmann, P. (2008). The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics. Multibody System Dynamics, Volume 19(1-2), 45-72. https://dx.doi.org/10.1007/s11044-007-9056-4
MLA:
Leyendecker, Sigrid, Peter Betsch, and Paul Steinmann. "The Discrete Null Space Method for the Energy Consistent Integration of Constrained Mechanical Systems. Part III: Flexible Multibody Dynamics." Multibody System Dynamics Volume 19.1-2 (2008): 45-72.
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