The premise of this work is that real-life mechanical systems limit the use of high order integration formulas due to the presence in the associated models of friction and contact/impact elements. In such cases producing a numerical solution necessarily relies on low order integration formulas. The resulting algorithms are generally robust and expeditious; their major drawback remains that they typically require small integration step-sizes in order to meet a user prescribed accuracy. This paper looks at three low order numerical integration formulas: Newmark, HHT, and BDF of order two. These formulas are used in two contexts. A first set of three methods is obtained by considering a direct index-3 discretization approach that solves for the equations of motion and imposes the position kinematic constraints. The second batch of three additional methods draws on the HHT and BDF integration formulas and considers in addition to the equations of motion both the position and velocity kinematic constraint equations. The first objective of this paper is to review the theoretical results available in the literature regarding the stability and convergence properties of these low order methods when applied in the context of multibody dynamics simulation. When no theoretical results are available, numerical experiments are carried out to gauge order behavior. The second objective is to perform a set of numerical experiments to compare these six methods in terms of several metrics: (a) efficiency, (b) velocity constraint drift, and (c) energy preservation. A set of simple mechanical systems is used for this purpose: a double pendulum, a slider crank with rigid bodies, and a slider crank with a flexible body represented in the floating frame of reference formulation.
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ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 4–7, 2007
Las Vegas, Nevada, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-4806-X
PROCEEDINGS PAPER
A Discussion of Low Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics
Naresh Khude,
Naresh Khude
University of Wisconsin at Madison, Madison, WI
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Laurent O. Jay,
Laurent O. Jay
University of Iowa, Iowa City, IA
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Andrei Schaffer,
Andrei Schaffer
MSC.Software, Ann Arbor, MI
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Dan Negrut
Dan Negrut
University of Wisconsin at Madison, Madison, WI
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Naresh Khude
University of Wisconsin at Madison, Madison, WI
Laurent O. Jay
University of Iowa, Iowa City, IA
Andrei Schaffer
MSC.Software, Ann Arbor, MI
Dan Negrut
University of Wisconsin at Madison, Madison, WI
Paper No:
DETC2007-35666, pp. 149-160; 12 pages
Published Online:
May 20, 2009
Citation
Khude, N, Jay, LO, Schaffer, A, & Negrut, D. "A Discussion of Low Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 149-160. ASME. https://doi.org/10.1115/DETC2007-35666
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