Conference proceeding
A Discussion of Low Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics
Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Vol.5, pp.149-160
ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, Nevada, USA, Sept. 04 - 07, 2007
01/01/2007
DOI: 10.1115/DETC2007-35666
Abstract
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.
Details
- Title: Subtitle
- A Discussion of Low Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics
- Creators
- Naresh Khude - University of Wisconsin at Madison, Madison, WILaurent O Jay - University of IowaAndrei Schaffer - MSC.Software, Ann Arbor, MIDan Negrut - University of Wisconsin at Madison, Madison, WI
- Resource Type
- Conference proceeding
- Publication Details
- Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Vol.5, pp.149-160
- Conference
- ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, Nevada, USA, Sept. 04 - 07, 2007
- DOI
- 10.1115/DETC2007-35666
- Publisher
- ASMEDC
- Language
- English
- Date published
- 01/01/2007
- Academic Unit
- Mathematics
- Record Identifier
- 9984240770502771
Metrics
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