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Research Papers

Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems

[+] Author and Article Information
Olivier A. Bauchau

Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150

André Laulusa

 SIMUDEC Pte Ltd., Singapore Science Park II, Singapore 117628, Singapore

J. Comput. Nonlinear Dynam 3(1), 011005 (Nov 02, 2007) (8 pages) doi:10.1115/1.2803258 History: Received November 16, 2006; Revised June 18, 2007; Published November 02, 2007

A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically, when redundant generalized coordinates are used, equations of motion are simpler to derive but constraint equations are present. Approaches to dealing with high index differential algebraic equations, based on index reduction techniques, are reviewed and discussed. Constraint violation stabilization techniques that have been developed to control constraint drift are also reviewed. These techniques are used in conjunction with algorithms that do not exactly enforce the constraints. Control theory forms the basis for a number of these methods. Penalty based techniques have also been developed, but the augmented Lagrangian formulation presents a more solid theoretical foundation. In contrast to constraint violation stabilization techniques, constraint violation elimination techniques enforce exact satisfaction of the constraints, at least to machine accuracy. Finally, as the finite element method has gained popularity for the solution of multibody systems, new techniques for the enforcement of constraints have been developed in that framework. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others.

Copyright © 2008 by American Society of Mechanical Engineers
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