This paper addresses practical issues associated with the numerical enforcement of constraints in flexible multibody systems, which are characterized by index-3 differential algebraic equations (DAEs). The need to scale the equations of motion is emphasized; in the proposed approach, they are scaled based on simple physical arguments, and an augmented Lagrangian term is added to the formulation. Time discretization followed by a linearization of the resulting equations leads to a Jacobian matrix that is independent of the time step size, ; hence, the condition number of the Jacobian and error propagation are both : the numerical solution of index-3 DAEs behaves as in the case of regular ordinary differential equations (ODEs). Since the scaling factor depends on the physical properties of the system, the proposed scaling decreases the dependency of this Jacobian on physical properties, further improving the numerical conditioning of the resulting linearized equations. Because the scaling of the equations is performed before the time and space discretizations, its benefits are reaped for all time integration schemes. The augmented Lagrangian term is shown to be indispensable if the solution of the linearized system of equations is to be performed without pivoting, a requirement for the efficient solution of the sparse system of linear equations. Finally, a number of numerical examples demonstrate the efficiency of the proposed approach to scaling.
Skip Nav Destination
e-mail: olivier.bauchau@ae.gatech.edu
e-mail: alexander.epple@gatech.edu
e-mail: carlo.bottasso@polimi.it
Article navigation
April 2009
Research Papers
Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations
Olivier A. Bauchau,
Olivier A. Bauchau
Daniel Guggenheim School of Aerospace Engineering,
e-mail: olivier.bauchau@ae.gatech.edu
Georgia Institute of Technology
, Atlanta, GA 30332
Search for other works by this author on:
Alexander Epple,
Alexander Epple
Daniel Guggenheim School of Aerospace Engineering,
e-mail: alexander.epple@gatech.edu
Georgia Institute of Technology
, Atlanta, GA 30332
Search for other works by this author on:
Carlo L. Bottasso
Carlo L. Bottasso
Dipartimento di Ingegneria Aerospaziale,
e-mail: carlo.bottasso@polimi.it
Politecnico di Milano
, Milano 20156, Italy
Search for other works by this author on:
Olivier A. Bauchau
Daniel Guggenheim School of Aerospace Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332e-mail: olivier.bauchau@ae.gatech.edu
Alexander Epple
Daniel Guggenheim School of Aerospace Engineering,
Georgia Institute of Technology
, Atlanta, GA 30332e-mail: alexander.epple@gatech.edu
Carlo L. Bottasso
Dipartimento di Ingegneria Aerospaziale,
Politecnico di Milano
, Milano 20156, Italye-mail: carlo.bottasso@polimi.it
J. Comput. Nonlinear Dynam. Apr 2009, 4(2): 021007 (9 pages)
Published Online: March 9, 2009
Article history
Received:
November 30, 2007
Revised:
August 4, 2008
Published:
March 9, 2009
Citation
Bauchau, O. A., Epple, A., and Bottasso, C. L. (March 9, 2009). "Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations." ASME. J. Comput. Nonlinear Dynam. April 2009; 4(2): 021007. https://doi.org/10.1115/1.3079826
Download citation file:
Get Email Alerts
Numerical Simulation Method for the Rain-Wind Induced Vibration of the Three-Dimensional Flexible Stay Cable
J. Comput. Nonlinear Dynam
A Numerical Study for Nonlinear Time-Space Fractional Reaction-Diffusion Model of Fourth-Order
J. Comput. Nonlinear Dynam (March 2025)
An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains
J. Comput. Nonlinear Dynam (March 2025)
Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method
J. Comput. Nonlinear Dynam (March 2025)
Related Articles
A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems
J. Comput. Nonlinear Dynam (October,2011)
A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations
J. Comput. Nonlinear Dynam (July,2006)
Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems
J. Comput. Nonlinear Dynam (January,2008)
The Optimal Control Approach to Dynamical Inverse Problems
J. Dyn. Sys., Meas., Control (March,2012)
Related Proceedings Papers
Related Chapters
Non-linear Problems of Machine Accuracy
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Mash 2-1 Multi-Bit Sigma-Delta Modulator for WLAN
International Conference on Future Computer and Communication, 3rd (ICFCC 2011)
Simulation and Analysis for Motion Space of Spatial Series Mechanism
International Conference on Information Technology and Management Engineering (ITME 2011)