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Research Papers

Advances in the Application of the Divide-and-Conquer Algorithm to Multibody System Dynamics

[+] Author and Article Information
Jeremy J. Laflin

Computational Dynamics Laboratory,
Department of Mechanical, Aerospace,
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: laflij@rpi.edu

Kurt S. Anderson

Computational Dynamics Laboratory,
Department of Mechanical, Aerospace,
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: anderk5@rpi.edu

Imad M. Khan

Computational Dynamics Laboratory,
Department of Mechanical, Aerospace,
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: khani2@rpi.edu

Mohammad Poursina

Assistant Professor
Department of Aerospace
and Mechanical Engineering,
University of Arizona,
Tucson, AZ 85721
e-mail: mpoursina@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received June 3, 2013; final manuscript received November 19, 2013; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041003 (Jul 11, 2014) (8 pages) Paper No: CND-13-1121; doi: 10.1115/1.4026072 History: Received June 03, 2013; Revised November 19, 2013

This paper summarizes the various recent advancements achieved by utilizing the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with many aspects of modeling, designing, and simulating articulated multibody systems. This basic algorithm provides a framework to realize O(n) computational complexity for serial task scheduling. Furthermore, the framework of this algorithm easily accommodates parallel task scheduling, which results in coarse-grain O(logn) computational complexity. This is a significant increase in efficiency over forming and solving the Newton–Euler equations directly. A survey of the notable previous work accomplished, though not all inclusive, is provided to give a more complete understanding of how this algorithm has been used in this context. These advances include applying the DCA to constrained systems, flexible bodies, sensitivity analysis, contact, and hybridization with other methods. This work reproduces the basic mathematical framework for applying the DCA in each of these applications. The reader is referred to the original work for the details of the discussed methods.

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Figures

Grahic Jump Location
Fig. 1

Two articulated bodies assembled about a kinematic joint

Grahic Jump Location
Fig. 2

Hierarchic assembly and disassembly with binary tree

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