Inscrição na biblioteca: Guest
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

# International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v1.i23.80
18 pages

## Treatment of Constraints in Complex Multibody Systems. Part I: Methods of Constrained Dynamics

Taira Ozaki
Construction Equipment Technical Center 1, Development Division, Komatsu Ltd., Osaka, Japan
Ahmed A. Shabana
Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, Illinois, USA

### RESUMO

The objective of this investigation is to discuss the use of several nonlinear dynamic formulations for modeling constraints in large-scale multibody systems in general, and tracked vehicles in particular. Among the formulations discussed in this article are the augmented method, the nonpartitioning augmented method, the recursive method, and the penalty method. In the augmented formulation, the vehicle kinematic constraints that describe mechanical joints and specified motion trajectories are augmented to the system dynamic equations using the technique of Lagrange multipliers. A Newton–Raphson algorithm and a coordinate partitioning scheme are used to ensure that the kinematic constraint equations are satisfied at the position level. In the nonpartitioning augmented formulation, no check is made to satisfy the kinematic constraint equations and, as a consequence, no coordinate partitioning is required. In the recursive formulation, the system kinematic equations are expressed in terms of the joint degrees of freedom. This formulation allows for modeling spherical, revolute, prismatic, and cylindrical joints. Using this formulation, closed loop chains are modeled using the recursive joint formulation, and cuts are made at selected secondary joints in order to avoid the singular configurations. In the penalty formulation, mechanical joints are modeled using elastic force elements that have assumed stiffness and damping coefficients. These above-mentioned four formulations are discussed in this article. Results of the computer simulations of a large-scale bulldozer model are presented in Part II of this two-part article.

### Articles with similar content:

Treatment of Constraints in Complex Multibody Systems. Part II: Application to Tracked Vehicles
International Journal for Multiscale Computational Engineering, Vol.1, 2003, issue 2&3
Taira Ozaki, Ahmed A. Shabana
RECONCILED TOP-DOWN AND BOTTOM-UP HIERARCHICAL MULTISCALE CALIBRATION OF BCC FE CRYSTAL PLASTICITY
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 6
Aaron E. Tallman, David L. McDowell, Laura P. Swiler, Yan Wang
Extended Multiscale Finite Element Method for Mechanical Analysis of Periodic Lattice Truss Materials
International Journal for Multiscale Computational Engineering, Vol.8, 2010, issue 6
Hongwu Zhang, J. K. Wu, Zhendong Fu
ESSENTIAL FEATURES OF FINE SCALE BOUNDARY CONDITIONS FOR SECOND GRADIENT MULTISCALE HOMOGENIZATION OF STATISTICAL VOLUME ELEMENTS
International Journal for Multiscale Computational Engineering, Vol.10, 2012, issue 5
David L. McDowell, Darby Luscher, Curt Bronkhorst
STATIC FLEXURE OF CROSS-PLY LAMINATED CANTILEVER BEAMS
Composites: Mechanics, Computations, Applications: An International Journal, Vol.5, 2014, issue 3
Sangita B. Shinde, Yuwaraj M. Ghugal