# American Institute of Mathematical Sciences

September  2011, 16(2): 589-605. doi: 10.3934/dcdsb.2011.16.589

## A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP

 1 Department of Dynamics and Control, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China 2 Department of Dynamics and Control, Beijing University of Aeronautics and Astronautics, Beijing 100191, China, China

Received  March 2010 Revised  December 2010 Published  June 2011

In this paper, a constraint-stabilized numerical method is presented for the planar rigid multibody system with friction-affected translational joints, in which the sliders and the guides are treated as particles and bilateral constraints, respectively. The dynamical equations of the non-smooth system are obtained by using the first kind of Lagrange's equations and Baumgarte stabilization method. The normal forces of bilateral constraints are expressed by the Lagrange multipliers and described by complementarity condition, while frictional forces are characterized by a set-valued force law of the type of Coulomb's law for dry friction. Using event-driven scheme, the state transition problem of stick-slip and normal forces of bilateral constraints is formulated and solved as a horizontal linear complementarity problem (HLCP). Finally, the planar rigid multibody system with two translational joints is considered as a illustrative application example. The results obtained also show that the drift of constraints of the system remains bounded.
Citation: Qi Wang, Huilian Peng, Fangfang Zhuang. A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 589-605. doi: 10.3934/dcdsb.2011.16.589
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##### References:
 [1] in "Lecture Notes in Applied and Computational Mechanics," Springer-Verlag, Berlin Heidelberg, 34 (2008).  Google Scholar [2] Discrete and Continuous Dynamical Systems-Series B, 10 (2008), 43-72. doi: 10.3934/dcdsb.2008.10.43.  Google Scholar [3] Meccanica, 43 (2008), 533-554. doi: 10.1007/s11012-008-9139-1.  Google Scholar [4] International Journal for Numerical Methods in Engineering, 60 (2004), 2335-2371. doi: 10.1002/nme.1047.  Google Scholar [5] Applied Mechanics Reviews, 55 (2002), 107-150. doi: 10.1115/1.1454112.  Google Scholar [6] Journal of Vibration and Control, 9 (2003), 25-78.  Google Scholar [7] Computer Methods in Applied Mechanics and Engineering, 195 (2006), 6891-6908. doi: 10.1016/j.cma.2005.08.012.  Google Scholar [8] Journal of Computational and Nonlinear Dynamics, 011007(3) (2008), 1-10.  Google Scholar [9] Shanghai Scientific and Technical Publishers, Shanghai, 2006(in Chinese).  Google Scholar [10] Journal of Sound and Vibration, 197 (1996), 629-637. doi: 10.1006/jsvi.1996.0552.  Google Scholar [11] Journal of Sound and Vibration, 185 (1995), 364-371. doi: 10.1006/jsvi.1995.0385.  Google Scholar [12] Journal of Sound and Vibration, 254 (2002), 987-996. doi: 10.1006/jsvi.2001.4147.  Google Scholar [13] Chinese Journal of Theoretial and Applied Mechanics, 41 (2009), 105-112.  Google Scholar [14] Richard W. Cottle, Jong-Shi Pang and Richard E. Stone, "The Linear Complementarity Problem,", Academic Press, ().   Google Scholar
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