Model reduction of contact dynamics simulation using a modified Lyapunov balancing method

doi:10.1007/s11465-011-0244-9

Front Mech Eng

2011, Vol. 6

Issue (4) : 383-391 https://doi.org/10.1007/s11465-011-0244-9

RESEARCH ARTICLE

Model reduction of contact dynamics simulation using a modified Lyapunov balancing method

Jianxun LIANG¹, Ou MA¹(

), Caishan LIU²

1. Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces 88003, USA; 2. Department of Engineering Mechanics, College of Engineering, Peking University, Beijing 100871, China

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Abstract

Finite element models are often used to simulate impact and contact dynamics responses of multibody dynamical systems. However, such a simulation remains very inefficient because very small integration time step must be used when solving the involved differential equations, especially when the involved contact stiffness is high. Although many model reduction techniques have been available to improve the efficiency of finite element based simulations, these techniques cannot be readily applied to contact dynamics simulations due to the high nonlinearity of the contact dynamics models. This paper presents a model reduction approach for finite-element based multibody contact dynamics simulation, based on a modified Lyapunov balanced truncation method. An example is presented to demonstrate that, by applying the model reduction the simulation process is significantly speeded up and the resulting error is bounded within an acceptable level. The performance of the method with respect to some influential factors such as element size, shape and contact stiffness is also investigated.

Keywords contact dynamics dynamic simulation model reduction finite element method

Corresponding Author(s): MA Ou,Email:oma@nmsu.edu

Issue Date: 05 December 2011

Cite this article:

Caishan LIU,Jianxun LIANG,Ou MA. Model reduction of contact dynamics simulation using a modified Lyapunov balancing method[J]. Front Mech Eng, 2011, 6(4): 383-391.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-011-0244-9
https://academic.hep.com.cn/fme/EN/Y2011/V6/I4/383

Fig.1 Contact scenario of the example: (a) Initial configuration; (b) a snapshot during contact

Fig.2 Ball position in both directions

Fig.3 Beam’s central and free nodes’ displacement

Fig.4 A snapshot of the beam’s configuration at 0.5 s

Fig.5 Contact force in longitudinal and vertical directions

Tab.1 Time consumption for simulations with and without model reduction and the corresponding error

Fig.6 Simulation time versus system’s dimension

Fig.7 Displacement of the free end with and without model reduction for the 20-element case

Fig.8 Displacement of the free end with and without model reduction for the 40-element case

Tab.2 Contact stiffness on simulation errors arising from model reduction

Tab.3 Error corresponding to different element size

Tab.4 Error corresponding to different cross section area

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