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

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.