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Investigation on model order reduction methods for flexible bodies with contact-impact based on partition modeling

The finite element method is widely used to solve the problem of flexible bodies with contact-impact. To express the high-frequency and high-transient characteristics of the impact process and the high stress distribution of the local contact region, the amount of the node coordinates will be very large, which brings great burden to the dynamic simulation. It is particularly important to reduce the degrees of freedom of the system in the contact-impact problem. However, as the impact itself is a strong nonlinear problem, the linear model reduction techniques cannot be used directly. The partition method is presented to solve this problem, in which the deformation of the contact region is described by finite element node coordinates to preserve the local nonlinear characteristic while the deformation of the non-contact region is described by the reduced elastic coordinates. Different model reduction techniques including modal truncation method and Krylov subspace method are used to reduce the degrees of freedom of the non-contact region of an experimental rod-plate impact case, and the results are compared with that of the finite element method and the experiment. The simulation results show that the partition method can effectively reduce the degrees of freedom of the system and maintain good accuracy. Moreover, the Krylov subspace method has an advantage over the modal method in the model reduction of contact-impact problem.