An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

Abstract

In this paper, an efficient formulation based on the Lagrangian method is presented to investigate the contact–impact problems of flexible multi-body systems. Generally, the penalty method and the Hertz contact law are the most commonly used methods in engineering applications. However, these methods are highly dependent on various non-physical parameters, which have great effects on the simulation results. Moreover, a tremendous number of degrees of freedom in the contact–impact problems will influence the numerical efficiency significantly. With the consideration of these two problems, a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in flexible multi-body system numerically. Meanwhile, the finite element meshing laws of the contact bodies will be studied preliminarily. A numerical example with experimental verification will certify the reliability of the presented formulation in contact–impact analysis. Furthermore, a series of numerical investigations explain how great the influence of the finite element meshing has on the simulation results. Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficiency. In this paper, an efficient formulation based on the Lagrangian method is presented to investigate the contact–impact problems of flexible multi-body systems. A transformation from finite element coordinates p to component mode synthesis generalized coordinates y can be performed. When a contact pair is activated, a set of constraint equations should be added to the system