Conservative discretization of contact/impact problems for nearly rigid bodies
A discretization scheme for contact/impact problems related to modeling of gears is proposed. The problem is first discretized in time and then a variational formulation for the resulted one step problem is developed. A finite element discretization completes the discretization process. The scheme is a reinterpretation of the general SimoLaursenChavla algorithm in the context of the rigid body motion superimposed with small elastic deformation; it conserves precisely the linear momentum and total energy, and approximately the angular momentum. The discretization method is illustrated with two numerical examples: the standard 1D impact problem for an elastic rod and a 2D model problem of an elastic wheel bouncing within a constraining box.
contact/impact problems finite elements energy conservation