A Reduction Procedure for One-Dimensional Joint Models and Application to a Lap Joint

A reduction procedure for joint models that was developed in earlier work is extended to allow for relative motion between surfaces, and the effect of this procedure on timestep issues is considered. A general one-dimensional structure containing a frictional interface is considered. Coulomb friction is approximated with nonlinear springs of large but finite stiffness. The system of equations describing this structure is reduced in a procedure similar to Guyan reduction by assuming that the system deforms only in the shapes that it takes when the interface is massless. The result of this procedure is that the dynamics associated with the interface region are removed from the analysis. Following the development of the reduction procedure, the reduced formulation is specialized to the case of a simple lap joint. A numerical example problem is considered in which both the full and reduced equations of motion are integrated over time. It is seen that, for the example problem considered, the reduction procedure results in tremendous computational savings with little loss of accuracy. Based on the results of the simple example problem, it appears that the proposed reduction procedure has potential to be an accurate and effective method of alleviating the timestep difficulties associated with direct finite element analysis of joints in structural dynamics applications.