An evaluation of time integration schemes in the solution of contact problems

Abstract

Contact analysis is an important branch of structural mechanics. The finite element method has become a major solution approach because of the high nonlinearities in contact problems. A large number of algorithms have been proposed and extensively used to solve engineering problems, but some issues have not been addressed yet. The first purpose of this research is to evaluate attempts to achieve accurate and practical time integration schemes for contact problems. Towards this aim, this study proposes an analytical form of the solutions using the time integration schemes that can be used in the evaluation of different methods. Then, a simple velocity- and acceleration-update process that is combined with the conventional time integration methods is proposed to suppress (as much as possible) spuriously generated energy during the contact events.