MATHEMATICAL ENGINEERING TECHNICAL REPORTS A Non-Interior Implicit Smoothing Approach to Complementarity Problems for Frictionless Contacts

This paper presents a non-interior point method for a frictionless contact problem in the large deformation, where we can exploit the warm start condition in an incremental path-following method such as the arc-length method. We propose a novel reformulation of the nonlinear complementarity problem based on the smoothed Fischer–Burmeister function, in which the smoothing parameter is considered as an independent variable, and we add a nonlinear equation so that the smoothing parameter behaves as a measure of the residual of the complementarity conditions. The reduced system of nonlinear equations is solved by using a conventional method for nonlinear equations with a fast local convergence from the initial point which is defined by using the solution of the previous loading stage. Throughout numerical examples it is shown that in many cases the solution can be found within four iterations.