A non-interior implicit smoothing approach to complementarity problems for frictionless contacts

This paper presents a non-interior point method for solving frictionless contact problems in large deformations, where we solve the problems in an incremental path-following method from warm start. We propose a novel reformulation of the nonlinear complementarity problem, which is based on the smoothed Fischer–Burmeister function but is distinguished from the conventional formulations in the following two particular aspects: (i) the smoothing parameter is considered as an independent variable; (ii) an equality constraint is added so that the smoothing parameter serves as a measure of the residual of the complementarity conditions. The reduced system of nonlinear equations is solved with a conventional Newton method for nonlinear equations from the initial point which is defined by using the solution of the preceding loading stage. Throughout numerical examples it is shown that in many cases the solution can be found within four Newton iterations.