Combined interior-point method and semismooth Newton method for frictionless contact problems

In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior-point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior-point method. The simplest node-to-node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node-to-segment or segment-to-segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior-point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior-point method. Copyright q 2009 John Wiley & Sons, Ltd.