Cn continuous modelling of smooth contact surfaces using NURBS and application to 2D problems

This paper presents a strategy for the finite-element implementation of C-n continuous contact surfaces for deformable bodies undergoing finite deformations, whereby n represents an arbitrary level of continuity. The proposed novel approach avoids the non-physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries. In particular, for certain problems, the level of continuity may influence the rate of convergence significantly within a non-linear solution scheme. A hierarchical tree data structure is proposed for an efficient search algorithm to find the neighbour elements on adaptively refined meshes, which are involved in the smoothing process of a particular finite element. The same data structure is used for the automatic detection of the contact surfaces of a body. Three representative numerical examples demonstrate the increased rate of convergence, the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method. Copyright (C) 2003 John Wiley Sons, Ltd.