On the modelling of smooth contact surfaces using cubic splines

In this paper, a new strategy for the smooth representation of 2D contact s urfaces is developed and implemented. The contact surfaces are modelled usi ng cubic splines which interpolate the finite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge o f surface tangents and normals. C-2-continuous cubic splines are suitable f or representing rigid contact surfaces, while C-1-continuous Overhauser spl ines are shown to be most suitable for representing flexible contact surfac es. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline-based contact surfa ce interpolation scheme does not influence the element calculations. Conseq uently, it can be easily implemented in standard FE codes. Several numerica l examples are used to illustrate the advantages of the proposed smooth rep resentation of contact surfaces. The results show a significant improvement in accuracy compared to traditional piecewise element-based surface interp olation. The predicted contact stresses are also less sensitive to the mism atch in the meshes of the different contacting bodies. This property is use ful for problems where the contact area is unknown a priori and when there is significant tangential slip. Copyright (C) 2001 John Wiley & Sons, Ltd.