Research Article

On the modelling of smooth contact surfaces using cubic splines

  1. N. El-Abbasi,
  2. S. A. Meguid*,
  3. A. Czekanski

Article first published online: 22 JAN 2001

DOI: 10.1002/1097-0207(20010210)50:4<953::AID-NME64>3.0.CO;2-P

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 50, Issue 4, pages 953–967, 10 February 2001

Additional Information

How to Cite

El-Abbasi, N., Meguid, S. A. and Czekanski, A. (2001), On the modelling of smooth contact surfaces using cubic splines. Int. J. Numer. Meth. Engng., 50: 953–967. doi: 10.1002/1097-0207(20010210)50:4<953::AID-NME64>3.0.CO;2-P

Author Information

  1. Engineering Mechanics and Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, ON, Canada M5S 3G8

*Engineering Mechanics and Design Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, ON, M5S 3G8, Canada

Publication History

  1. Issue published online: 22 JAN 2001
  2. Article first published online: 22 JAN 2001
  3. Manuscript Revised: 9 MAR 2000
  4. Manuscript Received: 7 SEP 1999

Funded by

  • Natural Sciences and Engineering Research Council of Canada (NSERC-CRD)

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Keywords:

  • contact;
  • splines;
  • Overhauser splines;
  • smooth surfaces;
  • Lagrange multipliers

Abstract

In this paper, a new strategy for the smooth representation of 2D contact surfaces is developed and implemented. The contact surfaces are modelled using cubic splines which interpolate the finite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals. C2-continuous cubic splines are suitable for representing rigid contact surfaces, while C1-continuous Overhauser splines are shown to be most suitable for representing flexible contact surfaces. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline-based contact surface interpolation scheme does not influence the element calculations. Consequently, it can be easily implemented in standard FE codes. Several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces. The results show a significantimprovement in accuracy compared to traditional piecewise element-based surface interpolation. The predicted contact stresses are also less sensitive to the mismatch in the meshes of the different contacting bodies. This property is useful for problems where the contact area is unknown a priori and when there is significant tangential slip. Copyright © 2001 John Wiley & Sons, Ltd.

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