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On the modelling of smooth contact surfaces using cubic splines
Author(s) -
ElAbbasi N.,
Meguid S. A.,
Czekanski A.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010210)50:4<953::aid-nme64>3.0.co;2-p
Subject(s) - piecewise , interpolation (computer graphics) , spline interpolation , box spline , finite element method , tangent , surface (topology) , mathematics , contact analysis , kinematics , contact area , polygon mesh , mathematical analysis , geometry , algorithm , computer science , bilinear interpolation , structural engineering , materials science , engineering , computer graphics (images) , composite material , physics , classical mechanics , statistics , animation
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. C 2 ‐continuous cubic splines are suitable for representing rigid contact surfaces, while C 1 ‐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.