On the modelling of smooth contact surfaces using cubic splines

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.

On a Geometrically Exact Theory for Contact Interactions

“…The necessary optimum condition leads to the projection operation onto the curve 37) showing the orthogonality of the vector (r s − ρ) and the tangent vector τ . According to this, a new coordinate system τ , ν, β is introduced as a natural coordinate system of the curved line, see Fig.…”

“…The application of a control spline polygon for the searching procedure has been discussed in El-Abbasi et.al. [37] (2001) and in Al-Dojayli and Meguid [2] (2002) Since, in this thesis the linearization problems are resolved by the covariant derivation, we are free now to choose any kind of approximations. Here, Hermitian approximation as a simple subclass of the NURB spline approximation is taken.…”

“…Despite the enormous number of publications on contact mechanics, there are only a few publications covering 37 to some completeness the problem of uniqueness and existence of the closest point procedure for arbitrary approximations of the contact surfaces as well as describing effective numerical algorithms to overcome problems. The problem of non-uniqueness and non-existence of the projection for e.g.…”

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A new smooth contact element: 3D diffuse contact element

“…Rigid contact surfaces are smoothed by techniques used Article published by EDP Sciences International Journal for Simulation and Multidisciplinary Design Optimization in CAD surface modeling [15]. Bézier or B-Splines can be used with efficiency to represent deformable contact surfaces [12,18,25,27,32].…”