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Adaptive local surface refinement based on LR NURBS and its application to contact

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Abstract

A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient embedding into general finite element codes, the Bézier extraction operator for LR NURBS is formulated. An automatic remeshing technique is presented that allows adaptive local refinement and coarsening of LR NURBS. In this work, LR NURBS are applied to contact computations of 3D solids and membranes. For solids, LR NURBS-enriched finite elements are used to discretize the contact surfaces with LR NURBS finite elements, while the rest of the body is discretized by linear Lagrange finite elements. For membranes, the entire surface is discretized by LR NURBS. Various numerical examples are shown, and they demonstrate the benefit of using LR NURBS: Compared to uniform refinement, LR NURBS can achieve high accuracy at lower computational cost.

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Notes

  1. The index k is used as super- and sub-script but the position has no special meaning.

  2. Also known as degree.

  3. A primitive meshline extension is (a) a meshline spanning \(p+1\) elements, (b) elongating a meshline by one element or (c) raising the multiplicity of a meshline (length of \(p+1\) elements).

  4. The order in both parametric directions is set equally, i.e. \(q=p\).

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Acknowledgements

The authors are grateful to the German Research Foundation (DFG) for supporting this research through Project GSC 111.

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Authors and Affiliations

  1. Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

    Christopher Zimmermann & Roger A. Sauer

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  1. Christopher Zimmermann
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  2. Roger A. Sauer
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Correspondence to Roger A. Sauer.

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Zimmermann, C., Sauer, R.A. Adaptive local surface refinement based on LR NURBS and its application to contact. Comput Mech 60, 1011–1031 (2017). https://doi.org/10.1007/s00466-017-1455-7

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