Isogeometric finite element data structures based on Bézier extraction of NURBS

We present the B'ezier extraction operator and isogeometric Bézier elements for non‐uniform rational B‐Spline (NURBS)‐based isogeometric analysis. The Bézier extraction operator allows numerical integration of smooth functions to be performed on C0 Bézier elements. We show how the Bézier extrac...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2011-07, Vol.87 (1-5), p.15-47
Main Authors: Borden, Michael J., Scott, Michael A., Evans, John A., Hughes, Thomas J. R.
Format: Article
Language:English
Subjects:
Arrays
Assembly
Bezier
Bézier extraction
Exact sciences and technology
Extraction
Finite element method
finite elements
isogeometric analysis
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
NURBS
Operators
Sciences and techniques of general use
Standard data
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Summary:We present the B'ezier extraction operator and isogeometric Bézier elements for non‐uniform rational B‐Spline (NURBS)‐based isogeometric analysis. The Bézier extraction operator allows numerical integration of smooth functions to be performed on C0 Bézier elements. We show how the Bézier extraction operator is computed for NURBS. We then show that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays. All significant changes may be implemented in a shape function subroutine. Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.2968