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Isogeometric finite element data structures based on Bézier extraction of NURBS
Author(s) -
Borden Michael J.,
Scott Michael A.,
Evans John A.,
Hughes Thomas J. R.
Publication year - 2010
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/nme.2968
Subject(s) - isogeometric analysis , finite element method , subroutine , b spline , operator (biology) , cad , bézier curve , computer science , mathematics , topology (electrical circuits) , algorithm , mathematical analysis , geometry , structural engineering , engineering drawing , engineering , combinatorics , biochemistry , chemistry , repressor , transcription factor , gene , operating system
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 C 0 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.