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Isogeometric finite element data structures based on Bézier extraction of T‐splines
Author(s) -
Scott Michael A.,
Borden Michael J.,
Verhoosel Clemens V.,
Sederberg Thomas W.,
Hughes Thomas J. R.
Publication year - 2011
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.3167
Subject(s) - finite element method , smoothness , bézier curve , basis function , subroutine , finite element limit analysis , basis (linear algebra) , mixed finite element method , isogeometric analysis , computer science , extended finite element method , topology (electrical circuits) , b spline , mathematics , algorithm , mathematical analysis , geometry , structural engineering , engineering , combinatorics , operating system
We develop finite element data structures for T‐splines based on Bézier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bézier elements are defined in terms of a fixed set of polynomial basis functions, the so‐called Bernstein basis. The Bézier elements may be processed in the same way as in a standard finite element computer program, utilizing exactly the same data processing arrays. In fact, only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same. A byproduct of the extraction process is the element extraction operator. This operator localizes the topological and global smoothness information to the element level, and represents a canonical treatment of T‐junctions, referred to as ‘hanging nodes’ in finite element analysis and a fundamental feature of T‐splines. A detailed example is presented to illustrate the ideas. Copyright © 2011 John Wiley & Sons, Ltd.