Isogeometric finite element data structures based on Bézier extraction of T-splines

M.A. Scott, M.J. Borden, C.V. Verhoosel, T.W. Sederberg, T.J.R. Hughes

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    213 Citations (Scopus)
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    Abstract

    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, all other aspects of a finite element program remaining 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.
    Original languageEnglish
    Pages (from-to)126-156
    Number of pages31
    JournalInternational Journal for Numerical Methods in Engineering
    Volume88
    Issue number2
    DOIs
    Publication statusPublished - 2011

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