INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2011; 88:126–156 Published online 7 March 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.3167 Isogeometric finite element data structures based on Bézier extraction of T-splines Michael A. Scott 1, ∗, † , Michael J. Borden 1, 2 , Clemens V. Verhoosel 3 , Thomas W. Sederberg 4 and Thomas J. R. Hughes 1 1 Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, TX 78712, U.S.A. 2 Sandia National Laboratories, Albuquerque, NM 87185, U.S.A. 3 Department of Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands 4 Department of Computer Science, Brigham Young University, 3361 TMCB PO Box 26576, Provo, Utah 84602, U.S.A. SUMMARY 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. Received 3 November 2010; Revised 19 January 2011; Accepted 20 January 2011 KEY WORDS: Bézier extraction; isogeometric analysis; T-splines; finite elements 1. INTRODUCTION Isogeometric analysis was introduced in [1] and has been described in detail in [2]. In the isoge- ometric framework the basis which describes the geometry is also used as the basis for analysis. Investigations using simple tensor product NURBS constructions have shown that the use of a smooth basis in analysis provides computational advantages over standard finite elements in many areas, including turbulence [3–6], fluid–structure interaction [7–10], incompressibility [11–13], structural analysis [14, 15], plates and shells [16–20], phase-field analysis [21, 22], large defor- mation with mesh distortion [23], shape optimization [24–27], and electromagnetics [28]. This success has in turn stimulated efforts within the Computer Aided Geometric Design (CAGD) community to develop and integrate analysis-suitable geometric technologies and isogeometric analysis [29–35]. T-splines, which emanate from CAGD, overcome the tensor product restriction inherent in NURBS [36]. In fact, NURBS form a restricted subset of T-splines. Additionally, T-splines ∗ Correspondence to: Michael A. Scott, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, TX 78712, U.S.A. † E-mail: mscott@ices.utexas.edu Copyright  2011 John Wiley & Sons, Ltd.