Isogeometric finite element data structures based on Bezier extraction of NURBS

We present the Bezier extraction operator and isogeometric Bezier elements for non-uniform rational B-Spline (NURBS)-based isogeometric analysis. The Bezier extraction operator allows numerical integration of smooth functions to be performed on C(0) Bezier elements. We show how the Bezier extraction operator is computed for NURBS. We then show that the extraction operator and Bezier 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 (C) 2010 John Wiley & Sons, Ltd.