Generalized B-splines as a tool in Isogeometric Analysis

In this paper we propose an alternative to the rational model presenting an isogeometric analysis approach based on generalized B-splines. Geometric models exactly represented by generalized B-splines include those generated by NURBS. Moreover, generalized B-splines possess all fundamental properties of algebraic B-splines (and NURBS) including classical refinement processes as h–p–k refinements. Finally, since generalized B-splines are not confined to rational functions, they behave completely similar to algebraic B-splines with respect to differentiation and integration. This seems to be of interest in the treatment of some relevant problems. 2010 Elsevier B.V. All rights reserved.