Generalized B-splines as a tool in isogeometric analysis

The concept of isogeometric analysis has been proposed in [13], where NURBS are considered as basis of the analysis, thanks to their ability to construct an exact geometric model in several practical applications and to their popularity in commercial CAD systems. 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.