Object Oriented Implementation of the T-spline Based Isogeometric Analysis
Daniel Rypl, Bořek Patzák
Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic
Abstract:
Isogeometric analysis has been recently introduced
as a viable alternative to the standard, polynomial-based
finite element analysis. Initially, the isogeometric approach has been
developed using the NURBS and although it has been shown that it can
outperform the classical finite element method in many aspects, there
are several drawbacks, namely related to the handling trimmed geometries
and to the refinement of the adopted discretization. These may be overcome
by extending the concept of isogeometric analysis to so-called
T-splines which are a generalization of NURBS. This paper presents how
the isogeometric analysis based on T-spline can be integrated within
an object oriented finite element environment. The class
hierarchy and corresponding methods are designed in such a way, that
most of the existing functionality of the finite element code is
reused. The missing data and algorithms are developed and
implemented in such a way that the object oriented features are fully
retained. The performance of the implemented T-spline based isogeometric analysis
methodology is presented on a simple example.