Isogeometric Finite Element Analysis based on Bézier Extraction of NURBS and T-splines

Abstract

This thesis will give a theoretical overview of B-splines, as well as NURBS and T-splines which are based on B-splines, and also the concept of Bézier decomposition of these spline functions. Bézier decomposition will decompose the splines into Bernstein polynomials which are defined over the domain of one quadrature element. This theoretical background will then be used to implement a Matlab isogeometric finite element analysis program. Two different choices for implementation are explored, a isogeometric finite element solver built from scratch for use of NURBS, and the use of Bézier extraction to implement isogeometric analysis with NURBS and T-splines in an already existing finite element solver. The main focus will be on use of Bézier extraction, which will signicantly ease the implementation. Numerical studies are performed with problems of linear elasticity and heat conduction, to study the convergence of an isogeometric  analysis.The accuracy of isogeometric analysis will prove to be better than for a traditional FEA for the analyzed problems