Isogeometric analysis using Bezier elements

Resumo

Isogeometric Analysis (IGA) is a numerical analysis approach that integrates the concepts of CAD
(Computer-Aided Design) and CAE (Computer-Aided Engineering). It uses the same basis functions employed
by CAD systems to describe the model geometry (e.g. Bezier and NURBS surfaces) to approximate the solution ́
field (e.g. displacement or temperature). Therefore, the geometry of the models is exactly represented for any
level of discretization. The use of well-known geometric modeling algorithms (e.g. knot insertion and degree
elevation) simplifies the model refinement procedure, allowing an easy application of discretization schemes while
preserving the initial geometry. The modeling paradigm adopted in CAD systems uses boundary models that
cannot be directly used by CAE. The use of Bezier elements is a good alternative, as it facilitates the connection ́
between the geometric model, based on a Boundary Representation (B-Rep), and the isogeometric analysis model.
High-order mesh generation techniques are used to discretize geometric models through rational Bezier elements, ́

preserving the exact geometry and creating a suitable analysis model. This paper discusses the definition of two-
dimensional triangular Bezier elements and their performance in numerical analysis. The numerical results are ́

compared with an analytical solution, where the convergence rate of the Bezier elements is assessed in linear ́
elasticity problem.