Numerical integration over 2D NURBS-shaped domains with applications to NURBS-enhanced FEM

Author (s): Sevilla, R. and Fernández-Méndez S.
Journal: Finite Elements in Analysis and Design

Volume: 47
Pages: 1209 – 1220
Date: 2011

Abstract:
This paper focuses on the numerical integration of polynomial functions along non-uniform rational B-splines (NURBS) curves and over 2D NURBS-shaped domains, i.e. domains with NURBS boundaries. The integration of the constant function is of special interest in computer aided design software and the integration of very high-order polynomials is a key aspect in the recently proposed NURBS-enhanced finite element method (NEFEM). Several well-known numerical quadratures are compared for the integration of polynomials along NURBS curves, and two transformations for the definition of numerical quadratures in triangles with one edge defined by a trimmed NURBS are proposed, analyzed and compared. When exact integration is feasible, explicit formulas for the selection of the number of integration points are deduced. Numerical examples show the influence of the number of integration points in NEFEM computations.

Journal paper (from the publisher)  
UPCommons page Link  

Bibtex:

@article{2011-FEAD-SF,
author = "Sevilla, R. and Fernández-Méndez, S.",
title = "Numerical integration over 2D NURBS-shaped domains with applications to NURBS-enhanced \{FEM\} ",
journal = "Finite Elements in Analysis and Design ",
volume = "47",
number = "10",
pages = "1209 - 1220",
year = "2011",
issn = "0168-874X",
doi = "http://dx.doi.org/10.1016/j.finel.2011.05.011",
url = "http://www.sciencedirect.com/science/article/pii/S0168874X1100117X",
}