Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry

Summary This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer‐Aided Design (CAD) boundary representation with Non‐Uniform Rational B‐Splines (NURBS) or T‐splines. The common feature with other immersed methods is that the current ap...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2015-08, Vol.103 (6), p.445-468
Main Authors: Marco, Onofre, Sevilla, Ruben, Zhang, Yongjie, Ródenas, Juan José, Tur, Manuel
Format: Article
Language:English
Subjects:
Accuracy
Boundary representation
Bézier extraction
Cartesian grids
Computer aided design
Finite element method
Immersed Boundary Methods
Mathematical analysis
Mathematical models
Methodology
NEFEM
NURBS
T-spline
Three dimensional
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Summary:Summary This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer‐Aided Design (CAD) boundary representation with Non‐Uniform Rational B‐Splines (NURBS) or T‐splines. The common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation. In contrast, the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain. A novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests. The applicability, performance, and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions. It is also shown that the accuracy of the proposed methodology is independent on the CAD technology used to describe the geometry of the embedded domain. Copyright © 2015 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4914