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

Onofre Marco, Rubén Sevilla Orcid Logo, Yongjie Zhang, Juan José Ródenas, Manuel Tur

International Journal for Numerical Methods in Engineering, Volume: 103, Issue: 6, Pages: 445 - 468

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.4914

Abstract

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 s...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa21138
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Abstract: 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.
Keywords: Immersed Boundary Methods, Cartesian grids, NURBS, T-spline, Bezier extraction, NEFEM
College: College of Engineering
Issue: 6
Start Page: 445
End Page: 468