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

[EN] 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.With the support of the European Union Framework Program (FP7) under grant No. 289361 INSIST, Ministerio de Economia y Competitividad of Spain (DPI2010-20542)(DPI2013-46317-R), FPI program (BES-2011-044080), and Generalitat Valenciana (PROMETEO/2012/023). R. Sevilla gratefully acknowledges the financial support provided by the Ser Cymru National Research Network in Advanced Engineering and Materials. Y. Zhang was supported in part by the PECASE Award N00014-14-1-0234 and NSF CAREER Award OCI-1149591.Marco Alacid, O.; Sevilla, R.; Zhang, Y.; Ródenas, J.; Tur Valiente, M. (2015). Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. International Journal for Numerical Methods in Engineering. 103(6):445-468. https://doi.org/10.1002/nme.4914S445468103