Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Schmidt, Mathias (Lawrence Livermore National Laboratory)
Noel, L.F.P. (TU Delft Computational Design and Mechanics)
Doble, Keenan (University of Colorado)
Evans, John A. (University of Colorado)
Maute, Kurt (University of Colorado)

2023

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

Extended isogeometric analysis
Immersed finite element method
Lagrange extraction
Multi-material problems
Multi-physics problems
Truncated hierarchical B-splines

http://resolver.tudelft.nl/uuid:c4acbc81-6684-4bf4-9f95-9d06d27ce97e

https://doi.org/10.1007/s00466-023-02306-x

2023-09-20

0178-7675

Computational Mechanics, 71 (6), 1179-1203

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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© 2023 Mathias Schmidt, L.F.P. Noel, Keenan Doble, John A. Evans, Kurt Maute