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research article

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Wei, Xiaodong  
•
Li, Xin
•
Qian, Kuanren
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March 1, 2022
Computer Methods In Applied Mechanics And Engineering

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we allow multiple extraordinary points per face, i.e., we remove the restriction of preceding works that required extraordinary points to be at least four rings apart from each other. We do so by mathematically showing that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. This extension of the subset of AST-splines drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be constructed around small holes. The AST-spline spaces detailed in this work have C-1 inter-element continuity near extraordinary points and C-2 inter-element continuity elsewhere. For the convergence studies performed in this paper involving second-and fourth-order linear elliptic problems with manufactured solutions, we have not found any drawback caused by allowing multiple EPs per face in either the first refinement levels or the asymptotic behavior. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bezier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements and good agreement is found between AST-splines and conventional finite elements. (C)& nbsp;2021 Elsevier B.V. All rights reserved.

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Type
research article
DOI
10.1016/j.cma.2021.114494
Web of Science ID

WOS:000783076600005

Author(s)
Wei, Xiaodong  
•
Li, Xin
•
Qian, Kuanren
•
Hughes, Thomas J. R.
•
Zhang, Yongjie Jessica
•
Casquero, Hugo
Date Issued

2022-03-01

Publisher

ELSEVIER SCIENCE SA

Published in
Computer Methods In Applied Mechanics And Engineering
Volume

391

Article Number

114494

Subjects

Engineering, Multidisciplinary

•

Mathematics, Interdisciplinary Applications

•

Mechanics

•

Engineering

•

Mathematics

•

isogeometric analysis

•

analysis-suitable t-splines

•

extraordinary points

•

linear independence

•

optimal convergence

•

automotive engineering

•

b-rep analysis

•

numerical-integration

•

finite-elements

•

mesh generation

•

surfaces

•

approximation

•

construction

•

subdivision

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
MNS  
Available on Infoscience
May 23, 2022
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/188103
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