May, S., Vignollet, J. and Borst, R.D. (2016) Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting Bézier extraction. International Journal for Numerical Methods in Engineering, 107 (3). pp. 205-233. ISSN 0029-5981
Abstract
The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B-splines and unstructured standard T-splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B-splines result in inline image-continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non-uniform rational B-splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B-splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are inline image-continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, Powell–Sabin B-splines and NURBS-to-NURPS (non-uniform rational Powell–Sabin B-splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 John Wiley & Sons, Ltd. This is an author produced version of a paper subsequently published in International Journal for Numerical Methods in Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | isogeometric analysis; Powell–Sabin B-splines; NURBS-to-NURPS; NURBS; unstructured T-splines; Bézier extraction |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Jun 2016 08:38 |
Last Modified: | 02 Jul 2017 08:33 |
Published Version: | http://dx.doi.org/10.1002/nme.5163 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.5163 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:100537 |