Details

Autor(en) / Beteiligte

• May, Stefan
• Vignollet, Julien
• Borst, René de

Titel

Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting Bézier extraction

Ist Teil von

• International journal for numerical methods in engineering, 2016-07, Vol.107 (3), p.205-233

Ort / Verlag

Bognor Regis: Blackwell Publishing Ltd

Erscheinungsjahr

2016

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• Summary 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 CA1‐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 CA1‐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. Copyright © 2015 John Wiley & Sons, Ltd.