Isogeometric analysis using LR B-splines

Abstract The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al. (2013) [6] may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis. In this paper, we propose local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigate its performance by doing numerical tests on well known benchmark cases. The theory behind LR B-spline is not presented in full details, but the main conceptual ingredients are explained and illustrated by a number of examples.

[1]  Annalisa Buffa,et al.  Characterization of T-splines with reduced continuity order on T-meshes , 2012 .

[2]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[3]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..

[4]  M. Scott,et al.  On the Nesting Behavior of T-splines , 2011 .

[5]  T. Hughes,et al.  ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES , 2006 .

[6]  D. Schillinger,et al.  An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry , 2011 .

[7]  Thomas J. R. Hughes,et al.  On linear independence of T-spline blending functions , 2012, Comput. Aided Geom. Des..

[8]  B. Simeon,et al.  A hierarchical approach to adaptive local refinement in isogeometric analysis , 2011 .

[9]  Tom Lyche,et al.  Polynomial splines over locally refined box-partitions , 2013, Comput. Aided Geom. Des..

[10]  Hendrik Speleers,et al.  THB-splines: The truncated basis for hierarchical splines , 2012, Comput. Aided Geom. Des..

[11]  John A. Evans,et al.  Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .

[12]  David R. Forsey,et al.  Hierarchical B-spline refinement , 1988, SIGGRAPH.

[13]  B. Simeon,et al.  Adaptive isogeometric analysis by local h-refinement with T-splines , 2010 .

[14]  T. Hughes,et al.  Local refinement of analysis-suitable T-splines , 2012 .

[15]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[16]  Knut Morten Okstad,et al.  Error estimation based on Superconvergent Patch Recovery using statically admissible stress fields , 1998 .

[17]  B. Mourrain.  On the dimension of spline spaces on planar T-subdivisions , 2010 .

[18]  F. Cirak,et al.  A subdivision-based implementation of the hierarchical b-spline finite element method , 2013 .

[19]  Ping Wang,et al.  Adaptive isogeometric analysis using rational PHT-splines , 2011, Comput. Aided Des..

[20]  John A. Evans,et al.  An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces , 2012 .