Handling Extraordinary Nodes with Weighted T-spline Basis Functions

Abstract To generate analysis-suitable T-splines for arbitrary topologies, in this paper we introduce a new method to deal with extraordinary nodes in the T-mesh. Knot interval duplication method is used to extract knot vectors for the extraordinary nodes and spoke nodes. From defined bicubic weighted T-spline basis functions, the extracted Bezier coefficients are modified to obtain a gap-free T-spline surface. The boundaries shared by the first-ring neighboring Bezier elements are C0-continuous. Then we use biquartic Bezier basis functions with optimized coefficients to increase the surface continuity to G1. Comparison with other methods shows that our method generates T-spline surfaces with better surface continuity for analysis.

[1]  Fujio Yamaguchi,et al.  Computer-Aided Geometric Design , 2002, Springer Japan.

[2]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[3]  José María Escobar,et al.  Construction of polynomial spline spaces over quadtree and octree T-meshes , 2014 .

[4]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

[5]  Youdong Liang,et al.  Curvature continuity between adjacent rational Bézier patches , 1992, Comput. Aided Geom. Des..

[6]  Michael A. Scott,et al.  Isogeometric spline forests , 2014 .

[7]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[8]  I. Akkerman,et al.  Isogeometric analysis of Lagrangian hydrodynamics , 2013, J. Comput. Phys..

[9]  Giancarlo Sangalli,et al.  ANALYSIS-SUITABLE T-SPLINES OF ARBITRARY DEGREE: DEFINITION, LINEAR INDEPENDENCE AND APPROXIMATION PROPERTIES , 2013 .

[10]  Xin Li,et al.  Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis , 2014, 1404.4346.

[11]  Yongjie Zhang,et al.  A hybrid variational‐collocation immersed method for fluid‐structure interaction using unstructured T‐splines , 2016 .

[12]  John A. Evans,et al.  Isogeometric boundary element analysis using unstructured T-splines , 2013 .

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

[14]  Lei Liu,et al.  Weighted T-splines with application in reparameterizing trimmed NURBS surfaces , 2015 .

[15]  Jörg Peters,et al.  Point-augmented biquadratic C1 subdivision surfaces , 2015, Graph. Model..

[16]  P. Wriggers,et al.  Isogeometric large deformation frictionless contact using T-splines , 2014 .

[17]  Régis Duvigneau,et al.  Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications , 2013, Comput. Aided Des..

[18]  Jiansong Deng,et al.  Modified T-splines , 2013, Comput. Aided Geom. Des..

[19]  Charles T. Loop,et al.  G2 Tensor Product Splines over Extraordinary Vertices , 2008, Comput. Graph. Forum.

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

[21]  Jörg Peters,et al.  Biquintic G2 surfaces via functionals , 2015, Comput. Aided Geom. Des..

[22]  G. Sangalli,et al.  Isogeometric analysis in electromagnetics: B-splines approximation , 2010 .

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

[24]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

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

[26]  Thomas J. R. Hughes,et al.  Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow , 2007, IMR.

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

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

[29]  Tom Lyche,et al.  Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces , 1992 .

[30]  Yuri Bazilevs,et al.  Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines , 2012 .

[31]  T. Hughes,et al.  Converting an unstructured quadrilateral mesh to a standard T-spline surface , 2011 .

[32]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[33]  T. Hughes,et al.  Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline , 2012 .

[34]  Thomas J. R. Hughes,et al.  Truncated hierarchical Catmull–Clark subdivision with local refinement , 2015 .

[35]  Kestutis Kara.  Point-augmented biquadratic C 1 subdivision surfaces , 2014 .

[36]  C. C. Long,et al.  Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates , 2014, J. Comput. Phys..