Abstract
In isogeometric analysis splines are used for describing both the geometric shape and the solution fields of the analysis. Although splines are used in boundary structure CAD models, the CAD representation cannot be used directly in isogeometric analysis. We focus on how to build block structured models suited for isogeometric analysis from CAD-models. The blocks are quadrilateral or hexahedral depending on the dimension of the space. A CAD solid represented by its outer and inner hulls is replaced by a trivariate structure where each block is a spline volume and the blocks meet with at least C 0 continuity. To avoid continuity conditions involving several coefficients at block boundaries when representing the blocks by NURBS we do not allow T-joints, i.e., the blocks have to meet in a corner-to-corner configuration. No such conditions are necessary for LR B-splines as LR B-splines are constructed on domains with T-junctions. The local refinement properties of LR B-splines facilitate adapting the structure of the spline space to the local variations of both the shape model and the analysis model. Although the data structure for LR B-splines is more complex than for NURBS, the data volume needed for representing a model using LR B-splines will in most cases be much smaller for LR B-splines than for NURBS.
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References
O.J.D. Barrowclough, T. Dokken, Approximate implicitization using linear algebra. J. Appl. Math. (2012, accepted)
K.A. Belibassakis, T.P. Gerostathis, C.G. Politis, P.D. Kaklis, A.I. Ginnnis, D.N. Mourkogiannis, A novel BEM-ISOGEOMETRIC method with application to the wavemaking resistance problem of bodies at constant speed, in 13th Congress of International Maritime Association of the Mediterranean IMAM 2009
J.S. Deng, F.L. Chen, X. Li, C.Q. Hu, W.H Tong, Z.W Yang, Y.Y. Feng, Polynomial splines over hierarchical T-meshes. Graph. Models 70 (4), 76–86 (2008)
T. Dokken, V. Skytt, Isogeometric representation and analysis – bridging the gap between CAD and analysis, in 47th AIAA Aerospace Sciences Meeting (2009)
T. Dokken, T. Lyche, K.-F. Pettersen, Polynomial splines over locally refined box-partitions. Comput. Aided Geom. Des. 30, 331–356 (2013)
D.R. Forsey, R.H. Barrels, Hierarchical B-spline refinement. Comput. Graph. 22, 205–212 (1988)
Y. Huang, M. Souli, R. Liu, BEM Methods for acoustic and vibroacoustic problems in LS-DYNA, in 8th European LS-DYNA Users Conference, Strasbourg (2011)
T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)
E. Mehlum, V. Skytt, Surface editing, in Numerical Methods and Software Tools in Industrial Mathematics, ed. by M. Dæhlen, A. Tveito (Birkhäuser, Basel, 1997), pp. 381–396
K.F. Pettersen, V. Skytt, Spline volume fairing, in Curves and Surfaces: 7th International Conference, Avignon, ed. by J.-D. Boissonnat, P. Chenin, A. Cohen, C. Gout, T. Lyche, M.-L. Mazure, L. Schumaker (Springer, Berlin, 2012), pp. 553–561
D. Schillinger, L. Dedè, M.A. Scott, J.A. Evans, M.J. Borden, E. Rank, T.J.R. Huges, An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS. Immersed Boundary Methods and T-spline CAD Surfaces. ICES Report 12-05
M.A. Scott, R.N. Simpson, J.A. Evans, S. Lipton, S.P.A. Bordas, T.J.R. Hughes, T.W. Sederberg, Isogeometric boundary element analysis using unstructured T-splines. Methods Appl. Mech. Eng. (submitted)
T.W. Sederberg, J. Zheng, A. Bakenov, A. Nasri, T-splines and T-NURCCS. ACM Trans. Graph. 22 (3), 161–172 (2003)
K.J. Weiler, Topological structures for geometric modeling. Ph.D. Thesis, Rensselaer Polytechnic Institute (1986)
Y. Zhang, W. Wang, T.J.R. Hughes, Solid T-spline construction from boundary representations for genus-zero geometry. ICES Report 11–40
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Skytt, V., Dokken, T. (2016). Models for Isogeometric Analysis from CAD. In: Buffa, A., Sangalli, G. (eds) IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs. Lecture Notes in Mathematics(), vol 2161. Springer, Cham. https://doi.org/10.1007/978-3-319-42309-8_2
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DOI: https://doi.org/10.1007/978-3-319-42309-8_2
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