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Models for Isogeometric Analysis from CAD

Models for Isogeometric Analysis from CAD

Category
Academic chapter/article/Conference paper
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.
Language
English
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
Year
Publisher
Springer
Book
IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs
Issue
2161
ISBN
978-3-319-42308-1
Page(s)
71 - 86