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Title: An optimization based method for the construction of 2D parameterizations for isogeometric analysis with T-splines
Authors: López, José Iván 
Brovka, Marina 
Escobar, José Marı́a 
Cascón, José Manuel
Montenegro, Rafael 
Issue Date: 2015
Publisher: 2199-3041
Journal: SEMA SIMAI Springer Series 
Conference: 4th Tetrahedron Workshop on Grid Generation for Numerical Computation, 2013 
Abstract: © 2015, Springer International Publishing Switzerland.We present a new strategy, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain in order to preserve the features of the object boundary with a desired tolerance. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry. Proposed method also permits the modeling of objects with embedded geometries that can be used to solve problems with domains composed of several materials. Application of the isogeometric analysis to these type of domains are presented. The effectiveness of the proposed technique is shown in several examples.
ISBN: 9783319060521
ISSN: 2199-3041
DOI: 10.1007/978-3-319-06053-8_5
Source: SEMA SIMAI Springer Series[ISSN 2199-3041],v. 5, p. 91-112
Appears in Collections:Actas de congresos
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