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Title: A new method for T-spline parameterization of complex 2D geometries
Authors: Brovka, Marina 
López, J. I. 
Escobar Sánchez, José María 
Cascón Barbero, José Manuel
Montenegro Armas, Rafael 
UNESCO Clasification: 12 Matemáticas
1204 Geometría
1206 Análisis numérico
120602 Ecuaciones diferenciales
Keywords: Método elementos finitos
Análisis de mallas
T-spline parameterization
Simultaneous T-mesh untangling and smoothing
Meccano method, et al
Issue Date: 2014
Project: Avances en Simulación de Campos de Viento y Radiación Solar. 
Journal: Engineering with Computers 
Abstract: 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 in the interior and on the boundary of the geometry. The efficacy of the proposed technique is shown in several examples. Also we present some results of the application of isogeometric analysis in a geometry parameterized with this technique.
ISSN: 0177-0667
DOI: 10.1007/s00366-013-0336-8
Source: Engineering with computers [ISSN 1435-5663], v. 30 (4), p. 457-473 (Octubre 2014)
Rights: by-nc-nd
Appears in Collections:Artículo preliminar
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