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 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.
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Acknowledgements
This work has been supported by the Spanish Government, “Secretaría de Estado de Universidades e Investigación,” “Ministerio de Economía y Competitividad,”, “Programa de FPU del Ministerio de Educación, Cultura y Deporte”, “Programa de FPI propio de la ULPGC” and FEDER, grant contracts: CGL2011-29396-C03-01 and CGL2011-29396-C03-03; “Junta Castilla León,” grant contract: SA266A12-2. It has been also supported by CONACYT-SENER (“Fondo Sectorial CONACYT SENER HIDROCARBUROS,” grant contract: 163723).
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López, J.I., Brovka, M., Escobar, J.M., Cascón, J.M., Montenegro, R. (2015). An Optimization Based Method for the Construction of 2D Parameterizations for Isogeometric Analysis with T-Splines. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_5
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DOI: https://doi.org/10.1007/978-3-319-06053-8_5
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