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The meccano method for isogeometric solid modeling and applications

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Abstract

We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

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Acknowledgments

This work has been partially supported by the Spanish Government, “Secretaría de Estado de Universidades e Investigación” of the “Ministerio de Economía y Competitividad” and FEDER, grant contracts: CGL2011-29396-C03-01 and CGL2011-29396-C03-03, by “Consejería de Educación” of the “Junta de Castilla León”, grant contract: SA266A12-2, and by CONACYT-SENER (“Fondo Sectorial CONACYT SENER HIDROCARBUROS”, grant contract: 163723).

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Authors and Affiliations

  1. University Institute for Intelligent Systems and Numerical Applications in Engineering (SIANI), University of Las Palmas de Gran Canaria, Las Palmas, Spain

    J. M. Escobar, R. Montenegro & E. Rodríguez

  2. Department of Economics and Economic History, Faculty of Sciences, University of Salamanca, Salamanca, Spain

    J. M. Cascón

Authors
  1. J. M. Escobar
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  2. R. Montenegro
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  3. E. Rodríguez
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  4. J. M. Cascón
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Correspondence to R. Montenegro.

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Escobar, J.M., Montenegro, R., Rodríguez, E. et al. The meccano method for isogeometric solid modeling and applications. Engineering with Computers 30, 331–343 (2014). https://doi.org/10.1007/s00366-012-0300-z

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  • DOI: https://doi.org/10.1007/s00366-012-0300-z

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