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An efficient parametrization of planar domain for isogeometric analysis using harmonic functions

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Abstract

A recent and unified methodology of isogeometric analysis (IGA) requires the geometric model of the domain in the form of a parametric spline. Developing such a geometric model for IGA is called parameterization, and it is a challenging task. The way quality of a mesh affects the results in finite element analysis; an effective parametrization is a key for accurate results and computational efficiency. Finding a spline representation for the domain involves two sets of unknowns, namely parameter values and control points. In this work, a new method is proposed to find them in two stages for planar domains. The domain is mapped to an equivalent convex domain using harmonic functions. Here, the domain is mapped to a circle and then to a square so that the resulting parameter values are suitable for the tensor–product form of B-spline surface. The B-spline control points for the domain are computed with inverse of tensor–product B-spline. Most existing methodologies involve iterative optimization-based methods which makes them expensive. Experimental results of a few cases of complex domains are reported to demonstrate the effectiveness of the method in comparison with other methods. Moreover, metrics are developed to assess the quality of parametrization are included.

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References

  1. Gondegaon S, Voruganti HK (2016) Static structural and modal analysis using isogeometric analysis. J Theor Appl Mech 46(4):36–75

    Article  MathSciNet  Google Scholar 

  2. Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJ, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199(5):229–263

    Article  MathSciNet  Google Scholar 

  3. Xu G, Mourrain B, Galligo A, Rabczuk T (2014) High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. Comput Mech 54(5):1303–1313

    Article  MathSciNet  Google Scholar 

  4. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194(39):4135–4195

    Article  MathSciNet  Google Scholar 

  5. Farin G, Hansford D (1999) Discrete coons patches. Comput Aided Geom Des 16(7):691–700

    Article  MathSciNet  Google Scholar 

  6. Martin T, Cohen E, Kirby M (2008) Volumetric parameterization and trivariate B-spline fitting using harmonic functions. In: Proceedings of the 2008 ACM symposium on solid and physical modeling. ACM, pp 269–280

  7. Xu G, Mourrain B, Duvigneau R, Galligo A (2011) Parameterization of computational domain in isogeometric analysis: methods and comparison. Comput Methods Appl Mech Eng 200(23):2021–2031

    Article  MathSciNet  Google Scholar 

  8. Speleers H, Manni C (2015) Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines. J Comput Appl Math 289:68–86

    Article  MathSciNet  Google Scholar 

  9. Nian X, Chen F (2016) Planar domain parameterization for isogeometric analysis based on teichmüller mapping. Comput Methods Appl Mech Eng 311:41–55

    Article  Google Scholar 

  10. Xu G et al (2013) Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method. J Comput Phys 252:275–289

    Article  MathSciNet  Google Scholar 

  11. Xu J, Chen F, Deng J (2015) Two-dimensional domain decomposition based on skeleton computation for parameterization and isogeometric analysis. Comput Methods Appl Mech Eng 284:541–555

    Article  MathSciNet  Google Scholar 

  12. Xu G et al (2013) Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis. Comput Aided Des 45(4):812–821

    Article  MathSciNet  Google Scholar 

  13. Xu G, Kwok TH, Wang CC (2017) Isogeometric computation reuse method for complex objects with topology-consistent volumetric parameterization. Comput Aided Des 91:1–13

    Article  Google Scholar 

  14. Xu G et al (2013) Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Comput Aided Des 45(2):395–404

    Article  MathSciNet  Google Scholar 

  15. Voruganti HK, Dasgupta B, Hommel G (2006) Harmonic function based domain mapping method for general domains. WSEAS Trans Comput 5(10):2495–2502

    Google Scholar 

  16. Cohen E, Martin T, Kirby RM, Lyche T, Riesenfeld RF (2010) Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis. Comput Methods Appl Mech Eng 199(5):334–356

    Article  MathSciNet  Google Scholar 

  17. Hosseini SF, Moetakef-Imani B, Hadidi-Moud S, Hassani B (2016) The effect of parameterization on isogeometric analysis of free-form curved beams. Acta Mech 227(7), 1983–1998

    Article  MathSciNet  Google Scholar 

  18. Pilgerstorfer E, Jüttler B (2014) Bounding the influence of domain parameterization and knot spacing on numerical stability in isogeometric analysis. Comput Methods Appl Mech Eng 268:589–613

    Article  MathSciNet  Google Scholar 

  19. Nguyen T, Jüttler B (2010) Parameterization of contractible domains using sequences of harmonic maps. In: International conference on curves and surfaces. Springer, Berlin, pp 501–514

    Chapter  Google Scholar 

  20. Saxena A, Sahay B (2007) Computer aided engineering design. Springer, Berlin

    Google Scholar 

  21. Wang W et al (2013) Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology. Comput Aided Des 45(2):351–360

    Article  MathSciNet  Google Scholar 

  22. Nguyen VP, Anitescu C, Bordas SP, Rabczuk T (2015) Isogeometric analysis: an overview and computer implementation aspects. Math Comput Simul 117:89–116

    Article  MathSciNet  Google Scholar 

  23. Srinivas P, Chaitanya SK, Kumar DR (2010) Finite element analysis using ANSYS 11.0. PHI Learning Pvt. Ltd, New Delhi

    Google Scholar 

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Authors and Affiliations

  1. National Institute of Technology, Warangal, Telangana, 506004, India

    Sangamesh Gondegaon & Hari K. Voruganti

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  1. Sangamesh Gondegaon
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  2. Hari K. Voruganti
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Correspondence to Sangamesh Gondegaon.

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Technical Editor: Paulo de Tarso Rocha de Mendonça.

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Gondegaon, S., Voruganti, H.K. An efficient parametrization of planar domain for isogeometric analysis using harmonic functions. J Braz. Soc. Mech. Sci. Eng. 40, 493 (2018). https://doi.org/10.1007/s40430-018-1414-z

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  • DOI: https://doi.org/10.1007/s40430-018-1414-z

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