On Isogeometric Analysis and Its Usage for Stress Calculation

  • Anh-Vu VuongEmail author
  • B. Simeon
Conference paper


A concise treatment of isogeometric analysis with particular emphasis on the relation to isoparametric finite elements is given. Besides preserving the exact geometry, this relatively new extension of the finite element method possesses the attractive feature of offering increased smoothness of the basis functions in the Galerkin projection. Such a property is particularly beneficial for stress analysis in linear elasticity problems, which is demonstrated by means of a 3D simulation example.


Parameter Domain Nodal Basis Spline Space Isogeometric Analysis Galerkin Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Aigner, Ch. Heinrich, B. Jüttler, E. Pilgerstorfer, B. Simeon, and A.-V. Vuong. Swept volume parametrization for isogeometric analysis. In E. Hancock and R. Martin, editors, The Mathematics of Surfaces (MoS XIII 2009), pages 19 – 44. Springer, 2009.Google Scholar
  2. 2.
    W. Bangerth and R. Rannacher. Adaptive Finite Element Methods for Differential Equations. Lectures in Mathematics. Birkhäuser, Basel, 2003.zbMATHGoogle Scholar
  3. 3.
    Y. Bazilevs, L. Beirão da Veiga, J. A. Cottrell, T. J. R. Hughes, and G. Sangalli. Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes. Mathematical Methods and Models in Applied Sciences, 16:1031–1090, 2006.zbMATHCrossRefGoogle Scholar
  4. 4.
    E. Cohen, T. Martin, R. M. Kirby, T. Lyche, and R. F. Riesenfeld. Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 199:334–356, 2010.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    O. Davydov. Stable local bases for multivariate spline spaces. Journal of Approximation Theory, 111:267–297, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    M. R. Dörfel, B. Jüttler, and B. Simeon. Adaptive isogeometric analysis by local h-refinement with T-splines. Computer Methods in Applied Mechanics and Engineering, 199:264–275, 2010.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    T. J. R. Hughes. The Finite Element Method. Dover Publ., Mineola, New York, 2000.zbMATHGoogle Scholar
  8. 8.
    T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194:4135–4195, 2005.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    T. J. R. Hughes, A. Reali, and G. Sangalli. Efficient quadrature for NURBS-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 199:301–313, 2010.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    L. Piegl and W. Tiller. The NURBS Book. Monographs in Visual Communication. Springer, New York, 2nd edition, 1997.CrossRefGoogle Scholar
  11. 11.
    W. A. Wall, M. A. Frenzel, and Ch. Cyron. Isogeometric stuctural shape optimization. Computer methods in applied mechanics and engineering, 197:2976–2988, 2008.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Y. Zhang, Y. Bazilevs, S. Goswami, Ch. L. Bajaj, and T. J. R. Hughes. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Computer methods in applied mechanics and engineering, 196:2943–2959, 2007.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Centre for Mathematical SciencesTechnische Universität MünchenGarchingGermany

Personalised recommendations