Subdivision shells with exact boundary control and non-manifold geometry

Fehmi Cirak*, Quan Long

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


We introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non-smooth and non-manifold joints. To this end, extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals. Furthermore, shells with boundaries in the form of conic sections, such as circles or parabolas, are represented with rational subdivision schemes, which are defined in analogy to rational b-splines. In terms of implementation, the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features. Hence, the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces. The particular subdivision scheme used in this paper constitutes an improved version of the original Loop's scheme and is as such based on triangular meshes. As in the original subdivision shells, surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations. At the integration points, the subdivision surface is evaluated using a newly developed discrete parameterization approach. In the resulting finite elements, the only degrees of freedom are the mid-surface displacements of the nodes and additional Lagrange parameters for enforcing normal constraints. The versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples.

Original languageEnglish (US)
Pages (from-to)897-923
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
StatePublished - Dec 2 2011


  • Isogeometric analysis
  • Non-manifold geometry
  • Rational subdivision
  • Shells
  • Subdivision interpolation

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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