A rotation-free quadrilateral thin shell subdivision finite element

Seth Green, George M. Turkiyyah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We present a rotation-free, subdivision-based, isoparametric quadrilateral finite element for the analysis of doubly-curved thin shells. The element is a generalization of spline-based C1 finite elements to curved domains, and general mesh connectivity. It uses semi-local basis functions that span the two-neighbourhood of a node. The traditional difficulty with this class of elements comes from the fact that these basis functions depend on the valence of the nodes of the element. For elements with 4-valence nodes the basis functions are bicubic polynomials, but there are no simple closed-form expressions for them when the nodes have general connectivity patterns. In the paper, we show how the basis functions for the general case may be efficiently evaluated as linear combinations of translation and scaling transformations of the bicubic polynomials. The performance of the resulting element is illustrated on a hemispherical shell model problem.

Original languageEnglish (US)
Pages (from-to)757-767
Number of pages11
JournalCommunications in Numerical Methods in Engineering
Issue number12
StatePublished - Dec 2005
Externally publishedYes


  • Finite elements
  • Rotation-free
  • Shells
  • Subdivision surfaces

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • General Engineering
  • Computational Theory and Mathematics
  • Applied Mathematics


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