Shear-flexible subdivision shells

Quan Long, P. Burkhard Bornemann, Fehmi Cirak*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


We present a new shell model and an accompanying discretisation scheme that is suitable for thin and thick shells. The deformed configuration of the shell is parameterised using the mid-surface position vector and an additional shear vector for describing the out-of-plane shear deformations. In the limit of vanishing thickness, the shear vector is identically zero and the Kirchhoff-Love model is recovered. Importantly, there are no compatibility constraints to be satisfied by the shape functions used for discretising the mid-surface and the shear vector. The mid-surface has to be interpolated with smooth C 1-continuous shape functions, whereas the shear vector can be interpolated with C 0-continuous shape functions. In the present paper, the mid-surface as well as the shear vector are interpolated with smooth subdivision shape functions. The resulting finite elements are suitable for thin and thick shells and do not exhibit shear locking. The good performance of the proposed formulation is demonstrated with a number of linear and geometrically non-linear plate and shell examples.

Original languageEnglish (US)
Pages (from-to)1549-1577
Number of pages29
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
StatePublished - Jun 29 2012


  • Isogeometric analysis
  • Shells
  • Subdivision surfaces

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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