Benchmark computations of stresses in a spherical dome with shell finite elements

Antti H. Niemi*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
232 Downloads (Pure)


We present a computational framework for analyzing thin shell structures using the finite element method. The framework is based on a mesh-dependent shell model which we derive from the general laws of three-dimensional elasticity. We apply the framework for the so-called Girkmann benchmark problem involving a spherical shell stiffened with a foot ring. In particular, we compare the accuracy of different reduced strain four-node elements in this context. We conclude that the performance of the bilinear shell finite elements depends on the mesh quality but reasonable accuracy of the quantities of interest of the Girkmann problem can be attained in contrast to earlier results obtained with general shell elements for the problem.

Original languageEnglish
Pages (from-to)B440-B457
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed


  • Convergence
  • Finite elements
  • Locking
  • Shell structures
  • Stabilized methods
  • Thin shell theory


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