Improvements in 3‐node triangular shell elements

Nicholas Carpenter, Henryk Stolarski, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Low‐order triangular finite shell elements are computationally economical and easy to implement, but often exhibit very slow convergence. Two new membrane formulations for triangular shell elements are examined which rectify these drawbacks. The first element is based on the Marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy. Resulting expressions are provided in an explicit form for easy implementation of the element. The second element is based on a linear membrane field governed by normal rotations and reduced quadrature. The difficulties with shell‐normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested. Finally, a set of test problems are examined which show the importance of mesh patterns and degrees‐of‐freedom per node on triangular element performance.

Original languageEnglish (US)
Pages (from-to)1643-1667
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
StatePublished - Sep 1986


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