Assumed strain stabilization procedure for the 9‐node Lagrange shell element

Ted Belytschko, Bak Leong Wong, Henryk Stolarski

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9‐node shell element. The stabilization procedure can be justified based on the Hellinger–Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co‐ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9‐node element. Example problems show good accuracy and an almost optimal rate of convergence.

Original languageEnglish (US)
Pages (from-to)385-414
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Issue number2
StatePublished - Feb 1989


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