Resultant-stress degenerated-shell element

Wing K. Liu*, E. S. Law, D. Lam, T. Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


In this paper, a resultant-stress degenerated-shell element is described and a variety of numerical examples, including the post-buckling analysis of an axially loaded perfect cylinder, are presented. The general degenerated nonlinear shell theory of Hughes and Liu is employed in deriving this resultant-stress degenerated-shell element. Contrary to the traditional integration through the thickness approach, which assumes no coupling between the in-plane and transverse material and structural response matrices, the present approach can permit use of arbitrary, three-dimensional (3-D) nonlinear constitutive equations. Furthermore, explicit expressions of the element matrices for a 4-node shell element are developed. This rank-sufficient 4-node shell element, termed the resultant-stress degenerated-shell (RSDS) element, avoids the need for the costly numerical quadrature function evaluations of the element matrices and force vectors. And thus there are large increases in computational efficiency with this method. The comparisons of this RSDS element with six other shell elements are also given in this paper.

Original languageEnglish (US)
Pages (from-to)259-300
Number of pages42
JournalComputer Methods in Applied Mechanics and Engineering
Issue number3
StatePublished - May 1986

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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