Implementation and application of a 9-node Lagrange shell element with spurious mode control

Ted Belytschko*, Liu Wing-Kam, Shau-Jen Ong Jame Shau-Jen Ong, Dennis Lam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


The implementation of a 9-node Lagrange element with uniform reduced quadrature (2 × 2) and spurious mode control for plates and shells is described. Both linear and nonlinear problems are considered. Comparisons are made with full integration (3 × 3) and selective reduced integration versions of this element. It is shown that in all cases, the rate of convergence of this element is significantly superior over that of the other two elements and that the spurious mode control procedure effectively eliminates all difficulties associated with zero-energy modes. The element does not exhibit any symptoms of membrane or shear locking nor any spatial oscillations in the solutions.

Original languageEnglish (US)
Pages (from-to)121-128
Number of pages8
JournalComputers and Structures
Issue number1-3
StatePublished - 1985

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications


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