A consistent control of spurious singular modes in the 9-node Lagrange element for the laplace and mindlin plate equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

Abstract

When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C0 plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h3 convergence in the L2-norm is almost retained.

Original languageEnglish (US)
Pages (from-to)269-295
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume44
Issue number3
DOIs
StatePublished - Aug 1984

ASJC Scopus subject areas

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

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