A consolidation of various approaches in developing naturally based quadrilaterals

William E. Bachrach*, Wing Kam Liu, Rasim Aziz Uras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Four-node quadrilateral elements which do not require any numerical integration are developed by means of the Hu-Washizu variational principle. For these elements, the physical strain and stress fields are expressed in a transformed natural coordinate system so that the elements are less sensitive to geometric distortion. The method is presented for linear plane-strain applications involving incompressible materials so that the benefits of these elements are evident. Displacement-norm and energy-norm convergence-rate studies for uniform and skewed meshes are given. For skewed meshes, results show that these elements perform better than their physical plane counterparts which have been discussed in this literature review.

Original languageEnglish (US)
Pages (from-to)43-62
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Issue number1-2
StatePublished - Apr 1986

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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