Stabilization of pressure solutions in four-node quadrilateral elements

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Abstract

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babuška-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges proposed by Hughes and Franca is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. Also, a solid mechanics problem is presented by which the stability of mixed elements can be studied. It is shown that the pressure solutions, although stable, are shown to exhibit sensitivity to the stabilization parameters.

Original languageEnglish
Pages (from-to)711-725
Number of pages15
JournalStructural Engineering and Mechanics
Volume6
Issue number6
DOIs
Publication statusPublished - 1998 Sep

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All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanics of Materials
  • Mechanical Engineering

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