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Structural Engineering and Mechanics
  Volume 6, Number 6, September 1998 , pages 711-725

Stabilization of pressure solutions in four-node quadrilateral elements
Lee SH, Kim SH

    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 Babuska-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.
Key Words
    stabilization of pressure, pressure oscillations, pressure modes, incompressible materials, mixed finite elements, volumetric locking
Lee SH, Yonsei Univ, Dept Civil Engn, Seoul 120749, South Korea
Yonsei Univ, Dept Civil Engn, Seoul 120749, South Korea

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