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 language | English |
|---|---|
| Pages (from-to) | 711-725 |
| Number of pages | 15 |
| Journal | Structural Engineering and Mechanics |
| Volume | 6 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1998 Jan 1 |
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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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Stabilization of pressure solutions in four-node quadrilateral elements. / Lee, Sang-Ho; Kim, Sang Hyo.
In: Structural Engineering and Mechanics, Vol. 6, No. 6, 01.01.1998, p. 711-725.Research output: Contribution to journal › Article
TY - JOUR
T1 - Stabilization of pressure solutions in four-node quadrilateral elements
AU - Lee, Sang-Ho
AU - Kim, Sang Hyo
PY - 1998/1/1
Y1 - 1998/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0032157961&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032157961&partnerID=8YFLogxK
U2 - 10.12989/sem.1998.6.6.711
DO - 10.12989/sem.1998.6.6.711
M3 - Article
AN - SCOPUS:0032157961
VL - 6
SP - 711
EP - 725
JO - Structural Engineering and Mechanics
JF - Structural Engineering and Mechanics
SN - 1225-4568
IS - 6
ER -