Details
| Original language | English |
|---|---|
| Pages (from-to) | 77-95 |
| Number of pages | 19 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 84 |
| Issue number | 1 |
| Publication status | Published - Nov 1990 |
| Externally published | Yes |
Abstract
In order to develop an efficient and manageable tool for checking stability and optimal convergence of mixed finite elements (LBB- and 'equilibrium' condition), three mechanical conditions are stated. The first requires the continuity of the normal component of the stress tensor across interelement boundaries, the second forbids spurious modes on a two element patch, and the third is to avoid zero-energy-stresses on an element. The mathematical proof shows that the conditions are necessary and sufficient. Finally, the hybrid implementation of two plane mixed elements is carried out, and comparisons are made with two standard displacement elements. In particular, the mixed element with constant displacement shape functions (MMC) surpasses the linear displacement element by far and also the quadratic displacement element if the computational effort is compared.
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 84, No. 1, 11.1990, p. 77-95.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mechanical conditions for stability and optimal convergence of mixed finite elements for linear plane elasticity
AU - Stein, Erwin
AU - Rolfes, R.
PY - 1990/11
Y1 - 1990/11
N2 - In order to develop an efficient and manageable tool for checking stability and optimal convergence of mixed finite elements (LBB- and 'equilibrium' condition), three mechanical conditions are stated. The first requires the continuity of the normal component of the stress tensor across interelement boundaries, the second forbids spurious modes on a two element patch, and the third is to avoid zero-energy-stresses on an element. The mathematical proof shows that the conditions are necessary and sufficient. Finally, the hybrid implementation of two plane mixed elements is carried out, and comparisons are made with two standard displacement elements. In particular, the mixed element with constant displacement shape functions (MMC) surpasses the linear displacement element by far and also the quadratic displacement element if the computational effort is compared.
AB - In order to develop an efficient and manageable tool for checking stability and optimal convergence of mixed finite elements (LBB- and 'equilibrium' condition), three mechanical conditions are stated. The first requires the continuity of the normal component of the stress tensor across interelement boundaries, the second forbids spurious modes on a two element patch, and the third is to avoid zero-energy-stresses on an element. The mathematical proof shows that the conditions are necessary and sufficient. Finally, the hybrid implementation of two plane mixed elements is carried out, and comparisons are made with two standard displacement elements. In particular, the mixed element with constant displacement shape functions (MMC) surpasses the linear displacement element by far and also the quadratic displacement element if the computational effort is compared.
UR - http://www.scopus.com/inward/record.url?scp=0025522403&partnerID=8YFLogxK
U2 - 10.1016/0045-7825(90)90090-9
DO - 10.1016/0045-7825(90)90090-9
M3 - Article
AN - SCOPUS:0025522403
VL - 84
SP - 77
EP - 95
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - 1
ER -