Abstract
This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.
| Original language | English |
|---|---|
| Pages (from-to) | 1651-1674 |
| Number of pages | 24 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 83 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2010 Sep 17 |
| Externally published | Yes |
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Keywords
- A sum of norms
- CS-FEM
- Limit analysis
- Second-order cone programming
- Strain smoothing
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis
Cite this
A cell-based smoothed finite element method for kinematic limit analysis. / Le, Canh V.; Nguyen-Xuan, H.; Askes, H.; Bordas, Stéphane P A; Rabczuk, Timon; Nguyen-Vinh, H.
In: International Journal for Numerical Methods in Engineering, Vol. 83, No. 12, 17.09.2010, p. 1651-1674.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A cell-based smoothed finite element method for kinematic limit analysis
AU - Le, Canh V.
AU - Nguyen-Xuan, H.
AU - Askes, H.
AU - Bordas, Stéphane P A
AU - Rabczuk, Timon
AU - Nguyen-Vinh, H.
PY - 2010/9/17
Y1 - 2010/9/17
N2 - This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.
AB - This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.
KW - A sum of norms
KW - CS-FEM
KW - Limit analysis
KW - Second-order cone programming
KW - Strain smoothing
UR - http://www.scopus.com/inward/record.url?scp=77954957167&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954957167&partnerID=8YFLogxK
U2 - 10.1002/nme.2897
DO - 10.1002/nme.2897
M3 - Article
AN - SCOPUS:77954957167
VL - 83
SP - 1651
EP - 1674
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 12
ER -