| Title:
|
On numerical solution of a variational inequality of the 4th order by finite element method (English) |
| Author:
|
Haslinger, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
5 |
| Year:
|
1978 |
| Pages:
|
334-345 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution. (English) |
| Keyword:
|
quadratic programming |
| Keyword:
|
elastic clamped plate |
| Keyword:
|
algorithm |
| Keyword:
|
energy functional |
| Keyword:
|
convergence |
| Keyword:
|
minimization problem |
| Keyword:
|
numerical solution |
| Keyword:
|
finite element method |
| MSC:
|
31A30 |
| MSC:
|
35J20 |
| MSC:
|
49A29 |
| MSC:
|
65K05 |
| MSC:
|
65N30 |
| MSC:
|
73K10 |
| MSC:
|
74K20 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| MSC:
|
90C20 |
| idZBL:
|
Zbl 0399.65084 |
| idMR:
|
MR0502470 |
| DOI:
|
10.21136/AM.1978.103760 |
| . |
| Date available:
|
2008-05-20T18:10:10Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103760 |
| . |
| Reference:
|
[1] Cea J.: Optimisation théorie et algorithmes.Dunod, Paris 1971. Zbl 0211.17402, MR 0298892 |
| Reference:
|
[2] Ciarlet P. G.: Conforming and nonconforming finite element methods for solving the plate problem.Conference on the numerical solution of differential equations, University of Dundee, July 1973, 03-06. MR 0423832 |
| Reference:
|
[3] Ciarlet P. G., Raviart P. A.: General Lagrange and Hermite interpolation in $R_n$ with applications to finite element methods.Arch. Rat. Anal. Vol. 46 (1972), 177- 199. Zbl 0243.41004, MR 0336957, 10.1007/BF00252458 |
| Reference:
|
[4] Glowinski R.: Analyse numerique d'inequations variationnelles d'ordre 4.(preprint of University Paris VI). |
| Reference:
|
[5] Jakovlev G. N.: The boundary properties of the functions belonging to the class $W^{1,p} on domains with conical or angular points.Trans. Moscow Math. Soc. (1967), 227--313. |
| Reference:
|
[6] Janovský V., Procházka P.: The nonconforming finite element method in the problem of clamped plate with ribs.Apl. Mat. 21 (1976), No 4, 273 - 289. MR 0413548 |
| Reference:
|
[7] Glowinski R., Lions J. L., Trémolieres R.: Analyse numérique des inéquations variationnelles.Dunod, Paris 1976. |
| . |
