| Title:
|
A mixed finite element method for plate bending with a unilateral inner obstacle (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
25-44 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented. (English) |
| Keyword:
|
unilateral plate problem |
| Keyword:
|
inner obstacle |
| Keyword:
|
mixed finite elements |
| Keyword:
|
Herrmann-Johnson mixed model |
| Keyword:
|
fourth order variational inequality |
| MSC:
|
49D29 |
| MSC:
|
65N30 |
| MSC:
|
73K10 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0796.73062 |
| idMR:
|
MR1254745 |
| DOI:
|
10.21136/AM.1994.134241 |
| . |
| Date available:
|
2009-09-22T17:42:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134241 |
| . |
| Reference:
|
[1] Brezzi, F.: On the existence, uniqueness and approximations of saddle-point problems arising from Lagrange multipliers.vol. 8-R2, R. A. I. R. O., 1974, pp. 129–151. MR 0365287 |
| Reference:
|
[2] Brezzi, F.–Raviart, P. A.: Mixed finite element methods for 4th order elliptic equations.Topics in Numer. Anal., vol. III (ed. by J. J. H. Miller), Academic Press, London, 1977, pp. 33–56. Zbl 0434.65085, MR 0657975 |
| Reference:
|
[3] Ekeland, I.–Temam, R.: Analyse convexe et problèmes variationnels.Dunod, Paris, 1974. Zbl 0281.49001 |
| Reference:
|
[4] Glowinski, R.–Lions, J. L.–Trémolières, R.: Numerical analysis of variational inequalities.North-Holland, Amsterdam, 1981. Zbl 0463.65046, MR 0635927 |
| Reference:
|
[5] Haslinger, J.: Mixed formulation of variational inequalities and its approximation.Apl. Mat. 26 (1981), 462–475. MR 0634283 |
| Reference:
|
[6] Nečas, J.: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[7] Comodi, M. I.: Approximation of a bending plate problem with a boundary unilateral constraint.Numer. Math. 47 (1985), 435–458. Zbl 0581.73022, MR 0808562, 10.1007/BF01389591 |
| Reference:
|
[8] Ciarlet, P.G.: The finite element method for elliptic problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| . |
