| Title:
|
On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle (English) |
| Author:
|
Bock, Igor |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
281-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case. (English) |
| Keyword:
|
elliptic variational inequality |
| Keyword:
|
pseudoplate |
| Keyword:
|
thickness |
| Keyword:
|
optimal control |
| Keyword:
|
penalization |
| MSC:
|
35J85 |
| MSC:
|
49J20 |
| MSC:
|
49J40 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0980.49008 |
| idMR:
|
MR1844269 |
| DOI:
|
10.21136/MB.2001.134022 |
| . |
| Date available:
|
2009-09-24T21:50:35Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134022 |
| . |
| Reference:
|
[1] Bock, I., Lovíšek, J.: Optimal control problems for variational inequalities with controls in coefficients.Appl. Math. 32 (1987), 301–314. MR 0897834 |
| Reference:
|
[2] Bock, I., Lovíšek, J.: An optimal control problem for a pseudoparabolic variational inequality.Appl. Math. 37 (1992), 62–80. MR 1152158 |
| Reference:
|
[3] Haslinger, J., Neittaanmäki, P.: Finite Element Approximation for Optimal Shape, Material and Topology Design.John Wiley and Sons, Chichester, 1996. MR 1419500 |
| Reference:
|
[4] Hlaváček, I., Bock, I., Lovíšek, J.: Optimal control of a variational inequality with applications to structural analysis.Applied Math. Optim. 11 (1984), 111–143. MR 0743922, 10.1007/BF01442173 |
| Reference:
|
[5] Hlaváček, I., Lovíšek, J.: Optimal design of an elastic plate with unilateral elastic foundation and rigid supports using Reissner-Mindlin model. I. Continuous problems; II. Approximate problems.Z. Angew. Math. Mech. 5 (1997), 377–385. 10.1002/zamm.19970770513 |
| Reference:
|
[6] Khludnev, A. M., Sokolowski, J.: Modelling and Control in Solid Mechanics.Birkhäuser Verlag, Basel, 1997. MR 1433133 |
| Reference:
|
[7] Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications.Academic Press, New York, 1980. MR 0567696 |
| Reference:
|
[8] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Paris, 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[9] Myslinski, A., Sokolowski, J.: Nondifferentiable optimization problems for elliptic systems.SIAM J. Control Optim. 23 (1985), 632–648. MR 0791892, 10.1137/0323040 |
| Reference:
|
[10] Rodriguez, J.-F.: Obstacle Problems in Mathematical Physics.North-Holland Mathematical Studies 134, Amsterdam, 1987. MR 0880369 |
| Reference:
|
[11] Schwartz, L.: Théorie des Distributions.(Second edition). Hermann, Paris, 1966. Zbl 0149.09501, MR 0209834 |
| . |
