On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

Igor Bock; Ján Lovíšek

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 281-292
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Bock, Igor, and Lovíšek, Ján. "On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle." Mathematica Bohemica 126.2 (2001): 281-292. <http://eudml.org/doc/248859>.

@article{Bock2001,
abstract = {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.},
author = {Bock, Igor, Lovíšek, Ján},
journal = {Mathematica Bohemica},
keywords = {elliptic variational inequality; pseudoplate; thickness; optimal control; penalization; elliptic variational inequality; pseudoplate; thickness; optimal control; penalization},
language = {eng},
number = {2},
pages = {281-292},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle},
url = {http://eudml.org/doc/248859},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Bock, Igor
AU - Lovíšek, Ján
TI - On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 281
EP - 292
AB - 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.
LA - eng
KW - elliptic variational inequality; pseudoplate; thickness; optimal control; penalization; elliptic variational inequality; pseudoplate; thickness; optimal control; penalization
UR - http://eudml.org/doc/248859
ER -

References

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  5. 10.1002/zamm.19970770513, Z. Angew. Math. Mech. 5 (1997), 377–385. (1997) DOI10.1002/zamm.19970770513
  6. Modelling and Control in Solid Mechanics, Birkhäuser Verlag, Basel, 1997. (1997) MR1433133
  7. An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980. (1980) MR0567696
  8. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. (1969) Zbl0189.40603MR0259693
  9. 10.1137/0323040, SIAM J. Control Optim. 23 (1985), 632–648. (1985) MR0791892DOI10.1137/0323040
  10. Obstacle Problems in Mathematical Physics, North-Holland Mathematical Studies 134, Amsterdam, 1987. (1987) MR0880369
  11. Théorie des Distributions, (Second edition). Hermann, Paris, 1966. (1966) Zbl0149.09501MR0209834

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