Geodesic
Control in obstacle-pseudoplate problems with friction on the boundary. optimal design and problems with uncertain data
Ivan Hlaváček1 ; Ján Lovíšek2
1 Mathematical Institute Academy of Sciences of the Czech Republic Žitná 25 CZ-115 67 Praha 1, Czech Republic
2 Faculty of Civil Engineering Slovak Technical University Radlinského 11 SK-813 68 Bratislava, Slovak Republic Institute of Computer Science Pod vodárenskou věží 2 CZ-182 07 Praha 8, Czech Republic
Applicationes Mathematicae, Tome 28 (2001) no. 4, pp. 407-426.

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Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. If some input data are allowed to be uncertain a new method of reliable solutions is employed. We prove the existence of a solution to the above-mentioned problems on the basis of a general theorem on the control of variational inequalities.
DOI : 10.4064/am28-4-3
Keywords: optimal design problems weight minimization problem considered elastic plates small bending rigidity resting unilateral elastic foundation inner rigid obstacles friction condition part boundary state problem represented variational inequality design variables influence coefficients set admissible state functions input allowed uncertain method reliable solutions employed prove existence solution above mentioned problems basis general theorem control variational inequalities

Ivan Hlaváček 1 ; Ján Lovíšek 2

1 Mathematical Institute Academy of Sciences of the Czech Republic Žitná 25 CZ-115 67 Praha 1, Czech Republic
2 Faculty of Civil Engineering Slovak Technical University Radlinského 11 SK-813 68 Bratislava, Slovak Republic Institute of Computer Science Pod vodárenskou věží 2 CZ-182 07 Praha 8, Czech Republic 
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Ivan Hlaváček; Ján Lovíšek. Control in obstacle-pseudoplate problems
with friction on the boundary. optimal
design and problems with uncertain data. Applicationes Mathematicae, Tome 28 (2001) no. 4, pp. 407-426. doi : 10.4064/am28-4-3. http://geodesic.mathdoc.fr/articles/10.4064/am28-4-3/

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