Control in obstacle-pseudoplate problems with friction on the boundary. optimal design and problems with uncertain data

Volume 28 / 2001

Ivan Hlaváček, Ján Lovíšek Applicationes Mathematicae 28 (2001), 407-426 MSC: 49J40, 74K20, 74P05, 93C30. DOI: 10.4064/am28-4-3

Abstract

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.

Authors

  • Ivan HlaváčekMathematical Institute
    Academy of Sciences of the Czech Republic
    Žitná 25
    CZ-115 67 Praha 1, Czech Republic
    e-mail
  • Ján LovíšekFaculty 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
    e-mail

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