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Title: Modelling and control in pseudoplate problem with discontinuous thickness (English)
Author: Lovíšek, Ján
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 54
Issue: 6
Year: 2009
Pages: 491-525
Summary lang: English
Category: math
Summary: This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control is introduced. Taking into account the results of $G$-convergence theory, we prove the existence of an optimal solution of extended control problem. Moreover, approximate optimization problem is introduced, making use of the finite element method. The solvability of the approximate problem is proved on the basis of a general theorem. When the mesh size tends to zero, a subsequence of any sequence of approximate solutions converges uniformly to a solution of the continuous problem. (English)
Keyword: control of variational inequalities
Keyword: optimal design
Keyword: minimization
Keyword: pseudoplate with obstacles
Keyword: cost functional
Keyword: thickness
Keyword: $G$-convergence
Keyword: coercive variational inequality
Keyword: approximate optimization problem
Keyword: finite element
MSC: 49J40
MSC: 49K30
MSC: 49M15
MSC: 49N90
MSC: 65K15
MSC: 65N30
MSC: 70Q05
MSC: 74K20
MSC: 93C20
MSC: 93C30
idZBL: Zbl 1212.49009
idMR: MR2563122
DOI: 10.1007/s10492-009-0031-7
Date available: 2010-07-20T13:26:00Z
Last updated: 2020-07-02
Stable URL:
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