Modelling and control in pseudoplate problem with discontinuous thickness |
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Authors: | Ján Loví?ek |
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Institution: | (3) Charles Univ., Prague, Czech Republic; |
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Abstract: | 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. |
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Keywords: | |
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