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An Optimal Design Problem for Two-dimensional Composite Materials. A Constructive Approach
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Дата издания
2006Издательство
Cambridge Scientific Publishers PrintedБиблиографическое описание
Makaruk, S. F. An Optimal Design Problem for Two-dimensional Composite Materials. A Constructive Approach / S. F. Makaruk, V. V. Mityushev, S. V. Rogosin // Analytic Methods of Analysis and Differential Equations: AMADE 2003 / ed.: A. A. Kilbas, S. V. Rogosin. – Cambridge : Cambridge Scientific Publishers Ltd, 2006. – P. 155−169.Аннотация
We consider an optimal design problem, when it is necessary to locate circular inclusions of
fixed size having a given conductivity in a material of fixed shape and a given conductivity
in such a way that with prescribed concentration of the inclusions and prescribed external
field the whole composite material has extremal conductivity in a given direction. The
problem is reformulated in terms of a boundary value problem for analytic functions with
unknown geometrical parameters and constraints. The boundary value problem in special
cases is solved in closed form and the optimization problem is reduced to the classical
problem of the extrema of a continuous function on a compact set.
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