An Optimal Design Problem for Two-dimensional Composite Materials. A Constructive Approach
PublisherCambridge Scientific Publishers Printed
CitationMakaruk, 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.
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.
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial» («Атрибуция-Некоммерчески») 4.0 Всемирная.