Naslov
Sequential laminates in multiple state optimal design problems

Autori
Antonić, Nenad ; Vrdoljak, Marko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Treći hrvatski matematički kongres / Uglešić, N. i drugi - Split : Hrvatsko matematičko društvo, 2004, 57-58

Skup
Treći hrvatski matematički kongres

Mjesto i datum
Split, Hrvatska, 16.06.2004. - 18.06.2004

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
optimal design; homogenization

Sažetak
We consider stationary diffusion problems for two-phase materials. If two isotropic materials are given, with ${;\cal K};(\theta)$ are denoted all composite materials (in sense of homogenisation theory) with given local proportion $\theta$ of the first material. In some optimal design problems (Tartar and Murat 1985, Tartar 1995), the description of the set ${;\cal K};(\theta)e$, for some vector $e$, showed to be important for solving the necessary conditions of optimality. We address the question of describing the set $\{;(Ae, Af):A\in{;\cal K};(\theta)\};$, for given vectors $e$ and $f$. In order to visualize this set, we fix first coordinates and study the set $\{;Af:A\in{;\cal K};(\theta), Ae=t\};$. We obtain parametrisation of this set, for any vector $t$, although the calculations becomes very complicated. Using the computer program, we notice that the border of the set is obtained by rank two sequential laminates and this can be proved in some special cases. This question appears in optimal design problems with multiple state equations. There, one is trying to find the best arrangement of given materials such that the temperatures corresponding to the two given right hand sides are optimal in sense of minimising some functional.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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