Naslov
Optimal design on annulus: numerical approximation obtained by the shape gradient method

Autori
Kunštek, Petar ; Vrdoljak, Marko

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

Skup
Applications of Generalized Functions in Harmonic Analysis, Mechanics, Stochastics and PDE

Mjesto i datum
Novi Sad, Srbija, 25.10.2017. - 27.10.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Podatak o recenziji nije dostupan

Ključne riječi
stationary diffusion, optimal design, homogenization, shape design, gradient method

Sažetak
We optimize a distribution of two isotropic materials that occupy an annulus in two or three dimensions, heated by a uniform heat source, aiming to maximize the total energy. In elasticity, the problem models the maximization of the torsional rigidity of a cylindrical rod with annular cross section made of two homogeneously distributed isotropic elastic materials. Commonly, optimal design problems do not have solutions (such solutions are called classical ), so one considers proper relaxation of the original problem. Relaxation by the homogenization method consists in introducing generalized materials, which are mixtures of original materials on the micro-scale. However, by analysing the optimality conditions, we are able to show that the solution is unique, classical and radial. Depending on the amounts of given materials, we find two possible optimal configurations. The precise solution can be determined by solving a system of nonlinear equations, which can be done only numerically.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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