Naslov
Sequential laminates in multiple state optimal design problems

Autori
Antonić, Nenad ; Vrdoljak, Marko

Izvornik
Mathematical Problems in Engineering (1024-123X) 2006 (2006); 1-14

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
homogenisation; diffusion equation; optimal design; multiple states

Sažetak
In the study of optimal design related to stationary diffusion problems with multiple state equations, the description of the set H={; ; ; ; (Aa_1, ..., Aa_m): A in K(theta)}; ; ; ; , for given vectors a_1, ..., a_m in R^d (m<d) is crucial. K(theta) denotes all composite materials (in the sense of homogenisation theory) with given local proportion theta of the first material. We prove that the boundary of H is attained by sequential laminates of rank at most m with matrix phase alpha and core beta (alpha<beta). Examples showing that the information on the rank of optimal laminate cannot be improved, as well as the fact that sequential laminates with matrix phase alpha are preferred to those with matrix phase beta, are presented. This result can significantly reduce the complexity of optimality conditions, with obvious impact on numerical treatment, as demonstrated on a simple numerical example.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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