Vector variational problems and applications to optimal design. (English) Zbl 1089.49022
The paper provides a self-contained review on the recent progresses on the use of techniques from non-convex vector variational problems in the analysis of optimal design problems in conductivity.
First, the main ideas of the underlying analysis are introduced, together with the Young measure approach, and some standard material is recalled. Then, applications are given to a typical optimal design problem with two different conducting materials. The equivalent relaxed formulation of the basic optimal design problem is then examined. Eventually, a new formulation for it is provided, whose numerical simulations lead to approximated optimal configurations, that are developed in a two- and three-dimensional situations.
First, the main ideas of the underlying analysis are introduced, together with the Young measure approach, and some standard material is recalled. Then, applications are given to a typical optimal design problem with two different conducting materials. The equivalent relaxed formulation of the basic optimal design problem is then examined. Eventually, a new formulation for it is provided, whose numerical simulations lead to approximated optimal configurations, that are developed in a two- and three-dimensional situations.
Reviewer: Riccardo De Arcangelis (Napoli)
MSC:
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 74P10 | Optimization of other properties in solid mechanics |
| 74Q15 | Effective constitutive equations in solid mechanics |
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