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3D-2D asymptotic analysis of an optimal design problem for thin films. (English) Zbl 0917.73052
Summary: We compute explicitly the gamma-limit of a rescaled version of an optimal material distribution problem for a cylindrical two-phase elastic mixture in a thin three-dimensional domain. Its limiting form is a two-dimensional optimal design problem on the cross-section of the thin domain; it involves optimal energy bounds on two-dimensional mixtures of a related two-phase bulk material. Thus, it is shown that 3D-2D asymptotics and optimal design commute from a variational viewpoint.

74P99 Optimization problems in solid mechanics
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