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Buttazzo, Giuseppe; Santambrogio, Filippo; Varchon, Nicolas

Asymptotics of an optimal compliance-location problem. (English) Zbl 1114.49016

ESAIM, Control Optim. Calc. Var. 12, 752-769 (2006).
Summary: We consider the problem of placing a Dirichlet region made by \(n\) small balls of given radius in a given domain subject to a force \(f\) in order to minimize the compliance of the configuration. Then we let \(n\) tend to infinity and look for the \(\Gamma\)-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

Cited in 9 Documents

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49Q10 Optimization of shapes other than minimal surfaces
74P05 Compliance or weight optimization in solid mechanics

Keywords:

compliance; optimal location; shape optimization; \(\Gamma\)-convergence
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References:

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