Asymptotics of an optimal compliance-network problem

Al-hassem Nayam; Al-hassem Nayam

doi:10.3934/nhm.2013.8.573

Networks and Heterogeneous Media

2013, Volume 8, Issue 2: 573-589. doi: 10.3934/nhm.2013.8.573

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Asymptotics of an optimal compliance-network problem

Al-hassem Nayam ^{1
,}

1.
International Centre for Theoretical Physics, Strada Costiera,11, I - 34151 Trieste

Received: 01 October 2012 Revised: 01 March 2013
Primary: 49J45; Secondary: 49Q10, 74P05.

We consider the problem of the optimal location of a Dirichlet region in a $d$-dimensional domain $\Omega$ subjected to a given force $f$ in order to minimize the $p$-compliance of the configuration. We look for the optimal region among the class of all closed connected sets of assigned length $l.$ Then we let the length $l$ tend to infinity and we look at the $\Gamma$-limit of a suitable rescaled functional, from which we get information of the asymptotic distribution of the optimal region. We also study the case where the Dirichlet region is a discrete set of finite cardinality.
- $\Gamma$-convergence,
- shape optimization,
- compliance,
- network,
- Dirichlet regions
Citation: Al-hassem Nayam. Asymptotics of an optimal compliance-network problem[J]. Networks and Heterogeneous Media, 2013, 8(2): 573-589. doi: 10.3934/nhm.2013.8.573

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Abstract

We consider the problem of the optimal location of a Dirichlet region in a $d$-dimensional domain $\Omega$ subjected to a given force $f$ in order to minimize the $p$-compliance of the configuration. We look for the optimal region among the class of all closed connected sets of assigned length $l.$ Then we let the length $l$ tend to infinity and we look at the $\Gamma$-limit of a suitable rescaled functional, from which we get information of the asymptotic distribution of the optimal region. We also study the case where the Dirichlet region is a discrete set of finite cardinality.

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