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IMA Journal of Applied Mathematics Advance Access published online on November 3, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp031
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A surface energy approach to the mass reduction problem for elastic bodies

P. D'Ambrosio{dagger} and D. De Tommasi{ddagger}

Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Bari, via Re David 200, 70125 Bari, Italy

L. Granieri§ and F. Maddalena

Dipartimento di Matematica, Politecnico di Bari, via Re David 200, 70125 Bari, Italy

{ddagger}Corresponding author. Email: d.detommasi{at}poliba.it

Received on July 24, 2008; Revision received May 29, 2009. Accepted on September 30, 2009

We consider the problem of mass reduction for elastic bodies by appearance of cavities. In this work, this problem is related to the minimization of a surface energy, depending on the stress tensor in the original equilibrium configuration. Special cases of mechanical interest are also analysed.

Keywords: Wulff shapes; shape optimization; variational problems in elasticity.

{dagger} Email: p.dambrosio{at}poliba.it

§ Email: l.granieri{at}poliba.it

Email: f.maddalena{at}poliba.it


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