We carry out an asymptotic analysis of the following shape optimization problem: a given volume fraction of elastic material must be distributed in a cylindrical design region of infinitesimal cross section in order to maximize resistance to a twisting load. We derive a limit rod model written in different equivalent formulations and for which we are able to give necessary and sufficient conditions characterizing optimal configurations. Eventually we show that for a convex design region and for very small volume fractions, the optimal shape tends to concentrate section by section near the boundary of the Cheeger set of the design. These results were announced in [G. Bouchitté, I. Fragalà, and P. Seppecher, C. R. Math., 348 (2010), pp. 467-471]. © 2012 Society for Industrial and Applied Mathematics.
Optimal thin torsion rods and cheeger sets / Bouchitte G.; Fragala I.; Lucardesi I.; Seppecher P.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 44:(2012), pp. 483-512. [10.1137/110828538]
Optimal thin torsion rods and cheeger sets
Lucardesi I.;
2012
Abstract
We carry out an asymptotic analysis of the following shape optimization problem: a given volume fraction of elastic material must be distributed in a cylindrical design region of infinitesimal cross section in order to maximize resistance to a twisting load. We derive a limit rod model written in different equivalent formulations and for which we are able to give necessary and sufficient conditions characterizing optimal configurations. Eventually we show that for a convex design region and for very small volume fractions, the optimal shape tends to concentrate section by section near the boundary of the Cheeger set of the design. These results were announced in [G. Bouchitté, I. Fragalà, and P. Seppecher, C. R. Math., 348 (2010), pp. 467-471]. © 2012 Society for Industrial and Applied Mathematics.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.