The optimal compliance problem for thin torsion rods: A 3D-1D analysis leading to Cheeger-type solutions |
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Authors: | Guy Bouchitté Ilaria Fragalà Pierre Seppecher |
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Affiliation: | 1. Laboratoire IMATH, université de Toulon et du Var, 83957 La Garde cedex, France;2. Dipartimento di Matematica, Politecnico, Piazza L. da Vinci, 20133 Milano, Italy |
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Abstract: | We consider the variational problem which consists in minimizing the compliance of a prescribed amount of isotropic elastic material placed into a given design region when it is subjected to a given load. We perform the asymptotics of this problem when the design region is a straight cylinder with infinitesimal cross section. The results presented in this Note concern the pure torsion regime and state the existence of optimal shapes for the limit problem. When the filling ratio tends in turn to zero, these optimal shapes concentrate on the boundary of the Cheeger set of the section of the design region. |
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