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Some estimates for the torsional rigidity of composite rods
Author(s) -
Crasta Graziano,
Fragalà Ilaria,
Gazzola Filippo
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410478
Subject(s) - homogenization (climate) , rigidity (electromagnetism) , rod , mathematics , moduli , elasticity (physics) , torsion (gastropod) , composite number , shear modulus , mathematical analysis , composite material , materials science , physics , algorithm , ecology , alternative medicine , surgery , pathology , quantum mechanics , biology , medicine , biodiversity
A well‐known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain Ω, so as to maximize the torsional rigidity of the resulting rod; moreover, the proportion of these materials is prescribed. Such a problem may not have a classical solution as the optimal design may contain homogenization regions, where the two materials are mixed in a microscopic scale. Then, the optimal torsional rigidity becomes difficult to compute. In this paper we give some different theoretical upper and lower bounds for the optimal torsional rigidity, and we compare them on some significant domains. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)