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Some estimates for the torsional rigidity of composite rods

✍ Scribed by Graziano Crasta; Ilaria Fragalà; Filippo Gazzola

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
196 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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)

📜 SIMILAR VOLUMES

A Sharp Minimum Principle for the Proble
A Sharp Minimum Principle for the Problem of Torsional Rigidity
✍ Xi-nan Ma 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 66 KB

For the equation of torsional rigidity, using the unique continuation of analytic function, we get a sharp minimum principle for a combination of the solution and its gradient. As an application, a lower bound for the minimum stress on the boundary is obtained.