Calculus of Variations and Geometric Measure Theory
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G. Crasta - I. FragalĂ  - F. Gazzola

Some estimates for the torsional rigidity of composite rods

created on 19 Apr 2004
modified by fragala on 18 Jan 2006


Accepted Paper

Inserted: 19 apr 2004
Last Updated: 18 jan 2006

Journal: Math. Nachr.
Year: 2004


A well-known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain $\Omega$, 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.


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