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Quasi-periodic structure optimization of the torsional rigidity. (English) Zbl 0796.73047
We study the torsional rigidity of an \(\epsilon\)-perforated material, subjected to a volume constraint. It is proved that for any \(\epsilon>0\) there exists a distribution of the holes which maximizes the torsional rigidity functional. Also, we prove the existence of an optimal control of the material governed by the system obtained by homogenization. The main result is that when \(\epsilon\to 0\) the torsional rigidity of the optimal \(\epsilon\)-perforated material tends to the torsional rigidity of the optimal distribution of the macroscopic material.

MSC:
74P99 Optimization problems in solid mechanics
74E30 Composite and mixture properties
74E05 Inhomogeneity in solid mechanics
49K40 Sensitivity, stability, well-posedness
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