Poliševski, Dan Quasi-periodic structure optimization of the torsional rigidity. (English) Zbl 0796.73047 Numer. Funct. Anal. Optimization 15, No. 1-2, 121-129 (1994). 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. Cited in 2 Documents MSC: 74P99 Optimization problems in solid mechanics 74E30 Composite and mixture properties 74E05 Inhomogeneity in solid mechanics 49K40 Sensitivity, stability, well-posedness Keywords:volume constraint; existence of an optimal control PDF BibTeX XML Cite \textit{D. Poliševski}, Numer. Funct. Anal. Optim. 15, No. 1--2, 121--129 (1994; Zbl 0796.73047) Full Text: DOI References: [1] Murat F., Calcul des variations et homogeneisation, Les Methodes de I Homogeneisation pp 316– (1985) [2] Kohn R.V., Comm.Pure Appl.Math. 39 pp 113, 353– (1986) [3] DOI: 10.1007/BF00934953 · Zbl 0464.73109 · doi:10.1007/BF00934953 [4] DOI: 10.1016/0045-7825(86)90073-3 · Zbl 0591.73119 · doi:10.1016/0045-7825(86)90073-3 [5] Dal Masso G., The local character of G-closure [6] DOI: 10.1007/BF01650949 · doi:10.1007/BF01650949 [7] Kikuchi N., Comp. Meth. Appl. Mech. Engrg. [8] Mascarenhas, M.L. and Poliševski, D. 1992.Homogenization of the torsion problem with quasi-periodic structure, Vol. 4, 1–17. Lisboa: C.M.A.F. Preprint [9] Mascarenhas, M.L. and Poliševski, D. 1992. ”The warping, the torsion and the Neumann problem in a quasi-periodically perforated domain”. Vol. 11, 1–24. Lisboa: C.M.A.F. Preprint [10] Ladyzhenskaya O.A., Linear and Quasilinear Elliptic Equations (1968) · Zbl 0164.13002 [11] Sperb, R.P. 1981. ”Maximum principles and their applications”. New York: Academic Press. Ch. 4, Sec. 1, Ch. 5, Sec. 3 · Zbl 0454.35001 [12] Protter M.H., Maximum principles in differential equations (1967) · Zbl 0153.13602 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.