Abstract:
This article shows construction of a geometrical model of a well-known 'mattress effect', it is similar to that observed while opening an umbrella. The main hypothesis is: the surface of metallic mesh of parabolic reflector — in an isotropic case — takes a shape close to a minimal surface. We have taken into account the fact that for the orthotropic metalic mesh the sum of principal curvatures is farther from zero than in the isotropic case. The area of model's reliability has been studied in detail. Mathematical apparatus of the model is the classical differential geometry.
Keywords:
parabolic reflector, principal curvatures, orthotropy, minimal surface, plotting the surface by forming a family of curves.
This publication is cited in the following 7 articles:
M. S. Bukhtyak, D. E. Esipov, “Psevdominimalnye poverkhnosti vrascheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2022, no. 76, 5–19
Di Wu, Minger Wu, Ping Xiang, Zhongxi Yan, “Surface accuracy analysis and optimization design of rib-mesh paraboloidal antenna reflectors”, Aerospace Science and Technology, 129 (2022), 107817
M. S. Bukhtyak, “Psevdominimalnost i lineichatye poverkhnosti”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 67, 18–27
M. S. Bukhtyak, “Obobschenie minimalnykh poverkhnostei i modelirovanie formy konstruktsii iz ortotropnogo materiala”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 45, 5–24
M. S. Bukhtyak, “Sostavnaya poverkhnost, blizkaya k psevdominimalnoi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 46, 5–13
M. S. Bukhtyak, “Konechno-elementnaya model psevdominimalnoi poverkhnosti”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 48, 5–16
M. S. Bukhtyak, “Defekt otobrazheniya dlya deformirovannogo lepestka setepolotna”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 2(40), 5–18
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