Geodesic
Numerical calculation of the optimum shape of a body of revolution at its penetration into soil media
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 95-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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An efficient method for finding the optimum shape of a body penetrating into soil media has been developed. The method is based on an approximation of the required generator of a body of revolution with minimum penetration resistance by a parametric Bezier polynomial. The numerical calculations have been carried out in the formulation of continuum mechanics, taking into account shock compressibility and soil shear strength within Grigoryan's model of a soil medium. The range of the optimum shapes with a permissible (for practical application) error of 5 % has been obtained.
Keywords: penetration, soil medium, Grigoryan's model, resistance, numerical calculation, unconstrained optimization.
Mots-clés : Bezier polynomial 
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     title = {Numerical calculation of the optimum shape of a~body of revolution at its penetration into soil media},
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E. Yu. Linnik. Numerical calculation of the optimum shape of a body of revolution at its penetration into soil media. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 2, pp. 95-101. http://geodesic.mathdoc.fr/item/UZKU_2014_156_2_a8/

[1] Bazhenov V. G., Kotov V. L., Linnik E. Yu., “O modelyakh rascheta form osesimmetrichnykh tel minimalnogo soprotivleniya pri dvizhenii v gruntovykh sredakh”, Dokl. RAN, 449:2 (2012), 156–159 | DOI

[2] Kotov V. L., Balandin Vl. V., Linnik E. Yu., Balandin Vl. Vl., “O primenimosti modeli lokalnogo vzaimodeistviya dlya opredeleniya sil soprotivleniya vnedreniyu sfery v nelineino-szhimaemyi grunt”, Vychisl. mekhanika sploshnykh sred, 5:4 (2012), 435–442

[3] Linnik E. Yu., “Chislennoe modelirovanie udara i pronikaniya v myagkie gruntovye sredy optimalnykh tel vrascheniya”, Materialy XII Vseros. molod. shk.-konf. “Lobachevskie chteniya – 2013”, Trudy Matem. tsentra imeni N. I. Lobachevskogo, 47, Kazan. matem. o-vo, Kazan, 2013, 103–105

[4] Kraiko A. A., Pyankov K. S., “Effektivnye pryamye metody v zadachakh postroeniya optimalnykh aerodinamicheskikh form”, Zhurn. vychisl. matem. i matem. fiziki, 50:9 (2010), 1624–1631 | MR

[5] Grigoryan S. S., “Ob osnovnykh predstavleniyakh dinamiki gruntov”, Prikl. matem i mekhanika, 24:6 (1960), 1057–1072 | MR

[6] Bazhenov V. G., Zefirov S. V., Kochetkov A. V., Krylov S. V., Feldgun V. R., “Paket programm “Dinamika-2” dlya resheniya ploskikh i osesimmetrichnykh nelineinykh zadach nestatsionarnogo vzaimodeistviya konstruktsii so szhimaemymi sredami”, Matem. modelirovanie, 12:6 (2000), 67–72

[7] Foks A., Pratt M., Vychislitelnaya geometriya. Primenenie v proektirovanii i na proizvodstve, Per. s angl., Mir, M., 1982, 304 pp. | MR

[8] Trukhin B. V., Chernikov A. A., Matematicheskie metody planirovaniya i obrabotka eksperimenta, Ucheb. posobie, N. Novgorod, 1990, 95 pp.

[9] Kotov V. L., Balandin Vl. V., Linnik E. Yu., Balandin Vl. Vl., “Primenenie modeli lokalnogo vzaimodeistviya dlya opredeleniya sily soprotivleniya vnedreniyu udarnikov v peschanyi grunt”, Prikl. mekhanika i tekhn. fizika, 54:4 (2013), 114–125 | Zbl