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Isoepiphanic shapes of high-pressure vessels. (Russian, English) Zbl 1399.49022

Sib. Zh. Ind. Mat. 20, No. 3, 3-10 (2017); translation in J. Appl. Ind. Math. 11, No. 3, 305-311 (2017).
Summary: We consider generalized statements of the problems of optimization of geometric shapes for simple and complex domains under given constraints. Along with the condition of minimization of the domain boundary, some additional constraints are introduced on the pointwise or contour “fastening” of the domain. The obtained results can be used for optimal design of high-pressure tanks and vessels, including the multisection ones.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
52A40 Inequalities and extremum problems involving convexity in convex geometry

Software:

Surface Evolver
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References:

[1] Golushko, S. K., The Analysis of Behaviour of Multilayered Nodoid Shells on the Basis of Nonclassical Theory, 205-216 (2005), Berlin · doi:10.1007/3-540-32376-7_12
[2] S. K. Golushko and Yu. V. Nemirovskii, Direct and Inverse Problems in Mechanics of Elastic Composite Plates and Rotation Shells (Fizmatlit, Moscow, 2008) [in Russian].
[3] I. M. Yaglomand V. G. Boltyanskii, Convex Figures (Gostekhizdat, Moscow, 1951) [in Russian].
[4] L. Fejes Tot, Lagerungen in der Ebene auf der Kugel und im Raum (Springer, Berlin, 1953; Fizmatlit, Moscow, 1958). · Zbl 0052.18401
[5] D. A. Kryzhanovskii, Isoperimetric Problem: Maximal and Minimal Properties of Geometric Figures (Editorial URSS, Moscow, 2010) [in Russian].
[6] Ya. S. Pul’pinskii, Mathematical Modeling of Rotation Shells of Complex Forms, Candidate’s Dissertation in Technical Sciences (Gos. Univ. Arkhitekt. Stroit., Penza, 2006).
[7] S. S. Kutateladze, “Three Unavoidable Problems,” Vladikavkaz. Mat. Zh. 8 (1), 40-52 (2006). · Zbl 1299.52014
[8] S. S. Kutateladze, “Multiobjective Problems of Convex Geometry,” Sibirsk. Mat. Zh. 50 (5), 1123-1136 (2009) [Siberian Math. J. 50 (5), 887-897 (2009)]. · Zbl 1224.52017
[9] A. V. Pogorelov, “Imbedding a ‘Soap Bubble’ into a Tetrahedron,” Mat. Zametki 56 (2), 90-93 (1994) [Math. Notes 56 (2), 824-826 (1994)]. · Zbl 0842.52001
[10] W. Tamm and I. Ballinger, “Conceptual Design of Space Efficient Tanks,” АIAA, 2006-5058. · doi:10.2514/6.2006-5058
[11] M. Hutchings, F. Morgan, M. Ritore, and A. Ros, “Proof of the Double Bubble Conjecture,” Ann. Math. No. 155, 459-489 (2002). · Zbl 1009.53007 · doi:10.2307/3062123
[12] Astrakov, S. N.; Golushko, S. K., Design of Multisection Pressure Tanks, 73 (2014), Novosibirsk
[13] Korolenko, L. A.; Astrakov, S. N., Kelvin Problem on Partitioning Bounded Figures, 97 (2014), Novosibirsk
[14] Plateau J. A. F. Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires. Paris: Gauthier-Villars, 1873. · JFM 06.0516.03
[15] J. E. Taylor, “The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces,” Anal. Math. No. 103, 489-539 (1967). · Zbl 0335.49032
[16] K. Brakke, “The Surface Evolver,” Experiment. Math. No. 1, 141-165 (1992). · Zbl 0769.49033 · doi:10.1080/10586458.1992.10504253
[17] S. J. Cox and S. A. Jones “Instability of Stretched and Twisted Soap Films in a Cylinder,” J. Engrg. Math. No. 86, 1-7 (2004). · Zbl 1356.76039 · doi:10.1007/s10665-013-9657-2
[18] S. J. Cox, D. Weaire, and M. F. Vaz, “The Transition from Two-Dimensional to Three-Dimensional Foam Structures,” Europ. Phys. J. E, No. 7, 311-315 (2002). · doi:10.1140/epje/i2001-10099-1
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