Geodesic
Isoepiphanic forms of pressure vessels
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 3, pp. 3-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the generalized statements of the optimization problems of the geometric shape of simple and composed domains under given constrains. Alongside the condition of the minimality of the boundary of the domain, some additional constraints are introduced on pointwise or contour “fastening” of the domain. The obtained results can be used for the optimal design of tanks and pressure vessels including multisection ones.
Keywords: pressure vessels, isoperimetric problems, the minimum weight. 
@article{SJIM_2017_20_3_a0,
     author = {S. N. Astrakov and S. K. Golushko and L. A. Korolenko},
     title = {Isoepiphanic forms of pressure vessels},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a0/}
}
TY  - JOUR
AU  - S. N. Astrakov
AU  - S. K. Golushko
AU  - L. A. Korolenko
TI  - Isoepiphanic forms of pressure vessels
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 3
EP  - 10
VL  - 20
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a0/
LA  - ru
ID  - SJIM_2017_20_3_a0
ER  - 
%0 Journal Article
%A S. N. Astrakov
%A S. K. Golushko
%A L. A. Korolenko
%T Isoepiphanic forms of pressure vessels
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 3-10
%V 20
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a0/
%G ru
%F SJIM_2017_20_3_a0
S. N. Astrakov; S. K. Golushko; L. A. Korolenko. Isoepiphanic forms of pressure vessels. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 3, pp. 3-10. http://geodesic.mathdoc.fr/item/SJIM_2017_20_3_a0/

[1] Golushko S. K., “The analysis of behaviour of multilayered nodoid shells on the basis of nonclassical theory”, Comput. Sci. High Performance Computing II, The 2nd Russian–German Advanced Research Workshop, Stuttgart, 2005, 205–216 | DOI

[2] Golushko S. K., Nemirovskii Yu. V., Pryamye i obratnye zadachi mekhaniki uprugikh kompozitnykh plastin i obolochek vrascheniya, Fizmatlit, M., 2008

[3] Yaglom I. M., Boltyanskii V. G., Vypuklye figury, Gostekhizdat, M., 1951 | MR

[4] Feiersh Tot L., Raspolozhenie na ploskosti, na sfere i v prostranstve, Fizmatgiz, M., 1958

[5] Kryzhanovskii D. A., Izoperimetry: maksimalnye i minimalnye svoistva geometricheskikh figur, Editorial URSS, M., 2010

[6] Pulpinskii Ya. S., Matematicheskoe modelirovanie obolochek vrascheniya slozhnykh form, Avtoref. dis. $\dots$ kand. tekhn. nauk, Penza, 2006

[7] Kutateladze S. S., “Tri neizbezhnye zadachi”, Vladikavkaz. mat. zhurn., 8:1 (2006), 40–52 | MR | Zbl

[8] Kutateladze S. S., “Mnogotselevye zadachi vypukloi geometrii”, Sib. mat. zhurn., 50:5 (2009), 1123–1136 | MR | Zbl

[9] Pogorelov A. V., “Vlozhenie “mylnogo puzyrya” vnutr tetraedra”, Mat. zametki, 56:2 (1994), 90–93 | MR | Zbl

[10] Tamm W., Ballinger I., Conceptual Design of Space Efficient Tanks, AIAA, 2006-5058

[11] Hutchings M., Morgan F., Ritore M., Ros A., “Proof of the double bubble conjecture”, Ann. Math., 155 (2002), 459–489 | DOI | MR | Zbl

[12] Astrakov S. N., Golushko S. K., “Design of multisection pressure tanks”, Abstracts Internat. Conf. Advanced Mathematics, Computations and Applications-2014 (Novosibirsk, June 8–11, 2014), 73

[13] Korolenko L. A., Astrakov S. N., “Kelvin problem on partitioning bounded figures”, Abstracts Internat. Conf. Advanced Mathematics, Computations and Applications-2014 (Novosibirsk, June 8–11, 2014), 97

[14] Plateau J. A. F., Statique Experimentale et Theorique des Liquides Soumis aux Seules Forces Moleculaires, Gauthier-Villars, Paris, 1873

[15] Taylor J. E., “The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces”, Anal. Math., 103 (1967), 489–539 | MR

[16] Brakke K., “The surface evolver”, Experiment. Math., 1 (1992), 141–165 | DOI | MR | Zbl

[17] Cox S. J., Jones S. A., “Instability of stretched and twisted soap films in a cylinder”, J. Engrg. Math., 86 (2004), 1–7 | DOI

[18] Cox S. J., Weaire D., Vaz M. F., “The transition from two-dimensional to three-dimensional foam structures”, Europ. Phys. J. E, 7 (2002), 311–315 | DOI