employee from 01.01.2014 until now
Moscow, Russian Federation
UDK 004.925.8 Геометрическое моделирование
Abstract. A large number of new surfaces are presented, formed by congruent curves with variable curvature, but remaining in the same class, and superellipses. All surfaces are included in the class-es Rotation Surfaces, Velaroidal Translaation Surfaces, and Algebraic Surfaces with a Carcass of Three Main Flat Curves. All surfaces of the same class are defined by the same general explicit and para-metric equations, and thanks to the presence of many constants in the superellipse equation, it is possible to obtain a lot of known and new surfaces. Despite the fact that the method of construction of the considered surfaces is known, in the presented article it is il-lustrated and visualized on many examples. The surfaces were constructed using a numeric computing environment MATLAB. The surfaces of a general-view superellipse were built on the basis of a new computer program that allows them to be visualized in a multimedia mode by a set change in the exponents contained in the meridian-superellipse formula. All built rotation surfaces have a common name — superellipsoids of rotation. For the first time it is shown that algebraic surfaces with a given frame in three mutually perpendicular planes, applied in shipbuilding, can also find application in the architecture of public buildings. Superellipses are used as the rigid frame of surfaces. In the overview section of the article on the basis of the available publications it is shown that the geometry of the form affects the stress-deformable state of shells with the proposed medial surfaces. The materials of the article give an opportunity in the future to find the optimal shells outlined on the considered analytical surfaces of three different classes, which are considered in the article, taking into account the criteria of optimality applied in architecture, construction, engineering and shipbuilding.
computer simulation, analytical geometry, Velaroidal Surfaces, surfaces of rotation, superellipse, algebraic surfaces with a given frame from three plane curves, shell optimization
1. Alborova L.A. Minimal’nye poverkhnosti v stroitel’stve I arkhitekture [Minimal surfaces in building and architecture]. Biosfernaya sovmestimost': che-lovek, region, tekhnologii [Biosphere compatibility: human, region, technologies]. 2021, I. 1, pp.3-11. DOI:https://doi.org/10.21869/2311-1518-2021-33-1-3-11. (in Russian)
2. Berestova S.A., Misyura N.E., Mityushov E.A. Geometriya samonesushchikh pokrytiy na pryamougol`nom plane [Geometry of self-supporting coatings on rectangular plan]. Stroitel`naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Buildings]. 2017, I. 4, pp. 15 - 18. DOI:https://doi.org/10.22363/1815-5235-2017-4-15-18. (in Russian)
3. Bondarenko I.A. Ob umestnosi I umerennosti arkhitekturnykh novaciy [On the appropriateness and moderation of architectural innovation]. Academia. Arkhitektura i Stroitel'stvo [Academia. Architecture and Construction]. 2020, I. 1, rr. 13-18 (in Russian).
4. Vanin V.V., Shambina S.L., Virchenko G.I. Variantnoe komputernoe maketirovanie obolochek na osnove poliparametrizacii ih seredinnyh poverkhnostey [Variant computer shell prototyping based on polyparameterization of middle surfaces]. Stroitel`naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Buildings]. 2015, I. 6, pr. 3-8. (in Russian)
5. Grinko E.A. Klassifikatsiya analiticheskikh poverkhnostey primenitel`no k parametricheskoy arkhitekture i mashinostoreniyu [Classification of analytical surfaces in relation to parametric architecture and engineering]. Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Inzhenernye issledovaniya [RUDN Journal of engineering researches]. 2018, V. 19, I. 4, pp. 438 - 456. (in Russian)
6. Ermolenko E.V. Formy I postroeniya v arkhitekture sovetskogo avangarda I ih interpretaciya v sovremennoy zarubejnoy praktike [Forms and constructions on the architecture of the soviet avant-garde and their interpretation in modern foreign practice]. Academia. Arkhitektura i Stroitel'stvo [Academia. Architecture and Construction]. 2020, I. 1, pp. 39-48. DOI:https://doi.org/10.22337/2077-2020-1-39-48. (in Russian)
7. Zgoda Yu. N., Semenov A.A. Avtomatizirovannoe modelirovanie obolochek konstrukciy v Autodesk Revit s ispol’zovaniem Dynamo [Automated shell modeling in Autodesk Revit using Dynamo] V sbornike “Novye informacionnye tekhnologii v arkhitekture i stroitel’stve”: Materialy IV Mejdunarodnoy nauchno-prakticheskoy konferencii. Ekaterinburg [In the collection "New Information Technologies in Architecture and Construction": Proceedings of the IV International Scientific and Practical Conference. Yekaterinburg]. 2021, p. 40. (in Russian)
8. Ivanov V.N. Geometriya I formoobrazovanie modificirovannyh poverkhnostey Kunsa [Forming the surfaces on fourangle curved plan] Vestnik Rossiyskogo universiteta drujby narodov. Seriya: Ingenernye issledovaniya [RUDN Journal of Engineering Researches]. 2011, I. 2, pp. 85-90. (in Russian)
9. Ignat'ev S. A., Folomkin A. I., Muratbakeev E. H. Funkcional’nue vozmojnosti sredu Wolfram Mathematica dlya vizualizacii krivuh liniy i poverhnostey [Wolfram Mathematica Functional Possibilities for Curved Lines and Surfaces Visualization]. Geometriya i grafika [Geometry and graphics]. 2021, V. 9, I. 1, pp. 29 - 38. (in Russian)
10. Korotich A.V. Innovacionnye resheniya arkhitekturnyh obolochek: alternativa tradicionnomy stroitel’stvy [Innovative Solutions Of Architectural Shells: Alternative To Traditional Building Construction] Akademicheskiy Vetnik UralNIIproekt, 2015, No. 4, pp. 70-75. (in Russian)
11. Krivoshapko S.N. Gidrodinamicheskie poverkhnosti [Hydrodynamic surfaces]. Sudostroenie [Shipbuilding]. 2021, I. 3, rp. 64-67. [ISSN 0039-4580]. (in Russian)
12. Krivoshapko S.N. Novye analiticheskie formy poverkhnostey primenitel’no k metalliceskim khydojestvennym izdeliyam [New analytical forms of surfaces as applied to metal art products]. Technologiya Mashinostroeniya [Engineering Technology]. 2006, I. 7, pp. 49-51 (in Russian)
13. Krivoshapko S.N. Uproshchennyj kriterij optimal'nosti dlya obolochek vrashcheniya [A simplified criterion of optimality for shells of revolution]. Privolzhskiy Nauchnuy Zhurnal [Privolzhsky Scientific Journal]. 2019, I. 4, pp. 108-116. (in Russian)
14. Krivoshapko S.N., Ivanov V.N. Algebraicheskie poverkhnosti dlya sudovyh korpusov [Analytical surfaces for ship hulls]. Vestnik Rossiyskogo universiteta drujby narodov. Seriya: Ingenernye issledovaniya [RUDN Journal of Engineering Researches]. 2021, V. 22, I. 3, pp. 283-292. DOI:https://doi.org/10.22363/2312- 8143-2021-22-3-283-292. (in Russian)
15. Mamieva I.A. Analiticheskie poverkhnosti dlya parametricheskoy arkhitektury v sovremennykh zdaniyakh i sooruzheniyakh [Analytical surfaces for parametric architecture in modern buildings and constructions]. Akademiya. Arkhitektura i stroitel`stvo [Academia. Architecture and construction]. 2020, I. 1, pp. 150 - 165. (in Russian)
16. Rynkovskaya M. I. Raschet i primenenie gelikoidal'nyh obolochek [Application And Analysis Of Right Helicoidal Shells]. Vestnik Rossiyskogo universiteta drujby narodov. Seriya: Ingenernye issledovaniya [RUDN Journal of Engineering Researches]. 2009, I. 3, pp. 113-116. (in Russian)
17. Sal`kov N.A. Obshchie printsipy zadaniya lineychatykh poverkhnostey. Chast`2 [General principles of definition of linear surfaces. Part 2]. Geometriya i grafika [Geometry and graphics]. 2019, V. 7, I. 4, pp. 14 - 27. (in Russian)
18. Simenko A.I., Kopeikin R.R. and Simenko E.V. Modelirovanie i vizualizaciya poverhnostej, ih osobennosti i primenenie [Simulation And Visualization Of Surfaces, Their Features And Applications] Sovremennye obrazovatel'nye tekhnologii v prepodavanii estestvenno-nauchnyh i gumanitarnyh disciplin: Sbornik nauchnyh trudov IV Mezhdunarodnoj nauchno-metodicheskoj konferencii, Sankt-Peterburg, 11-12 aprelya 2017 goda / Otvetstvennyj redaktor: A.B. Mahovikov. Sankt-Peterburg: Sankt-Peterburgskij gornyj universitet, 2017, pp. 888-895. (in Russian)
19. Strashnov S.V. Velaroidal’nye poverkhnosti i poverkhnosti velaroidal’nogo tipa [Velaroidal shells and shells of the velaroidal type] Geometriya i grafika [Geometry and graphics], 2022, V. 10, I. 2, pp. 11-19. DOI:https://doi.org/10.12737/2308-4898-2022-10-2-11-19. (in Russian)
20. Strashnov S. V., Rynkovskaya M. I. Funkcional’nue vozmojnosti sredu Wolfram Mathematica dlya vizualizacii krivuh liniy i poverhnostey [To the Question of the Classification for Analytical Surfaces]. Geometriya i grafika [Geometry and graphics]. 2022, V. 10, I. 1, pp. 36 - 43. DOI:https://doi.org/10.12737/2308-4898-2022-10-1-36-43 (in Russian)
21. Gil-oulbe M. Reserve of analytical surfaces for architecture and construction. Building and Reconstruction, 2021, I. 6 (98), pp. 63-72. DOI:https://doi.org/10.33979/2073-7416-2021-98-6-63-72.
22. Jasion P., Magnucki K. Buckling and post-buckling analysis of an untypical shells of revolution // Insights and Innovations in Structural Engineering, Mechanics and Computation: Proceedings of the 6th International Conference on Structural Engineering, Mechanics and Computation. 2016, rp. 766-771. DOI:https://doi.org/10.1201/9781315641645-125.
23. Jasion P., Magnucki K. Elastic buckling of clothoidal-spherical shells under external pressure - theoretical study. Thin-Walled Structures. 2015, V. 86, pp. 18-23. DOI:https://doi.org/10.1016/j.tws.2014.10.001.
24. Kheyfets A.L., Galimov D. and Shleykov I. Kinematic and analytical surfaces programming for solution of architectural designing tasks. GraphiCon 2001 Proceedings, 2001, pp. 283-286.
25. Kolmanič S., Guid N. The flattening of arbitrary surfaces by approximation with developable strips. From Geometric Modeling to Shape Modeling (U. Cugini, M. Wozny, eds.). Kluwer Academic Publishers; 2001. p. 35-44. DOI:https://doi.org/10.1007/978-0-387-35495-8_4.
26. Krivoshapko S.N. Optimal shells of revolution and main optimizations. Structural Mechanics of Engineering Constructions and Buildings. 2019, V. 15, I. 3, pp. 201-209 [DOI:https://doi.org/10.22363/1815-5235-2019-15-3-201-209].
27. Krivoshapko S.N. Shell structures and shells at the beginning of the 21st century. Structural Mechanics of Engineering Constructions and Buildings. 2021, V. 27, I. 6, pp. 553-561 DOIhttps://doi.org/10.22363/1815-5235-2021-17-6-553-561.
28. Nick B. Different domes for a sky dome // 3D Warehouse / Trimble Inc. The Netherlands, 2014. URL: https://3dwarehouse.sketchup.com/model/95afa0a51717cfc0763cd81c1b401a16/Different-domes-for-a-sky-dome (data obrashcheniya: 26.12.2022)
29. Postle B. Methods for creating curved shell structures from sheet materials. Buildings, 2012, 2, pp. 424-455. DOI:https://doi.org/10.3390/buildings2040424.
30. Stadler W., Krishnan V. Natural structural shapes for shells of revolution in the membrane theory of shells. Structural Optimization. March 1989, V. 1, I. 1, pp 19-27.
31. Van Mele T., Rippmann M., Lachauer L. and Block P. Geometry-based understanding of structures. Journal of the International Association for Shell and Spatial Structures, 2012, 53(174), pp. 1-5.
