Analytical ruled surfaces and their complete classification

Cover Page


The aim of the work - to give the possibility to expand mind of designers and architects projecting structures in the form of traditional and non-canonical ruled surfaces. These surfaces have several unquestionable advantages with a point of view of their forming, designing, and making of factory-made goods and erections in the form of ruled surfaces and analysis methods. Methods. Choosing ruled surfaces for classification, one can use methods of their determination by vector, parametrical, implicit, and in explicit equations. Only analytical ruled surfaces are considered which were examined and presented in scientific-and-technical literature. Results. All known at present time ruled surfaces are given in a graphic form. The determinations of some little known ruled surfaces are presented in a paper. The original sources, where these surfaces are examined or their application in real structures and erections are considered, or methods of determination of stress-strain state in thin-walled shells with ruled middle surfaces are presented, are given in references.

About the authors

Sergey N. Krivoshapko

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

DSc, Professor, Professor of the Department of Civil Engineering, Academy of Engineering


  1. Krivoshapko S.N., Ivanov V.N. Encyclopedia of Analytical Surfaces. Switzerland, Springer International Publishing; 2015. doi: 10.1007/978-3-319-11773-7.
  2. Mamieva I.А., Gbaguidi-Aisse G.L. Influence of the geometrical researches of rare type surfaces on design of new and unique structures. Building and Reconstruction, 2019;5(85):23–34.
  3. Grinko E.A. Classification of analytical surfaces as applied to parametricalт architecture and machine building. RUDN Journal of Engineering Researches, 2018;19(4):438–456. (In Russ.)
  4. Mamieva I.A. On classification of analytical surfaces. Engineering System – 2011: Abstracts of Papers of International Scientific-and-Practical Conference. Moscow, RUDN Publ.; 2011. pp. 63–65. (In Russ.)
  5. Mamieva I.A. Influence of the geometrical researches of ruled surfaces on design of unique structures. Structural Mechanics of Engineering Constructions and Buildings. 2019;15(4):299–307.
  6. Krivoshapko S.N. The classification of ruled surfaces. Structural Mechanics of Engineering Constructions and Buildings. 2006;(1):10–20. (In Russ.)
  7. Belyakova M.S. Povyshenie effektivnosti prozessov konstruktorsko-tekhnologichesko proektirovaniya na osnove razrabotki informazionnoy sistemy modelirovaniya poverkhnostey [The increasing effectivness of processes of design-and-technological planning on the basis of informative system of surface modelling] (abstract of the dissertation of the Candidate of Technical Sciences). Moscow, MGTU Stankin Publ.; 2007. (In Russ.)
  8. Mamieva I.A., Razin A.D. Parametrical architecture in Moscow. Architecture and Construction of Russia. 2014; (6):25–29. (In Russ.)
  9. Krivoshapko S.N., Mamieva I.A. The opportunities of applications of torse surfaces and developable shells in Dagestan. Herald of Dagestan State Technical University. Technical Sciences. 2011;3(22):118–127. (In Russ.)
  10. Krivoshapko S.N. Perspectives and advantages of tangential developable surfaces in modeling machine-building and building structures. Bulletin of Civil Engineers. 2019;1(72):20–30. doi: 10.23968/1999-5571-2019-16-1-20-30. (In Russ.)
  11. Mamieva I.A., Razin A.D. Landmark spatial structures in the form of conic surfaces. Industrial and Civil Engineering. 2017;(10):5–11. (In Russ.)
  12. Krivoshapko S.N., Mamieva I.A. Rod systems in the form of one-sheet hyperboloid of revolution. Montazhnye i spetsialnye raboty v stroitelstve. 2011;(11):19–23. (In Russ.)
  13. Krivoshapko S.N. The application of conoid and cylindroid in forming of buildings and structures of shell type. Building and Reconstruction. 2017;5(73):34–44. (In Russ.)
  14. Krivoshapko S.N. Static analysis of shells with developable middle surfaces. Applied Mechanics Reviews. 1998;51(12, Part 1):731–746.
  15. Aleshina O.O. Studies of geometry and calculation of torso shells of an equal slope. Structural Mechanics and Analysis of Constructions. 2019;(3):63–70 (In Russ.)
  16. Lee Y.S. Review on the cylindrical shell research. Transactions of the Korean Society of Mechanical Engineers, A. 2009;33(1):1–26.
  17. Ifayefunmi O., Błachut J. Imperfection sensitivity: a review of buckling behavior of cones, cylinders, and domes. Journal of Pressure Vessel Technology, Transactions of the ASME. 2018;140(5):050801.
  18. Shariyat M., Alipour M.M. Analytical bending and stress analysis of variable thickness FGM auxetic conical/ cylindrical shells with general tractions. Lat. Am. J. Solids Struct. 2017;14(5):805–843.
  19. Grinko E.A. Survey works on geometry, durability, stability, dynamics, and application of environments with middle surfaces of various classes. Montazhnye i spetsialnye raboty v stroitelstve. 2012;(2):15–21. (In Russ.)
  20. Bradshaw R., Campbell D., Gargari M., Mirmiran A., Tripeny P. Special structures. Past, present, and future. Journal of Structural Engineering. 2002:691–701.
  21. Kasyanov N.V. To the problem of the evolution of architectural spatial forms in the context of scientific and technological achievements. Academia. Architecture and Construction. 2019;(3):34–43. 9038-2019-3-34-43. (In Russ.)
  22. Blank Ya.P., Zagayniy N.A. Linejchatye poverhnosti Petersona [Ruled surfaces of Peterson]. Ukrainskiy geometricheskiy sbornik [Ukraine geometrical collection]. 1971;(10):3–10. (In Russ.)



Abstract - 76

PDF (Russian) - 43




Copyright (c) 2020 Krivoshapko S.N.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies