Email this article 
The pendulum type surfaces with congruential cross sections
- Authors: Krivoshapko S.N.1, Shambina S.L.1
-
Affiliations:
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 17, No 2 (2021)
- Pages: 165-174
- Section: Thin Elastic Shells Theory
- URL: https://journals.rcsi.science/1815-5235/article/view/325688
- DOI: https://doi.org/10.22363/1815-5235-2021-17-2-165-174
- ID: 325688
Cite item
Full Text
Abstract
The article discusses new kinematic surfaces that can be attributed to the class of surfaces of congruent cross sections. The surfaces of congruent cross sections were first identified in a separate class by Professor I.I. Kotov. Circular, elliptical and parabolic cylinders are taken as the guiding surfaces, and circles and parabolas are taken as generating plane curves, which can be located in the plane of the generating curve of the guiding cylinder or in a plane parallel to its longitudinal axis. The introduction of a new independent parameter helped to solve the set geometric problems. The analytical formulas are presented in generalized form, so the shape of the flat generatrix curve can be arbitrary. Two types of surfaces are considered: 1) when the local axes of the generating curves remain parallel during their movement; 2) when these axes rotate. The resulting surfaces can be of interest to architects, or can find application in machine-building thin-walled structures or in the study of the trajectories of bodies during their oscillatory-translational motion.
About the authors
Sergey N. Krivoshapko
Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: shambina_sl@mail.ru
ORCID iD: 0000-0002-9385-3699
Professor of the Department of Civil Engineering, Academy of Engineering, DSc, Professor
6 Miklukho-Maklaya St, Moscow, 117198, Russian FederationSvetlana L. Shambina
Peoples’ Friendship University of Russia (RUDN University)
Email: shambina_sl@mail.ru
ORCID iD: 0000-0002-9923-176X
Associate Professor of the Department of Civil Engineering, Academy of Engineering, PhD
6 Miklukho-Maklaya St, Moscow, 117198, Russian FederationReferences
- Kotov I.I. Descriptive geometry: a course of lectures for students of the faculty of advanced training for teachers. Moscow: MAI; 1973. (In Russ.)
- 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. CRC Press; 2016. p. 766-771. https://doi.org/10.1201/9781315641645-125.
- Filipova J., Rynkovskaya M. Carved Monge surfaces as new forms in the architecture. MATEC Web of Conferences. 2017;95(12):5. https://doi.org/10.1051/matecconf/20179517006
- Bock Hyeng Ch.A., Yamb E.B. Application of cyclic shells in architecture, machine design, and bionics. Int. J. of Modern Engineering Research. 2012;2(3):799-806.
- Andrews J., Séquin C.H. Generalized, basis-independent kinematic surface fitting. Computer-Aided Design. 2013; 45(3):615-620. https://doi.org/10.1016/j.cad.2012.10.047
- Savićević S., Ivandić Ž., Jovanović J., Grubiša L., Stoić A., Vukčević M., Janjić M. The model for helical shells testing. Tehnički Vjesnik. 2017;24(1):167-175. https://doi.org/10.17559/TV-20150816201404
- Krivoshapko S.N., Ivanov V.N. Encyclopedia of analytical surfaces. Switzerland: Springer International Publishing; 2015. https://doi.org/10.1007/978-3-319-11773-7
- Krivoshapko S.N., Bock Hyeng Ch.A. Geometrical research of rare types of cyclic surfaces. International Journal of Research and Reviews in Applied Sciences. 2012;12( 3):346-359.
- Čučaković A., Jović B., Komnenov M. Biomimetic geometry approach to generative design. Periodica Polytechnica Architecture. 2018;47(2):70-74. https://doi.org/10.3311/PPar.10082
- Pottmann H., Eigensatz M., Vaxman A., Wallner J. Architectural geometry. Computers & Graphics. 2015;47:145-164. https://doi.org/10.1016/j.cag.2014.11.002
- Krivoshapko S.N., Shambina S.L. On the question of surfaces of congruent sections of pendulum type on a circular cylinder. Applied Geometry and Engineering Graphics. 2011;88:196-200. (In Russ.)
- Knott G., Viquerat A. Helical bistable composite slit tubes. Composite Structures. 2019;207(1):711-726. https://doi.org/10.1016/j.compstruct.2018.09.045
- Mesnil R., Santerre Y., Douthe C., Baverel O., Leger B. Generating high node congruence in freeform structures with Monge’s surfaces. IASS 2015: Future Visions. Amsterdam; 2015.
- Ivanov V.N., Romanova V.A. Constructive forms of spatial structures (visualization of surfaces in MathCad, AutoCad). Moscow: ASV Publ.; 2016. (In Russ.)
- Bartoň M., Pottmann H., Wallner J. Detection and reconstruction of freeform sweeps. Computer Graphics Forum. 2014;33(2). https://doi.org/10.1111/cgf.12287
- Mesnil R., Douthe C., Baverel O., Léger B., Caron J.-F. Isogonal moulding surfaces: a family of shapes for high node congruence in free-form structures. Automation in Construction. 2015;59:38-47. https://doi.org/10.1016/j.autcon.2015.07.009
- Abd-Ellah H.N., Abd-Rabo M.A. Kinematic surface generated by an equiform motion of astroid curve. International Journal of Engineering Research & Science. 2017;3(7):100-114. https://doi.org/10.25125/engineering-journal-IJOER-JUL-2017-13
- Carmelo M., Biagio M. Quando due figure congruenti sono direttamente congruenti. Boll. Unione Mat. Ital. A. 1992;6(3):425-430.
- Ivanov V.N. Geometry of the cyclic translation surfaces with generating circle and directrix of the base sphere. Structural Mechanics of Engineering Constructions and Buildings. 2011;(2):3-8. (In Russ.)
- Krivoshapko S.N., Ivanov V.N. Surfaces of congruent sections on cylinder. Vestnik MGSU. 2020;15(12):1620-1631. (In Russ.) https://doi.org/ 10.22227/1997-0935.2020.12.1620-1631
Supplementary files
