GEOMETRY OF SELF-BEARING COVERING ON RECTANGULAR PLAN

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Abstract

       An algorithm for constructing an unlimited set of velaroid surfaces theoretically suitable for the formation of self-supporting spatial structures on ectangular plane is given. The general form of the equation of the velaroidal surface is given using two even functions satisfying special boundary conditions. The continuum capacity of the set of these surfaces is proved.

About the authors

SVETLANA ALEKSANDROVNA BERESTOVA

Ural Federal University (UrFU)

Author for correspondence.
Email: s.a.berestova@yandex.ru

BERESTOVA SVETLANA ALEKSANDROVNA was born in 1972 in Nizhny Tagil, Sverdlovsk region, graduated from Ural State University named after A.M. Gorky in in 1994, Doc- tor of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Theoretical Mechanics of the Institute of Fundamental Education, Ural Federal University named after the first President of Russia BN. Yeltsin, 620002, Ekaterinburg, ul. Mira, 19. Area of scientific interests: anisot- ropy of the properties of polycrystalline and composite materials, mathematical modeling of real objects and processes. E-mail: s.a.berestova@yandex.ru

620002, Екатеринбург, ул. Мира,19

N E MISYURA

Ural Federal University (UrFU)

Email: s.a.berestova@yandex.ru

MISYURA N.E. was born in 1976 in Ekaterinburg, graduated from the Mechanics and Mathematics Department of Moscow State University named after Lomonosov in 1999, senior lecturer of the Depart- ment of Theoretical Mechanics of the Institute of Fundamental Education, Ural Federal University named after the first President of Russia BN. Yeltsin, 620002, Ekaterinburg, ul. Mira, 19. Area of scien- tific interests: geometric modeling of real processes and phenomena, the development of invariant meth- ods of transformation and shaping of surfaces. Еmail: nmisura@mail.ru

620002, Екатеринбург, ул. Мира,19

E A MITYUSHOV

Ural Federal University (UrFU)

Email: s.a.berestova@yandex.ru

MITYUSHOV E.A. was born in 1946 in Sverdlovsk, graduated from Ural State University named after A.M. Gorky in 1970, Doctor of Physical and Mathematical Sciences, Professor of the Department of Theoretical Mechanics of the Ural Federal University named after the first President of Russia BN. Yeltsin, 630002, Ekaterinburg, ul. Mira, 19. Area of scientific interests: mathematical modeling of tech- nical systems and processes. E-mail: mityushov-e@mail.ru

620002, Екатеринбург, ул. Мира,19

References

  1. Krivoshapko, S.N., Ivanov, V.N. (2010). Encyclopedia of Analytic Surfaces. Moscow: The Book House "LIBROKOM". 560.
  2. Krivoshapko, S.N., Shambina, S.L.(2009). Investigation of velaroidal surfaces with two families of sinusoids on the ring plan. Structural Mechanics of Engineering Constructions and Buildings,(4), 9—12.
  3. Shambina, S.L., Neporada, V.I. (2012). Velaroid surfaces and their application in construction and architecture, Pratzi Tavriysk. Derjavn. Agrotechnol. Un-t, 53(4). 168 — 173.
  4. Neporada, V.I, Bagramyan, A.E, U. Juichen (2010). Use of velaroid shells in architecture on the example of the multifunctional sports complex project. International Scientific and Technical Conference of Students: Proc. of reports, RUDN, March 15 - 19, 2010. 225 — 228.
  5. Berestova, S.A., Zhilin, S.S., Misyura, N.E., Mityushov, E.A. (2015). A method for modeling an architectural drawing type solution for environmental objects using linear perspective on a flat surface, Mathematical Design & Technical Aesthetics, № 1 (3). 11 — 23.

Copyright (c) 2017 BERESTOVA S.A., MISYURA N.E., MITYUSHOV E.A.

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

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