Moskva, Moscow, Russian Federation
Moskva, Moscow, Russian Federation
Moskva, Moscow, Russian Federation
In 1960, the University of friendship of peoples was created by the Soviet government’s decision. In 1962 at the University’s faculty of engineering started the "Resistance of Materials, and Structural Analysis" chair. It was headed by doctor of engineering, professor Vladimir Germanovich Rekach. Simultaneously with the educational process at the chair was opened the postgraduate education in the field of study "Structural Mechanics". One of the main tasks set by V.G. Rekach before graduate students was developing of methods for calculating of shells for new complex forms. It was necessary to begin this work with the study of available in the scientific literature information on the considered class of surfaces, derivation of equations for the surfaces of considered forms, derivation of formulas for the quadratic forms’ coefficients, drawings for this class of surfaces and the concrete calculated construction. Currently, the work in this field of study at the “Resistance of Materials” chair (since 2006 the “Strength of Materials and Structures” chair) is carried out under the supervision of doctors of engineering, professors V.N. Ivanov and S.N. Krivoshapko – the disciples of V.G. Rekach. In 1990–2016 have been prepared and defended 12 dissertations on analysis of shells for surfaces with non-canonical forms. A large amount of material on surfaces geometry that has been accumulated at the RUDN University’s “Resistance of Materials” chair, and works variety in world literature has necessitated to systematize available materials, to create a reference manual on analytical surfaces. In 2006 has been published the 1st version of such reference manual. In 2011 has been published “Encyclopedia of Analytical Surfaces” [10]. This paper gives a short history of the encyclopedia creation, as well as its main tasks and principles of formation, the character of treatment for materials on surfaces classes and the concrete surfaces, and examples for classes and surfaces from encyclopedia. The possibilities for encyclopedia materials usage at architecture, building constructions, machine manufacturing and other areas of science and techniques are considered too.
geometry of surfaces, quadratic forms coefficients, classes of surfaces, thin-walled space constructions.
В 1960 г. решением Советского правительства был создан Университет дружбы народов. Основная задача университета была подготовка научных кадров для развивающихся стран Азии, Африки и Латинской Америки.
1. Brankov G.J. Njakoi voprosi ot momentnata i bezmomentnata teorija na cherupkite [Some questions from the instant and basementcat of the theory of shells]. Trudove na nauchnoizsledovatel'skija stroitelen institut [Labor at the Research Institute of Civil Engineering]. Sofija, 1959, I. 2. (in Russian).
2. Brankov G.J. Volnoobrazni cherepkovi konstrukcii [Wavy Cherepkova designs]. Sofija, Bolgarskata Akademija na naukite Publ., 1961. 80 p. (in Russian).
3. Vygodskij M.Ja. Differencial'naja geometrija [Differential geometry]. Moscow, GITTL Publ., 1949. 512 p. (in Russian).
4. Ivanov V.N. Raschet obolochek v forme ciklicheskih poverhnostej. Kand. Diss. [Calculation of shells in the form of cyclic surfaces. Cand. Diss.]. 1971. (in Russian).
5. Ivanov V.N., Krivoshapko S.N. Analiticheskie metody rascheta obolochek nekanonicheskoj formy [Analytical Methods of Design of the Shells of Noncanonic Forms]. Moscow, RUDN Publ., 2010. 540 p. (in Russian).
6. Ivanov V.N., Romanova V.A. Konstrukcionnye formy prostranstvennyh konstrukcij. Vizualizacija poverhnostej v sistemah "MathCad", i "AUTOCad" [Construction forms of the space constructions. Visualization of the surfaces at the systems "MathCad" and "AUTOCad"]. Moscow, ASV Publ., 2016. 412 p. (in Russian).
7. Kagan V.F. Osnovy teorii poverhnostej [The bases of the theory of surfaces]. Moscow, OGIZ Publ., 1947, V. 1. 512 p. (in Russian).
8. Krivoshapko S.N. Raschet torsovyh (nevyrozhdennyh) obolochek v krivolinejnyh neortogonal'nyh koordinatah. Kand. Diss. [Design of the developable shells at curvilinear coordinates. Cand. Diss.]. 1981. (in Russian).
9. Krivoshapko S.N., Ivanov V.N., Halabi S.M. Analiticheskie poverhnosti [Analytical surfaces]. Moscow, Nauka Publ., 2006. 540 p. (in Russian).
10. Krivoshapko S.N., Ivanov V.N. Enciklopedija analiticheskih poverhnostej [Encyclopedia of analytical surfaces]. Moscow, LIBROKOM Publ., 2010. 540 p. (in Russian).
11. Krivoshapko S.N., Mamieva I.A. Analiticheskie poverhnosti v arhitekture zdanij, konstrukcij i izdelij [Analytical surfaces in Architecture of buildings. Constructions and details]. Moscow, Knizhnyj dom «LIBROKOM» Publ., 2012. 328 p. (in Russian).
12. Krishna Reddi G.V. (Indija). Raschet obolochek v forme ciklid Djupena. Kand. Diss. [(India). "Calculation of shells in the form of Dupin cyclides". Cand. Diss.]. 1966. (in Russian).
13. Marulanda Juhanio Arbelaes. (Kolumbija). Raschet obolochek v forme poverhnostej Monzha. Kand. Diss. [Calculation of shells in the form of Monge surfaces. Cand. Diss.]. 1970. (in Russian).
14. Milinskij V.I. Diferencial'naja geometrija [Differential Geometry]. Kubuch Publ., 1934. 332 p. (in Russian).
15. Mihajlenko V.E., Obuhova V.S., Podgornyj A.L. Formoobrazovanie obolchek v arhitekture [Forming of the shells in architecture]. Kiev, Budevil'nik Publ., 1972. 206 p. (in Russian).
16. Mihajlenko V.E., Kovalev S.N. Konstruirovanie form sovremennyh arhitekturnyh sooruzhenij [Design of the forms of modern architectural constructions]. Kiev, Budevil'nik Publ., 1978. 112 p. (in Russian).
17. Monzh. G. Prilozhenie analiza k geometrii [The application of analysis to geometry]. Moscow, ONTI Publ., 1936. (in Russian).
18. Norden. A.P. Teorija poverhnostej [Theory of surfaces]. Moscow, GITTL Publ., 1956. 260 p. (in Russian).
19. Pajmushin V.N. K zadache parametrizacii sredinnoj poverhnosti obolochki slozhnoj geometrii [At problem of parameterization of the surface of the shell of complex geometry] Prochnosti i nadezhnost' slozhnyh system [Strengths and reliability of complex systems]. Kiev. 1979, pp. 78-84. (in Russian).
20. Rashevskij P.K. Kurs differencial'noj geometrii [Course of differential Geometry]. Moscow, GITTL Publ., 2004. 428 p. (in Russian).
21. Rekach V.G, Krivoshapko S.N. Raschet obolochek slozhnoj geometrii [Design of the shells of the complex Geometry]. Moscow, UDN Publ., 1988. 176 p. (in Russian).
22. Skidan I.A. Geometricheskoe modelirovanie kinematicheskih poverhnostej v special'nyh koordinatah. Dokt. Diss. [Geometrical Modeling of kinematic surfaces at special coordinates. Doct. Diss.]. Moscow. 1989. (in Russian).
23. Skidan I.A. Analiticheskaja teorija formoobrazovanija obolochek [Analitical theory of formation of shell]. Arhitektura obolochek i prochnostnoj raschet tonkostennyh stroitel'nyh i mashinostroitel'nyh konstrukcij slozhnoj formy: Trudy mezhdunarodnoj nauchnoj konferencii [Shell Architecture and Strength Calculation of Thin-Walled Construction and Engineering Constructions of Complex Form: Proceedings of the International Scientific Conference]. Moscow, 2001, RUDN Publ., pp. 366-371. (in Russian).
24. Stebljanko V.T. Ob odnom metode zadanija chastnogo vida jepitrohoidal'nyh poverhnostej [At one method of giving the partial type of epitrochoidal surfaces]. Prikladnaja geometrija i inzhenernaja grafika [Applied Geometry and Engineering Graphics]. Kiev, 1975. I. 20, pp. 89-91. (in Russian).
25. Finikov S.P. Teorija poverhnostej [Theory of surfaces]. Moscow, GTTI Publ., 1934. 285 p. (in Russian).
26. Shulikovskij V.I. Klassicheskaja differencial'naja geometrija [Classical differential Geometry]. Moscow, GIFML Publ., 1963. 540 p. (in Russian).
27. Jakupov N.M. Fragmenty obolochek slozhnoj geometrii v toroidal'noj sisteme koordinat. Issledovanija po teorii obolochek [Fragments of shells of complex geometry in orthogonal coordinate system. Investigations at theory of shells]. Trudy seminara [Proceedings of the seminar]. Kazan', Kazanskij fiziko-tehnicheskij institute Publ., 1988, I. 21, pp. 130- 137. (in Russian).
28. Jakupov N.M., Serazutdinov M.N. Raschet uprugih tonkostennyh konstrukcij slozhnoj geometrii [Design of thin wall constructions of complex forms]. Kazan', IMM RAN Publ., 1993. 206 p. (in Russian).
29. Davis R.F. On the cylindroid // The Mathematical Gazette. Jul., 1990. Vol. 1. = I. 22. P. 370-371.
30. Dupin Ch. Developpment de Geometrie. Paris, 1813.
31. Forsyth A.R. Lectures on the Differential Geometry of Curves and Surfaces. Cambridge. 1920.
32. Krivoshapko S.N., Ivanov V.N. Encyclopedia of Analytical Surfaces. Springer International Publishing Switzerland, 2015. 752 p.
33. Maxwell J.C. On the Cyclide. Quarterly Journal of Pure and Applied Mathematics, 9, 1868. P. 111.
34. Meszrios F. Die Zykliden 3. Ordnung im Pseudoisotropen Raum // Math. Pannon. 1993. 4, I. 2, II. Pp. 273-285
35. Steven A. Coons. Surfaces for Computer-Aided Design in Space Form. Massachusetts Institute of Technology Cambridge, MA, USA, 1967.
