Moskva, Moscow, Russian Federation
At present, a great amount of scientific papers, monographs, and reference books dealing with analytical and differential geometry of surfaces have been published. They contain materials for following geometric investigations, for implementation of received earlier geometrical results into architecture, building, and machinery manufacturing. In the paper it has been shown on the specific examples that sometimes the results of geometric investigations for shells’ middle surfaces taken in published references for the following application without check could lead to serious errors because of ones in the surfaces equations or inexactitudes in a surfaces class definition. At present, 38 classes of surfaces, uniting more than 600 ones that have their own names and are described in scientific publications, are known. The author has worked up a great number of researches and found errors, inaccuracies, and alternative versions in monographs and scientific papers, related to questions on geometry of developable surfaces (conic and torse surfaces), surfaces of rev olution (paraboloid and ellipsoid of revolution, nodoid), minimal surfaces (catenoids), conoids, and cyclic surfaces including the canal ones. In actual practice there are much more geometric errors, but in this paper are discussed only well-known geometricians and architects’ works, as well as in this paper there is no information on surfaces that are presented at specialized sites in Internet. Here are encountered misreckoned coefficients for surfaces’ fundamental quadratic forms, there are errors in the formulae for the quadratic forms’ coefficients determination, as well as in the formulae for the calculation a surface element’s area, surface’s principle curvatures, and so on. All of encountered errors have been divided into four groups. The fourth group’s errors named as “typographical errors and authors’ slips of the pen” have been considered fragmentarily because they are encountered the most frequently, and can be corrected by the authors themselves in the following papers.
analytical geometry of surfaces, differential geometry of surfaces, torse surface, nodoid, Agnesi curl, catenoid, cyclic surface, canal surface, paraboloid of revolution, conoid, Cartesian leaf.
Введение
В настоящее время больше всего внимания уделяется разработке методов решения геометрически и физически нелинейных задач теории оболочек. И это правильно, это запрос строительства и машиностроения.
1. Avdon'ev E.A., Protod'yakonov S.M. Primenenie algebraicheskikh krivykh vysshikh poryadkov k postroeniyu gidroaerodinamicheskikh profiley [Application of Higher-Order Algebraic Curves to the Construction of Hydro-Aerodynamic Profiles]. Prikladnaya geometriya i inzhenernaya grafika [Applied Geometry and Engineering Graphics]. Kiev, 1974, I. 18, pp. 111-114.
2. Avdon'ev E.A., Protod'yakonov S.M. Uravneniya i kharakteristiki nekotorykh algebraicheskikh poverkhnostey vysshikh poryadkov [Equations and characteristics of some higher-order algebraic surfaces]. Prikladnaya geometriya i inzhenernaya grafika [Applied Geometry and Engineering Graphics]. Kiev, 1976, I. 21, pp. 108-120.
3. Gmirach K.M., Kozlov A.V., Proskurov R.A. Podbor optimal'nykh parametrov ellipsoidnoy zhelezobetonnoy obolochki vrashcheniya [Selection of optimal parameters of the ellipsoidal ferroconcrete shell of rotation]. Mezhdunarodnyy nauchno-issledovatel'skiy zhurnal: Tekhnicheskie nauki [International Scientific and Research Journal: Technical Sciences]. 2017, I. 2(56).
4. Goloveshkin Yu.V. Metody teorii tonkikh obolochek v stroitel'noy mekhanike nadvodnogo korablya [Methods of the theory of thin shells in the structural mechanics of a surface ship]. St. Petersburg: «Sudostroenie» Publ., 1992, p. 55.
5. Gulyaev V.I., Bazhenov V.A., Gotsulyak E.A., Gaydaychuk V.V. Raschet obolochek slozhnoy formy [Calculation of shells of complex shape]. Kiev: Budivel'nik Publ., 1990, p. 109.
6. Ivanov V.N., Krivoshapko S.N. Konstruirovanie zontichnykh obolochek iz otsekov tsiklicheskikh obolochek perenosa [Construction of umbrella shells from compartments of cyclic transport shells]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Construction mechanics of engineering structures and structures]. 2011, I. 1, pp. 3-7.
7. Ivanov V.N., Shmeleva A.A.Geometriya i formoobrazovanie tonkostennykh prostranstvennykh konstruktsiy na osnove normal'nykh tsiklicheskikh poverkhnostey [Geometry and Formation of Thin-Walled Spatial Structures Based on Normal Cyclic Surfaces]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Building Mechanics of Engineering Constructions and Structures]. 2016, I. 6, pp. 3-8.
8. Illyustrirovannyy tolkovyy slovar' russkoy nauchnoy i tekhnicheskoy leksiki [Illustrated explanatory dictionary of Rus-sian scientific and technical vocabulary]. Moscow, «Russkiy yazyk» Publ., 1994, p. 379.
9. Kozyreva A.A., Rynkovskaya M.I., Tupikova E.M. Zontichnye obolochki dlya pokrytiya sportivnogo tsentra [Umbrellas for covering the sports center]. Vestnik Rossiyskogo universiteta druzhby narodov [Bulletin of the Russian University of Peoples' Friendship]. 2017, V. 18, I. 1, pp. 70-78.
10. Kotov I.I. Nachertatel'naya geometriya. Kurs lektsiy dlya slushateley fakul'teta povysheniya kvalifikatsii prepodavateley [Descriptive geometry. A course of lectures for students of the faculty for advanced training of teachers]. Moscow, MAI Publ., 1973. 200 p.
11. Krivoshapko S.N. K voprosu o primenenii parabolicheskikh obolochek vrashcheniya v stroitel'stve v 2000-2017 godakh [On the application of parabolic shells of revolution in construction in 2000-2017]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Construction mechanics of engineering structures and structures]. 2017, I. 4, pp. 4-14 .
12. Krivoshapko S.N., Mamieva I.A. Vozmozhnosti primeneniya torsov i torsovykh obolochek v usloviyakh Dagestana [Possibilities of using torsos and torso shells in the conditions of Dagestan]. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta [Bulletin of the Dagestan State Technical University]. 2011, I. 3, pp. 118-127.
13. Krivoshapko S.N. Novye primery poverkhnostey zontichnogo tipa i ikh koeffitsienty osnovnykh kvadratichnykh form [New examples of surfaces of the umbrella type and their coefficients of the basic quadratic forms]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Construction mechanics of engineering structures and structures]. 2005, I. 2, pp. 6-14.
14. Krivoshapko S.N. Ob oshibkakh v terminologii po teorii poverkhnostey i geometricheskogo modelirovaniya [On errors in terminology on the theory of surfaces and geometric modeling]. Sovremennye problemy geometricheskogo modelirovaniya. Materialy Ukraino-rossiyskoy nauchno-prakticheskoy konferentsii [Modern problems of geometric modeling. Materials of the Ukrainian-Russian scientific-practical conference]. Khar'kov, 2005, pp. 82-87.
15. Matematicheskaya entsiklopediya [Mathematical Encyclopedia]. «SE» Publ., 1979, V. 2, p. 765.
16. Mamieva I.A., Razin A.D. Znakovye prostranstvennye sooruzheniyav forme konicheskikh poverkhnostey [Signed spatial structures in the form of conical surfaces]. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and civil construction]. 2017, I. 10.
17. Mamieva I.A., Razin A.D. Parametricheskaya arkhitektura v Moskve [Parametric Architecture in Moscow]. Arkhitektura i stroitel'stvo Rossii [Architecture and Construction of Russia]. 2014, I. 6, pp. 24-29.
18. Monzh G. Prilozhenie analiza k geometrii [An appendix of analysis to geometry]. Moscow: ONTI Publ., 1936. 699 p.
19. Morozov A.P., Vasilenko O.V., Mironkov B.A. Prostranstvennye konstruktsii obshchestvennykh zdaniy [Spatial construction of public buildings]. Leningrad: Stroyizdat. Leningradskoe otd. Publ., 1977. 168 p.
20. Rekach V.G. Staticheskiy raschet tonkostennykh prostranstvennykh konstruktsiy [Static calculation of thin-walled spatial structures]. Moscow, Stroyizdat Publ., 1975. 256 p.
21. Sal'kov N.A. Parametricheskaya geometriya v geometricheskom modelirovanii [Parametric geometry in geometric modeling]. Geometriya i grafika [Geometry and graphics]. 2014, I. 3, pp. 7-13.
22. Shulikovskiy V.I. Klassicheskaya differentsial'naya geometriya [Classical differential geometry]. Moscow, Fizmatgiz Publ., 1963, p. 379.
23. Bhattacharya B. Theory of a new class of shells // Symposium on Industrialized Spatial and Shell Structures. Poland, 1973. Pp. 115-124.
24. Drăgan Delia, Bărbȋnţă Dorin, Pondichi-Alb Claudia. Study on the representation in projection with elevations of conoid type surfaces // Advanced Engineering Forum. 2017. Vol. 21. Pp. 118-425.
25. Krivoshapko S.N., Ivanov V.N. Encyclopedia of Analytical Surfaces. Springer International Publishing Switzerland, 2015. 752 p.
26. Mirza J.F. Stresses and deformations in umbrella shells// Proc. ASCE. Apr. 1967. 93, NCT2. P. 271-286.
27. Mladenov I.M. Delaunay surfaces revisited// Dokl. B"lg. AN. 2002. 55, I. 5. Pp. 19-24.
28. Rühle H., Kühn E., Weißbach K., Zeidler D. Räumliche Dachtragwerke. Konstruktion und Ausführung. Band 1, VEB Verlag für Bauweren, Berlin, 1969. 300 p.
29. Soldatos K.P. Mechanics of cylindrical shells with non-circular cross-section: A survey// Applied Mechanics Reviews. Vol. 52 (8), Aug. 1999. Pp. 237-274.
30. Stessel' S.A. Implementation of computer modeling methods in the design of nonlinear architecture objects// Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. ConstructionandArchitecture. 2016. I. 2 (30). Pp. 64-73.
