Tangential Developable Surfaces and Shells: New Results of Investigations


Sergey N. Krivoshapko,Iraida A. Mamieva,Andrey D. Razin,




Tangential Developable,Design of A Torse,Geodesic Curve,ParaBending,Tangential Developable Shell Geometric Modeling,Stress-Strain State ofthe Shell,


After publication of a monograph Geometry of Ruled Surfaces with Cuspidal Edge and Linear Theory of Analysis of Tangential Developable Shells (Krivoshapko, 2009) with 386 references, new papers, devoted to geometry, application and strength analyses of thin shells with the middle developable surface were published. Some results of investigations have newness and definite scientific and practical in-terest but some works improve methods presented before or propose new variants of application of tangent developable surfaces. In a paper, new results derived past the last 10 years and connected with needs of engineer practice and architecture of man-ufactured articles, structures, and erections, are analyzed. The analyses of the whole spectrum of investigations of torse surfaces and shells presented in the publications till present time will help researchers concerned to plan further investigations and to economize their time not repeating a conclusion of theorems, equations, and proposi-tions the well-known already.


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IV.Belyaeva Z.V., Berestova S.A., Mityushov E.A.(2017).Tangent developable surfaces elements in thin walled structures. Structural Membranes 2017:VIII International Conference on Textile Composites and Inflatable Structures, K. Bletzinger , E. Oñate and B. Kröplin (Eds.), 9-11 October,Munich, Germa-ny: 415-426.

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VI.Cui Jinglan, Ohsaki Makoto, Nakamura Keigo (July 2017). Shape optimiza-tion of free-form shells consisting of developable surfaces. Journal of Struc-tural and Construction Engineering (Transactions of AIJ)82(737): 1137-1143. VII.Filipova J.(2016).Comparative analysis of the results of calculation of a thin shell in the form of carved surface of Monge with an application of mem-brane (momentless) theory and finite element method. Structural Mechanics of Engineering Constructions and Buildings, 3: 8-13.

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IX.Gonzalez-Quintial F., Barrallo Javier, Artiz-Elkarte A.(2015).Freeform sur-faces adaptation using developable strips and planar quadrilateral facets. Journal of Facade Design and Engineering, 3(1): 59-70.

X.Kilian M., Flöry S., Chen Z., Mitra N.J., Sheffer A., Pottmann H. (2008). De-velopable surfaces with curved creases. Advances in Architectural Geometry: 33–36.

XI.Körpinar T., Turhan E.(2012).Inextensible flows of tangent developable sur-faces of biharmonic curves in SL2(R). J. Sci. Res., 4(2): 365-371.

XII.Krivoshapko S.N.(2006).Classification of ruled surfaces. Structural Me-chanics of Engineering Constructions and Buildings, 1: 10-20.

XIII.Krivoshapko S.N. (2009). Geometry of Ruled Surfaces with Cuspidal Edge and Linear Theory of Analysis of Tangential Developable Shells: Mono-graph. Moscow: RUDNPubl., 358 p. (In Russ.).

XIV.Krivoshapko S.N., Timoshin М.А. (2012). Static stability analysis of an ellip-tic shell of equal slope, two conical shells with the director ellipse and a torse with two ellipses placed in parallel planes.V Int. Scientific-and Practical Conference “Engineering System -2012”: Proc., Moscow:RUDN, April 16-18: 40-46.

XV.Krivoshapko S.N., Ivanov V.N. (2015). Encyclopedia of Analytical Surfaces. Springer International Publishing Switzerland, 752 p.

XVI.Krivoshapko S.N. (2017). Two types of governing equations for shells with the middle surfaces given in arbitrary curvilinear coordinates. Structural Me-chanics of Engineering Constructions and Buildings, 1: 15-22.

XVII.Krivoshapko S.N. (2018). Application, geometric, and strength investigation of tangential developable surfaces and shells: A review of works published after 2008. StroitelnayaMehanikai Raschet Sooruzheniy, 2: 19-25.

XVIII.Lawrence Snežana (2011). Developable surfaces: their history and applica-tion. Nexus Network Journal, 13 (3): 701-714.

XIX.Liu Y., Pottmann, H., Wallner J., Yang Y.-L., and Wang W. (2006). Geome-tric modeling with conical meshes and developable surfaces. ACM Transac-tion on Graphics, 25(3): 681-689.

XX.Mamieva I. A., Razin A. D.(2017).Symbol spatial structures in the form of conic surfaces. Industrial and Civil Engineering, 10: 5-11.

XXI.Olevs’kyy V.I.(2011). Features of the calculation of shells with technologi-cal imperfections by the modified method of parameter continuation. Prob-lemi Obchislyuval’noy Mehaniki i Mitsnosti Konstruktsiy, Vip. 17: 219-225.

XXII.ObradovićR., BeljinB., PopkonstantinovićB.(2014). Approximation of transitional developable surfaces between plane curve and polygon. Acta Po-lytechnica Hungarica, 11(9): 217-238.

XXIII.Perez Fr. and Suarez An. (2007). Quasi-developable B-spline surfaces in ship hull design. Comp. Aided Geom. Design, 39: 853-86.

XXIV.Postle B. (2012). Methods for creating curved shell structures from sheet ma-terials. Buildings, 2: 424-455.

XXV.Rynkovskaya M.(2017). Analysis of displacements in beam structures and shells with middle developable surfaces. MATEC Web of Conferences “IC-MAA 2017”, 108, 16001: 4 p.

XXVI.Rynkovskaya M. (2012). Generatrix slope angle influence on the mode of de-formation of open helicoidal shells calculated by analytical small parameter method with three terms of series. Structural Mechanics of Engineering Con-structions and Buildings, 4: 15-17.

XXVII.Rynkovskaya M. (2015). The influence of Poison coefficient to accuracy of analysis of developable open helicoid. Stroitelstvo i Rekonstruktsiya, 4: 51-56.

XXVIII.SavićevićS., IvandićŽ., JovanovićJ., GrubišaL., StoićA., VukčevićM., JanjićM. (2017), The model for helical shells testing. Tehnički Vjesnik 24, 1: 167-175.

XXIX.Soley Ersoy, Kemal Eren (2016). Timelike tangent developable surfaces and Bonnet suefaces. Abstract and Applied Analysis, Volume2016, Article ID6837543, 7 pageshttp://dx.doi.org/10.1155/2016/6837543

XXX.Solomon J., Vouga E., Wardetzky M., & Grinspun E. (2012). Flexible Deve-lopable Surfaces. Eurographics Symposium on Geometry Processing 2012. Eitan Grinspun and Niloy Mitra (Guest Editors), 31 (5): 1-10.

XXXI.Tang Ch., Pengbo Bo, Wallner J., Pottmann H. (January 2016). Interactive design of developable surfaces. ACM Transactions on Graphics, 35(2), Ar-ticle 12:12 p.

XXXII.Yi-chao, Eliot Fried (2016). Möbius bands, unstretchable material sheets and developable surfaces. Proc. of the Royal Society. A. Math., Phys. and Engi-neering Sciences. 472 (2192).

XXXIII.Zhao Hongyan, Wang Gupjin(2008). A new method for designing a deve-lopable surface utilizing the surface pencil through a given curve. Progress in Natural Science, 18: 105-110.


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