Design of a Thin Metal Product with the Developable Middle Surface from a Sheet by Parabolic Bending

Abstract:

In the paper, the method to calculate the bending moments arising due to the process of parabolic bending of a thin metal sheet into a torso shell is offered. The problem is solved with the help of methods of differential geometry and shell theory. The possibility of manufacturing any torso product without creases and tears from a thin sheet made of plastic materials is theoretically proved. A review of experimental and theoretical works on pure bending is given. In contradistinction to the mathematical approach to bending a thin sheet into a torso shell (where the thickness of a sheet is assumed to be zero), this paper considers a technical approach taking into account the sheet thickness. It is shown that the normal stresses occurring in a thin sheet as a result of the bending can reach the yield point. On the contrary mathematical possibility to bend a sheet into a torso product, and then unbend it back into a flat position, it is shown in the paper that under certain conditions a sheet cannot be bent back to a flat sheet again due to the occurrence of plastic strains. The results of the research can be used in marine design, civil engineering, air-space industry, and other manufacturing processes.

• Periodical: Materials Science Forum (Volume 986)
• Pages: 78-85
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.986.78
• Online since: April 2020
• Authors: Sergey Nikolayevich Krivoshapko, Marina Rynkovskaya*, Andrey Razin
• Keywords: Developable Surface, Geometrical Non-Linearity, Metal Product, Parabolic Bending, Thin-Walled Sheet Material

References

[1] Ch. Tang, B. Pengbo, J. Wallner and H. Pottmann: ACM Transactions on Graphics, 35(2) Article 12 (2016), pp.1-12.

[2] C.D. Barry: Boatbuilder (2001), pp.1-8.

[3] A.L. Martirosov, V.V. Barinov and G.S. Rachkovskaya: RISI № 4599-В90 (1990), pp.1-10.

[4] O.G. Williams and R.L. Skaggs: US Patent 4236399 (1980), Primary Class 72/295, B21D11/20.

[5] S. Alexandrov, K.-I. Manabe and T. Furushima: Archive of Applied Mechanics, 81(12) (2011), p.1935–(1952).

[6] S.N. Krivoshapko: Proc. of the ХХХI Scientific Conf. of the Faculty of Phys.-and-Math. and Natural Sciences, RUDN (1995), pp.1-17.

[7] S.N. Krivoshapko and G. L. A. Gbaguidi: Journal of the Ghana Institution of Engineers, V. 6-7, № 1 (2009), pp.51-56.

[8] M. Rynkovskaya: MATEC Web of Conferences 108, 16001 (2017), pp.1-4.

[9] S.N. Krivoshapko and S.S. Matveeva: Proc. of the Second Ukraine-and-Russian Sci.-and-Pract. Conf., Kharkov, KhGUPiT (2007), pp.46-52.

[10] S.N. Krivoshapko: Structural Mechanics of Engineering Constructions and Buildings, 5 (1995), pp.68-72.

[11] S.N. Krivoshapko: Tehnologiya Mashinostroeniya, 2 (2008), pp.25-28.

[12] L.S. Kokhan and Yu.A. Morozov: Conditions, Problems, and Perspectives of Development of Metallurgy and Plastic Metal Working, 3 (2003), pp.90-91.

[13] S.N. Krivoshapko: Geometry of Ruled Surfaces with Cuspidal Edge and Linear Theory of Analysis of Tangential Developable Shells (RUDN, Russian Federation 2009).

[14] K. Miyatani, K. Minematsu and I. Sato: Appl Opt., 20(20) (1981), pp.3470-3472.

[15] Z. Marciniak, J.L. Duncan and S.J. Hu: Mechanics of Sheet Metal Forming, Butterworth-Heinemann (2002), pp.1-205.

[16] G. Arnold, S. Calloch, D. Dureisseix and R. Billardon: Proceedings of ESAFORM (2003), pp.1-4.

[17] J. Supasuthakul, P.D. Hodgson and C. Yang: AIP Conference Proceedings 1383 (2011), pp.541-548.

[18] S.N. Krivoshapko and M. Rynkovskaya: MATEC Web of Conferences 95, 06002 (2017), pp.1-5.

[19] J. Schlaich,, R. Bergermann and W. Sobek: Tensile membrane structures, Invited Lecture in the IASS-Congress in Madrid (September 1989), pp.19-32.