Published April 30, 2018 | Version v1
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MINIMIZING THE MASS OF A FLAT BOTTOM OF CYLINDRICAL APPARATUS

Creators

  • 1. Odessa National Polytechnic University

Description

In the bodies of cylindrical apparatuses that operate under pressure, one of the weak elements is a flat bottom whose thickness is increased by 4…5 times in comparison with the wall thickness. This is due to the fact that the bottom is exposed to a more unfavorable bending deformation compared to the wall that «works» on stretching. In order to reduce specific metal consumption for the bottom, we propose the optimization of the shape of a radial cross-section by a rational redistribution of the material: to increase thickness of the bottom in the region of its contact with the wall and to significantly reduce it in the central zone. To describe a variable thickness of the bottom, we applied the Gauss equation with an arbitrary parameter that determines the intensity of change in the thickness in radial direction.

We have obtained a general solution to the differential equation of the problem on bending a bottom at a given law of change in its thickness, which is represented using the hypergeometric Kummer’s functions. A technique for concretizing the resulting solution was proposed and implemented, based on the application of conditions of contact between a cylindrical shell and a bottom. The solution derived was used to minimize the mass of the bottom. We have designed a zone of transition from the bottom to the wall whose strength was verified by the method of finite elements under actual conditions

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References

  • Stanovskiy, A. L., Naumenko, E. A. Osama, A. Sh. (2017). Matematicheskoe modelirovanie i optimizaciya v SAPR ravnonapryazhennyh detaley mashin. Vysoki tekhnolohiyi v mashynobuduvanni, 1 (27), 143–154.
  • Saveleva, O., Khomyak, Y., Stanovska, I., Toropenko, A., Naumenko, E. (2016). Optimization of uniformly stressed structures of cylindrical tanks in CAD. Eastern-European Journal of Enterprise Technologies, 6 (7 (84)), 10–16. doi: 10.15587/1729-4061.2016.85451
  • Temis, Yu. M., Yakushev, D. A. (2012). Mnogokriterial'noe optimal'noe proektirovanie diskov turbomashin. Izvestiya Moskovskogo gosudarstvennogo tekhnicheskogo universiteta MAMI, 2 (2 (14)), 330–336.
  • Ginzburg, A. V., Vasil'kin, A. A. (2014). Postanovka zadachi optimal'nogo proektirovaniya stal'nyh konstrukciy. Vestnik MGSU, 6, 52–62.
  • Khomiak, Yu. M., Tshyham, H. Zh. (2015). Rozviazok zadachi vyhynu kruhloi plastyny zminnoi tovshchyny z vykorystanniam funktsiyi Uittekera. Pedagogicheskoe masterstvo prepodavatelya vysshey shkoly, 3, 94–95.
  • Aryassov, G., Gornostajev, D. (2013). The calculation of round plates under the action of local loading by generalized functions. 13th International Symposium «Topical Problems in the Field of Electrical and Power Engineering». Pärnu, 296–299.
  • Ahlawat, N., Lal, R. (2016). Axisymmetric Vibrations of Variable Thickness Functionally Graded Clamped Circular Plate. Advances in Intelligent Systems and Computing, 261–271. doi: 10.1007/978-981-10-0448-3_21
  • Starkov, V. N., Semenov, A. A., Gomonay, E. V. (2014). Operatornoe uravnenie pervogo roda v probleme nakopleniya statistiki chisla fotonov kvantovogo sveta. Elektron. modelirovanie, 36 (3), 81–94.
  • Kirpichnikov, A. P., Flax, D. B., Valeeva, L. R. (2015). Probabilistic characteristics of open multi-channel queuing system with limited average residence time of the application in the system. Theoretical & Applied Science, 25 (05), 44–49. doi: 10.15863/tas.2015.05.25.9
  • Dasibekov, A., Yunusov, A. A., Aymenov, Zh. T., Yunusova, A. A. (2014). Zadachi teorii uplotneniya gruntov, reshaemye v gipergeometricheskih funkciyah Kummera. Uspekhi sovremennogo estestvoznaniya, 4, 96–101.
  • Epifancev, B. N. (2010). Obnaruzhenie lokal'nyh izmeneniy na trasse magistral'nyh produktoprovodov na opticheskih izobrazheniyah: vvedenie v problemu. Neftegazovoe delo, 2, 31–41.
  • Vogl, C., Clemente, F. (2012). The allele-frequency spectrum in a decoupled Moran model with mutation, drift, and directional selection, assuming small mutation rates. Theoretical Population Biology, 81 (3), 197–209. doi: 10.1016/j.tpb.2012.01.001
  • Lemaitre, G. R. (2009). Dioptrics and Elasticity – Variable Curvature Mirrors (VCMs). Astronomical Optics and Elasticity Theory, 137–170. doi: 10.1007/978-3-540-68905-8_2
  • Holt, A. F., Buffett, B. A., Becker, T. W. (2015). Overriding plate thickness control on subducting plate curvature. Geophysical Research Letters, 42 (10), 3802–3810. doi: 10.1002/2015gl063834
  • Bouguenina, O., Belakhdar, K., Tounsi, A., Adda Bedia, E. A. (2015). Numerical analysis of FGM plates with variable thickness subjected to thermal buckling. Steel and Composite Structures, 19 (3), 679–695. doi: 10.12989/scs.2015.19.3.679
  • Shamekhi, A. (2013). On the use of meshless method for free vibration analysis of circular FGM plate having variable thickness under axisymmetric condition. IJRR Applied Sci., 14 (2), 257–268.
  • Zheglova, V., Khomiak, Y., Medvedev, S., Nikolenko, I. (2017). Numerical and Analytical Evaluation of Service Life of the Details of Axial Piston Hydraulic Machines with Complicated Configuration under Cyclic Loading. Procedia Engineering, 176, 557–566. doi: 10.1016/j.proeng.2017.02.298
  • Levchuk, S. A., Khmelnytskyi, A. A. (2015). Aproksymatsiya statychnoho deformuvannia kruhlykh plastyn riznykh profiliv za dopomohoiu matryts typu Hrina. Novi materialy i tekhnolohiyi v metalurhiyi ta mashynobuduvanni, 2, 115–118.
  • Seo, J. K., Kim, B. J., Ryu, H. S., Ha, Y. C., Paik, J. K. (2011). Validation of the equivalent plate thickness approach for ultimate strength analysis of stiffened panels with non-uniform plate thickness. Thin-Walled Structures, 49 (6), 753–761. doi: 10.1016/j.tws.2011.02.001
  • Hismatulin, E. R. et. al. (1990). Sosudy i truboprovody vysokogo davleniya. Moscow: Mashinostroenie, 384.
  • Aomoto, K., Kita, M. (2011). Theory of Hypergeometric Functions. Springer, 317. doi: 10.1007/978-4-431-53938-4
  • Brychkov, Yu. A. (2006). Special'nye funkcii. Proizvodnye, integraly, ryady i drugie formuly. Moscow: Fizmatlit, 512.
  • Kindratskyi, B. I., Sulym, H. T. (2003). Ratsionalne proektuvannia mashynobudivnykh konstruktsiyi. Lviv: KINPATRI LTD, 280.
  • Koreneva, E. B. (2009). Analiticheskie metody rascheta plastin peremennoy tolshchiny i ih prakticheskie prilozheniya. Moscow: Izd-vo ASV, 238.
  • Stanovskyi, O. L., Khomiak, Yu. M., Toropenko, A. V., Naumenko, Ye. O., Daderko, O. I. (2017). Upravlinnia napruzhenistiu system za dopomohoiu shtuchnoho intelektu. Visnyk natsionalnoho tekhnichnoho universytetu «KhPI». Seriya: Mekhaniko-tekhnolohichni systemy ta kompleksy, 44, 52–60.