SOLUTION TO THE PROBLEM OF BENDING PLATES BY THE METHOD OF FINITE ELEMENTS USING 5TH DEGREE SPLINES ON A TRIANGULAR GRID

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J. of Mech. Eng., 2017, vol. 20, no. 1, pp. 52-61

DOI:   https://doi.org/10.15407/pmach2017.01.052

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 1, 2017 (March)
Pages 52–61

 

Authors

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine), e-mail: academ_mail@ukr.net

I. S. Tomanova, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine)

 

Abstract

The use of 5th degree splines on a triangular grid of nodes for solving the bending problem for a rigidly clamped uniformly loaded plate is considered. The results of the computational experiment are compared with the known scientific results.

 

Keywords: 5th degree splines, biharmonic problem, rectangular plate, uniformly distributed load

 

References

  1. Sergienko, I. V., Lytvyn, O. N., Lytvyn, O. O., & Denisova, O. I. (2014). Javnye formuly dlja ynterpoljacyonnyx splajnov 5-j stepeny na treuhol’nyke [Explicit formulas for interpolation splines of 5th degree on a triangle]. Cybernetics and Systems Analysis, vol. 50, no. 5, pp. 17–33. https://doi.org/10.1007/s10559-014-9657-x
  2. Zlamal, M., Zenesek, A., Kolar, V., & Kratochvil, J. (1971). Mathematical aspect of the finite element method. Technical physical and mathematical principles of the finite element method, vol. 1, pp. 15–39.
  3. Timoshenko, S. P. & Voynovskiy-Kriger, S. (1966). Plastyny i obolochki [Plates and shells]. Moscow: Nauka, 635 p.
  4. Imrak, C. E. & Gerdemeli, I. (2007). The problem of isotropic rectangular plate with four clamped edges. Indian Academy of Sciences SADHANA, vol. 32, pp. 181–186. https://doi.org/10.1007/s12046-007-0016-8

 

Received 19 September 2016