Patterns in the distribution capacity of thin plates under different condition for their resting on supports

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.213776

Keywords:

longitudinal strip, transverse strip, fictitious pinching, system of equation, lateral distribution coefficient

Abstract

This paper reports a study into the distribution capacity of a flexible plate in different cross-sections exposed to the external vertical concentrated forces applied in any place of its area. A plate with one pinched side and a series of racks arranged at any distance from the pinching has been considered. In terms of the theory of elasticity and mathematics, solving this problem poses significant difficulties. This has study found that a lateral distribution coefficient could be used to simplify calculations aimed at determining the stressed-strained state of the system. In determining the stressed-strained state of the plate, the calculation method described in work [1] was applied. The plate is cut into a series of longitudinal strips that represent, from the standpoint of construction mechanics, a console strip with one pinched end and resting on a stationary support located at any distance from the pinching. It has been revealed that the distribution capacity of the examined plate in the same cross-section depends insignificantly on the point of application of the concentrated load along the length of the longitudinal strip (between 2.6 and 6.7 %). The distribution capacity in different cross-sections does differ greatly (in the range of 10 to 30 %). The result of this study is the proposed unified and easy-to-implement method of calculating plates under any conditions for their resting on supports and when exposed to any external loads. There is also no difficulty in calculating the plates backed by edges in both directions. Other estimation methods in these cases require a different mathematical approach, and, for the case of a series of external loads, or under difficult plate rest conditions, the issue relating to the stressed-strained state of the system remains open

Author Biographies

Vitaly Kozhusko, Kharkov National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor

Department of Bridges, Structures and Building Mechanics

Sergey Krasnov, Kharkov National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Bridges, Structures and Building Mechanics

Kateryna Berezhna, Kharkov National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Bridges, Structures and Building Mechanics

Serhii Oksak, Kharkov National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Technologies of Road-Building Materials and Chemistry

Roman Smolyanyuk, Kharkov National Automobile and Highway University Yaroslava Mudroho str., 25, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Automobile Road Construction and Maintenance

References

  1. Kozhushko, V. P. (2010). Modeliuvannia prolotnykh budov mostiv. Kharkiv: KhNADU, 196.
  2. Maslennikov, A. M. (1987). Raschet stroitel'nyh konstruktsiy chislennymi metodami. Leningrad: Izd-vo Leningr. un-ta, 224.
  3. Rabotnov, Yu. N. (1988). Mehanika deformiruemogo tverdogo tela. Moscow: Nauka, 712.
  4. Gabbasov, R. F., Anh, H. T., Anh, N. H. (2014). Comparison of results of calculation of thin flexible slabs with the use of generalized equations of finite-difference method (FDM) and method of successive approximations (MSA). Promyshlennoe i grazhdanskoe stroitel'stvo, 1, 62–64. Available at: http://www.pgs1923.ru/archiv/2014/01/16.pdf
  5. Ignat'ev, F. V. (2002). Primenenie MKE v smeshannoy forme pri raschete tonkih plastin. Vestnik Volgograd. gos. arhit.-stroit. akad. Seriya: Estestvennye nauki, 2, 251–255.
  6. Zaporozhets, E. V., Zaporozhets, V. B., Frolova, L. V. (2002). Nekotorye osobennosti rascheta balochnyh plastin i balok pri bol'shih progibah. Visnyk Prydnipr. derzh. akad. bud-va ta arkhit., 6, 22–27.
  7. Ignat’ev, A. V., Ignat’ev, V. A., Gamzatova, E. A. (2018). Analysis of thin plates with excluding the displacements of the finite element as an absolutely rigid body by the fem in the form of a classical mixed method. News of higher educational institutions. Construction, 3, 5–13. Available at: http://izvuzstr.sibstrin.ru/uploads/vorotnikov/%E2%84%96-03-(2018).pdf
  8. Akimov, P. A., Negrozov, O. A. (2016). About one sample of plate analysis based on combined application of finite element method and discrete-continual finite element method. International Journal for Computational Civil and Structural Engineering, 12 (2), 14–41.
  9. Akimov, P. A., Mozgaleva, M. L., Sidorov, V. N., Mojtaba Aslami, Negrozov, O. A. (2014). Advanced wavelet-based discrete-continual finite element method for local plate analysis. International Journal for Computational Civil and Structural Engineering, 10 (2), 47–55.
  10. Timoshenko, S., Woinowsky-Krieger, S. (1966). Theory of Plates and Shells. Moscow: Nauka, 636. Available at: http://books.totalarch.com/theory_of_plates_and_shells_timoshenko
  11. Rektoris, K. (1985). Variatsionnye metody v matematicheskoy fizike i tehnike. Moscow: Mir, 590.
  12. Manuylov, G. A. (2017). The approximate solution for plates using modified rayleigh-ritz method. International Journal for Computational Civil and Structural Engineering, 13 (4), 121–127. doi: https://doi.org/10.22337/2587-9618-2017-13-4-121-127
  13. Pradhan, K. K., Chakraverty, S. (2015). Static analysis of functionally graded thin rectangular plates with various boundary supports. Archives of Civil and Mechanical Engineering, 15 (3), 721–734. doi: https://doi.org/10.1016/j.acme.2014.09.008
  14. Galerkin, B. G. (1953). Sobranie sochineniy. Vol. 2. Moscow: Izd-vo AN SSSR, 440.
  15. Vaynberg, D. V., Vaynberg, E. D. (1959). Plastiny, diski, balki-stenki (prochnost', ustoychivost' i kolebaniya). Kyiv: Gos. izd-vo l-ry po stroitel'stvu i arhitekture USSR, 1049.
  16. Konchkovskiy, Z. (1984). Plity. Staticheskie raschety. Moscow: Stroyizdat, 480.
  17. Vlasova, E. V. (2003). Metody rascheta pryamougol'nyh plastin pri izgibe sosredotochennymi silami. Moscow: Ros. gos. otkr. meh. un-t putey soobshcheniya, 116.
  18. Kozhushko, V. P., Krasnov, S. N., Berezhnaya, K. V. (2019). Flexible clamped plates with rig, installed under its center. Naukovyi visnyk budivnytstva, 98 (4), 314–318.
  19. Kozhushko, V. P. (2016). Raschet gibkoy plity, odna storona kotoroy zashchemlena, a protivopolozhnaya ee gran' opiraetsya na stoyki. Avtomobil'nye dorogi i mosty, 1 (17), 62–66.
  20. Kozhushko, V. (2015). Flexible plate one side of which is restrained and the opposite one rests on two legs set at the corner points. Vestnik Har'kovskogo natsional'nogo avtomobil'no-dorozhnogo universiteta, 71, 54–58. Available at: http://nbuv.gov.ua/UJRN/vhad_2015_71_11

Downloads

Published

2020-10-31

How to Cite

Kozhusko, V., Krasnov, S., Berezhna, K., Oksak, S., & Smolyanyuk, R. (2020). Patterns in the distribution capacity of thin plates under different condition for their resting on supports. Eastern-European Journal of Enterprise Technologies, 5(7 (107), 37–44. https://doi.org/10.15587/1729-4061.2020.213776

Issue

Vol. 5 No. 7 (107) (2020): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2020 Vitaly Kozhusko, Sergey Krasnov, Kateryna Berezhna, Serhii Oksak, Roman Smolyanyuk

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.