Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions

Authors

  • Anatolii Alpatov
  • Victor Kravets
  • Dmytro Kolosov
  • Volodymyr Kravets
  • Erik Lapkhanov Institute of Technical Mechanics NASU and SSAU

DOI:

https://doi.org/10.14738/tmlai.96.11295

Abstract

The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.

References

. Sedov L. I. Metody podobiya i razmernostey v mechanike [Similarity and Dimensional Methods in Mechanics], M:Nauka. 1987. 448 p. (in Russian).

. Alabyzhev P. M., Geronimus V. B., Minkevich L. M. Teoriya podobiya i razmernostey. Modelirovaniye [Similarity and dimension theory. Modeling ]. M., Vyshaya Shkola. 1968. 208 p. (in Russian).

. Venikov V. A. Teoriya podobiya i modelirovaniya [Similarity and modeling theory]. M., Vyshaya Shkola. 1976. 480 p. (in Russian).

. Polchevskyi B. O. Doslidzhenia tehnologichnyh system ( modelyvannia, proektyvannia, optimizaciya) [Research of technological systems (modeling, design, optimization)]. Navch. Posibnyk, Lviv, Svit. 2001. 238 p. (in Ukrainian).

. Kepych T. Yu, Kutsenko O. T. Osnovy teorii podibnosti ta analizy rozmirnostey ta ih zastosyvannia v zadachah mechaniky [Fundamentals of similarity theory and dimensional analysis and their application in the problems of mechanics]. Navch. Posibnyk. K. 2004. 101 p. (in Ukrainian)

. Ivanov I. E., Ereshenko V. E. Metody podobiya fizicheskih processov. Uchebnoye posobiye [Methods for the similarity of physical processes. Tutorial]. M., MADI. 2015. 144 p. (in Russian)

. Sedov L. I. Ploskie zadachi hidrodinamiki i aerodinamiki [Plane problems of hydrodynamics and aerodynamics]. M., Nauka. 1966. 443 p. (in Russian)

. Bazarov I. P. Termodinamika [Thermodynamics]. ]. M., Nauka. 1983. 376 p. (in Russian)

. Pavlovskij, M.A., Teoretichna mexanika [Theoretical mechanics], Kyiv, Technika Publ., 2002, 512 p. (in Ukrainian).

. Volmyr A. S. Ustoichivost deformiruemyh system [Stability of deformable systems]. M., Nauka. 1967. 984 p. (in Russian).

. Korn, G., Korn, T., Spravochnik po matematike dlya nauchnyh rabotnikov i inzhenerov [Mathematical Handbook for Scientists and Engineers], Moscow, Nauka Publ., 1984, 832 p. (in Russian).

. Lur’e A. I. Analitical mechanics. Springer Science & Business Media. 2002. 824 p.

. Ventsel E. S. Issledovaniye operaciy: zadachi, principy, metodologiya [Operations Research: Objectives, Principles, Methodology]. M., Nauka. 1988. 208 p. (in Russian)

. Kravets, V. V., Kravets, Vl. V., Burov, O. V., Reliability of Systems. Part 1. Statics of Failures. Lap Lambert Academic Publishing, Omni Scriptum GmbH&Co. KG. 2016. 93 p. ISBN: 978-3-659-83413-4.

. Kravets, V., Kravets, T., Burov, O., Monomial (1, 0, -1)-matrices-(4х4). Part 1. Application to the transfer in space.Lap Lambert Academic Publishing, Omni Scriptum GmbH&Co. KG., 2016, 137 p. ISBN: 978-3-330-01784-9.

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Published

2021-12-06

How to Cite

Alpatov, A., Kravets, V. ., Kolosov, D., Kravets, V., & Lapkhanov, E. (2021). Algorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions . Transactions on Engineering and Computing Sciences, 9(6), 38–43. https://doi.org/10.14738/tmlai.96.11295