Analytical modelling of perforated geometrical domains by the R-functions

    Yuriy Semerich   Affiliation


This paper deals with the construction of boundary equations for geometric domains with perforation. Different types of perforated geometric domains are considered. The R-functions method for analytical modelling of perforated geometrical domains is used. For all constructed equations, function plots are obtained.

Keyword : perforated domain, R-functions, R-operations, boundary equation of domain

How to Cite
Semerich, Y. (2020). Analytical modelling of perforated geometrical domains by the R-functions. Mathematical Modelling and Analysis, 25(3), 490-504.
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Jul 8, 2020
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F. Bauer and E.L. Reiss. Stresses in a perforated cylindrical shell. International Journal of Solids and Structures, 2(2):141–156, 1966.

E.I. Grigolyuk and L.A. Filshtinsky. Perforated plates and shells. Nauka, Moscow (in Russian), 1970.

C. Kingery, R. Pearson and G. Coulter. Shock wave attenuation by perforated plates with various hole sizes. In USA Ballistic Research Laboratory(Ed.), BRL Memorandum report No 2757, p. 71, Maryland 21005, 1977. Aberdeen Proving Ground.

V.L. Rvachev. Theory of R-functions and some applications. Naukova Dumka, Kiev (in Russian), 1982.

V.L. Rvachev and T.I. Sheiko. R-functions in boundary value problems in mechanics. Applied Mechanics Reviews, 48(4):151–188, 1995.

Yu.S. Semerich. The R-functions method in boundary value problem for complex domain possessing symmetry. In Abstracts of the Seventh International Conference Mathematical Modelling and Analysis MMA2002, p. 55. Kaariku, Estonia, May 31-June 2, 2002, 2002.

Yu.S. Semerich. The R-functions method in the boundary value problem for a complex domain possessing the symmetry. Mathematical modelling and analysis, 8(1):77–86, 2003.

Yu.S. Semerich. The construction of loci with a cyclical symmetry by the R-functions. Mathematical modelling and analysis, 10(1):73–82, 2005.

H. Weyl. Symmetry. Princeton University Press, Princeton, New Jersey, 1952.