To the Study of the State of the System of Multiple Galleries under the Effect of Normal and Shear Stresses

Authors

  • Telyatnikov I.S. Southern Scientific Center of Russian Academy of Science, Rostov-on-Don, Russian Federation

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-17-1-1-42-48

Abstract

The method for studying the boundary value problems modeling multilayer structures with multiple interlayer bulkheads, developed in the works of scientists of the SSC RAS and KubSU, is generalized in this paper to the vector case of a general spatial problem.A complementary approach is presented, allowing analyzing the result of vertical and shearing effectson partitionsof ore formation. As a substrate and a coating layer, we consider homogeneous elastic layers that possess the same physical and mechanical properties but have different thicknesses.The boundary of the coating layer is considered free of stress. Linear static equations for the Kirchhoff plate system are used to describethe state of the ore formation. The block element method used in the work allowed us to reduce the boundary value problem for two elastic layers separated by a plate with a set of parallel linear holes to a system of integral equations of the Fredholm type solvableby the integral factorization method. The described approach can be applied to the study of different-sized block structures on other scales.

Keywords:

multilayer structure, Kirchhoff plates, normal and shear stresses, block element method, system of integral equations, integral factorization method

Acknowledgement

Отдельные фрагменты работы выполнены в рамках ГЗ ЮНЦ РАН, проект № 01201354241 и при частичной поддержке РФФИ (проекты 18-05-80008, 18-01-00124).

Author Info

Ilya S. Telyatnikov

канд. физ.-мат. наук, научный сотрудник лаборатории математики и механики Южного научного центра РАН

e-mail: ilux_t@list.ru

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Issue

2020. Vol. 17. No. 1. Part 1

Section

Mechanics

Pages

42-48

Submitted

2020-03-18

Published

2020-03-31

How to Cite

Telyatnikov I.S. To the Study of the State of the System of Multiple Galleries under the Effect of Normal and Shear Stresses. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 1, pp. 42-48. DOI: https://doi.org/10.31429/vestnik-17-1-1-42-48 (In Russian)

Copyright (c) 2020 Telyatnikov I.S.

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