Investigating a problem from the theory of elasticity for a half-space with cylindrical cavities for which boundary conditions of contact type are assigned

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.139567

Keywords:

cylindrical cavities in half-space, Lame's equation, generalized Fourier method, infinite systems of linear algebraic equations

Abstract

When designing spatial structures, it is necessary to know the stressed-strained state of a body. These problems include the calculation schemes, in which there is a half-space with cylindrical cavities, at the boundaries of which the contact type conditions are assigned. The segment of such problems is not enough researched and requires further attention.

The analytical and numerical algorithm for solving a special problem of the theory of elasticity for a half-space with cylindrical cavities was proposed in this paper. Radial displacements and tangential stresses are assigned at the boundaries of cavities, and one of the two types of the boundary conditions – displacement or stress – is assigned at the half-space boundary. Calculations revealed the stressed-strained state of the half-space.

Under the fixed geometrical conditions, a numerical analysis of the three variants of the problem, when displacements are assigned at the half-space boundary, and of the tree variants of the problem, when stresses are assigned at the half-space boundary, was conducted. A comparative analysis of the variants with different boundary conditions was carried out.

It was found that at the boundary conditions of the contact type, assigned at the boundaries of cylindrical cavities, if the assigned displacement function and the assigned function of stresses are the same, the boundary conditions at the half-space boundary in the form of stresses have more influence of the stressed state that boundary conditions in the form of displacements. It was also established that at different kinds of the assigned boundary conditions (stresses or displacements), stresses o and  on the surface of applying such conditions change for the opposite, that is, from stretching to compressing and vice versa.

The presented analysis can be used during designing the structures, in the calculation schemes of which there is a half-space boundary with boundary conditions of the contact type, assigned on it, and cylindrical cavities, on the surfaces of which displacements and stresses are assigned.

Author Biographies

Vladimir Protsenko, N. E. Zhukovsky National Aerospace University "Kharkiv Aviation Institute" Chkalovа str., 17, Kharkiv, Ukraine, 61070

Doctor of Physical and Mathematical Sciences, Professor

Department of Mathematics and Systems Analysis

Vitaly Miroshnikov, Kharkiv National University of Construction and Architecture Sumska str., 40, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of Construction Mechanics

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Published

2018-07-27

How to Cite

Protsenko, V., & Miroshnikov, V. (2018). Investigating a problem from the theory of elasticity for a half-space with cylindrical cavities for which boundary conditions of contact type are assigned. Eastern-European Journal of Enterprise Technologies, 4(7 (94), 43–50. https://doi.org/10.15587/1729-4061.2018.139567

Issue

Vol. 4 No. 7 (94) (2018): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2018 Vladimir Protsenko, Vitaly Miroshnikov

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