# FIRST MAIN TASK OF THE THEORY OF ELASTICITY IN THE SPACE WITH N PARALLEL CIRCULAR CYLINDRICAL CAVITIES

**J. of Mech. Eng., 2017, vol. 20, no. 4, pp. 45-52**

**DOI: **https://doi.org/10.15407/pmach2017.04.045

Journal | Journal of Mechanical Engineering |

Publisher | A. Podgorny Institute for Mechanical Engineering Problems National Academy of Science of Ukraine |

ISSN | 0131-2928 (Print), 2411-0779 (Online) |

Issue | Vol. 20, no. 4, 2017 (December) |

Pages | 45–52 |

**Author**

**V. Yu. Miroshnikov, **Kharkiv National University of Construction and Architecture (40, Sumska St., Kharkiv, 61002, Ukraine), e-mail: mivi30166@gmail.com, ORCID: 0000-0002-9491-0181

**Abstract**

A solution to the three-dimensional problem of the theory of elasticity is given for the case when stresses are set at the boundaries of parallel cylindrical cavities in an elastic space. A solution to the Lame system of equations is obtained by the generalized Fourier method in the cylindrical coordinates associated with cylinders. Infinite systems of linear algebraic equations, to which the problem is reduced, are solved by the truncation method. As a result, displacements and stresses are found in an elastic body. Numerical results are given for the case of two cylinders.

**Keywords**: cylindrical cavities in a space, Lamé equations, generalized Fourier method

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Received 31 August 2017