# Cylindrical pillar instability beyond elasticity limit

In the article, the problem on instability of cylindrical pillars under compression is solved. It is assumed that pillars can experience elastic and plastic strains, as well as strains beyond the elastic limit, when the resistance drops with increasing strains. The analysis focuses only on a barreling-type instability, when pillars are heaved in the middle more than at the top and bottom. The problem is solved in the formulation by Leibenson–Ishlinsky, with assumption of a new equilibrium condition of the structure, which is infinitely close to the normal state but with distorted geometry. It is intended to determine the moment of the barrel distortion initiation, i.e., it is required to estimate the critical load such that barrel distortion takes place in the elastic state, in the plastic state or in the post-limit deformation. The problem is solved using equations of deformable solid mechanics in axial symmetry. The inelastic deformation equations are formulated. It also assumed that loading is continuous at the moment of instability—F. Shenley’s hypothesis. The general solution is obtained for the system of equations for additional displacements at the moment of instability in axial symmetry. The solution is written as rows of cylindrical functions. The conditions of one half-wave along generatrix of a pillar are defined. At the fulfilled boundary conditions in the problem, the system of two linearly uniform equations with the zero determinant is constructed. The expression of the critical load as function of the initial condition and relative dimension of a pillar is found. The most realistic values of loads belong to the descending branch of the deformation curve. The influence of the decline modulus on the values of relative dimension of pillars is determined. Poisson’s ratio has a minor effect on the critical values, too.

Keywords: stability, continuous loading, plasticity, post-limit deformation, cylindrical functions of argument of complex number.
For citation:

Chanyshev A. I., Abdulin I. M., Belousova O. E. Cylindrical pillar instability beyond elasticity limit. MIAB. Mining Inf. Anal. Bull. 2021;(3):101-113. [In Russ]. DOI: 10.25018/0236-1493-2021-3-0-101-113.

Acknowledgements:

The work was carried out within framework of the state task of Ministry of Science and Higher Education of Russian Federation, Theme No. AAAAA17-117121140065-7.

Issue number: 3
Year: 2021
Page number: 101-113
ISBN: 0236-1493
UDK: 539.3
DOI: 10.25018/0236-1493-2021-3-0-101-113
Article receipt date: 28.10.2020
Date of review receipt: 14.12.2020
Date of the editorial board′s decision on the article′s publishing: 10.02.2021

A.I. Chanyshev1, Dr. Sci. (Phys. Mathem.), Professor, Chief Researcher, Novosibirsk State University of Economics and Management, 630099, Novosibirsk, Russia, e-mail: a.i.chanyshev@gmail.com,
I.M. Abdulin1, Researcher,
O.E. Belousova1, Cand. Sci. (Eng.), Assistant Professor, Senior Researcher,
1 Chinakal Institute of Mining Siberian Branch, Russian Academy of Sciences, 630091, Novosibirsk, Russia.

For contacts:

A.I. Chanyshev, e-mail: a.i.chanyshev@gmail.com.

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