Open AccessLeibenzon-Ishlinsky Criterion for the Axisymmetric Problem of Compression of the Pillar
Author(s) -
А. И. Чанышев,
И. М. Абдулин,
O. E. Belousova,
L. L. Efimenko,
И. В. Фролова
Publication year - 2021
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/666/3/032067
Subject(s) - pillar , mathematics , anisotropy , geometry , rotational symmetry , mathematical analysis , isotropy , surface (topology) , radius , boundary value problem , deformation (meteorology) , structural engineering , materials science , physics , engineering , computer science , composite material , computer security , quantum mechanics
In the framework of the Leibenzon-Ishlinsky approach, the problem of the loss of stability of a pillar of a cylindrical mine working is solved. The pillar material was assumed with an initial anisotropy corresponding to the layered structure. A criterion for loss of stability is being constructed, a solution to the system of differential equations of the problem in the form of combinations of cylindrical and trigonometric functions is determined. From the fact that the determinant of a system of homogeneous algebraic equations is equal to zero, the critical load value is found at which, along with the main continuation of the deformation of the pillar, something else is possible with a changed surface geometry. The influence of the initial anisotropy, the parameters of the pillar (height, radius) on the values of the ultimate load is investigated.