Open AccessOn problem of determining the stress state of elasto-plastic compressible area weakened by ellipsoidal cavity
Author(s) -
А. Н. Максимов,
E A Derevyannykh,
T. V. Mitrofanova,
Nadezhda Belova,
Yuriy Konstantinov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1889/4/042050
Subject(s) - ellipsoid , dimensionless quantity , stress field , stress (linguistics) , compressibility , mechanics , coordinate system , boundary (topology) , perpendicular , mathematical analysis , mathematics , geometry , classical mechanics , physics , thermodynamics , finite element method , linguistics , philosophy , astronomy
The work is one of the stages of solving the problem of determining the stress state for a compressible mass weakened by cavities. In the problem statement, there is no pressure inside the cavity, and mutually perpendicular forces are applied at infinity. The problem is solved by the small parameter method, in a spherical coordinate system, in dimensionless length units. The previously found values are taken as the known stress components in the zero approximation in the elastic area and as the perturbed stress components in the plastic area. Using the conjugation of stresses at the boundary of elasto-plastic zone, the stress components for the elastic area are determined in the first approximation. The obtained results can be used in the field of mining, construction mechanics and other related fields.