Open AccessCAUCHY PROMLEMS IN GEOMECHANICS
Author(s) -
В. Е. Миренков
Publication year - 2019
Publication title -
interèkspo geo-sibirʹ
Language(s) - English
Resource type - Journals
ISSN - 2618-981X
DOI - 10.33764/2618-981x-2019-2-4-176-181
Subject(s) - boundary value problem , cauchy distribution , mathematics , initial value problem , cauchy problem , geomechanics , plane (geometry) , field (mathematics) , class (philosophy) , stress field , cauchy stress tensor , plane stress , relaxation (psychology) , boundary (topology) , mathematical analysis , geometry , computer science , physics , finite element method , pure mathematics , geology , geotechnical engineering , social psychology , psychology , artificial intelligence , thermodynamics
Proposal about linear stress field of virgin solid and necessity for calculation stress-strain behavior near workings at actual mining cause to development analytical and numerical methods of the calculations. One-dimensional, two-dimensional and three-dimensional models of solids with relaxations, which are placed to the class of Couchy problems, for which Cauchy initial data are formulated, has been occurred. It is related to the fact that in rock mechanics plane with relaxation or space with cavity, for which there are infinitely remote points, are considered. There are known solutions, when boundary conditions represented by constants, determined by initial stress field adopted for concrete solid, are formulated on the infinity. In condition of numerical calculation, the software usually gives some result, accuracy of which does not control. Worldwide scientific schools represent same results which are in antimony with theory of equals of mathematical physics, which have outlined class of Cauchy problems for that with cancelled out boundary condition on the infinity. In the work, problems of rock mechanics for the plane relaxed with random holes are considered. The necessity to carry out points of the theory is proved. Method of solving of such problem class based on getting so-called additional solution formulated in class of Cauchy problem is proposed.