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Information × Registration Number 0226U002413, (0123U100016) , R & D reports Title Development of mathematical models and numerical analytical methods for solving applied problems of modern industry popup.stage_title Розробка математичних моделей та чисельно-аналітичних методів для розв'язання прикладних задач сучасної промисловості Head Kagadiy Tatyana Stanislavovna, д.ф.-м.н. Registration Date 24-02-2026 Organization National Technical University Dnipro Polytechnic popup.description1 The elaborating of effectiv numerical and analytical methods, construction of mathematical models, for dioagnostic of the complicated mining and engineering problems. popup.description2 Mathematical models have been constructed that allow the application of new numerical-analytical methods, or the generalization of certain approaches to solving the problem. The dynamic interaction of a curvilinear orthotropic half-space and an inclusion has been studied. An effective asymptotic method is applied, the distribution of contact forces in the matrix and the forces in the rod are found. As for the flat case, the boundary value problem is reduced to the sequential solution of potential theory problems (the basic functions are found from Laplace's equations). Boundary conditions are formulated for each type of stress state. It is shown that, without taking into account inertial forces, the forces in the stringer do not depend on time (quasi-static calculation). A number of limit transitions are performed, connecting the dynamic and static formulation of the problem. Based on the boundary element method, a numerical algorithm for determining the stress-strain state in an inhomogeneous mass consisting of two linear-elastic subregions has been developed. The obtained algorithm is applied for the modeling of mineral mining processes based on the analysis of the stress- strain state of the rock massif around the high extraction chambers. Different stages of working out the ore reserves have been studied. As a result of the numerical investigation, the main areas of stress concentration in the ore massif and the filling massif were established, the empirical dеpendence of the "equivalent" stresses on the distance to the chamber contour were obtained, and the equirements for the strength of the filling material were formulated depending on the working out depth. An analysis of soil stability was carried out based on the proposed modified strength criterion The research is aimed at improving methods for predicting landslide processes, as well as developing approaches to integrating laboratory data into numerical models to increase their accuracy. Product Description popup.authors Dmytro V. Babets Olena O. Sdvyzhkova Svitlana Y. Tymchenko Yurii M. Holovko Yuliia B. Olevska Dina V. Klimenko Vira V. Prykhodko Nataliia P. Ulanova Anna H. Shporta popup.nrat_date 2026-02-24 Close