# MATHEMATICAL AND NUMERICAL SIMULATION OF STRESSES AND DISPLACEMENTS LOCALIZATION PROBLEMS

• 1 I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University, Georgia

## Abstract

Mathematical and numerical simulation of the non-classical problems, namely problems of localization of stresses and displacements in the elastic body, are obtained by the boundary element method. The current work examines two localization problems, which have the following physical sense: on the middle point of the segment lying inside a body parallel to the border half plane in first case a point force is applied, and we must find such value of the normal stress along the section of the border half plane, which will cause this point force, while in the second case, there is given a vertical narrow deep trench outgoing of this point, and we must find such value of the normal stress along the section of the border half plane, which will result in such a pit. By using MATLAB software, the numerical results are obtained and corresponding graphs are constructed.

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