International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The paper stress-strain state of the homogeneous isotropic body bounded by coordinate lines of the parabolic coordinate system is studied, when on parabolic border normal or tangential stress is given. Analytical solution is obtained by the method of separation of variables. Using the MATLAB software, the numerical results are obtained of some specific problems and relevant graphs are presented.

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.

The strength of a sufficiently long thick-walled homogeneous isotropic circular tube (cylinder) under the action of external forces is studied using the problems of elasticity statics. In particular, there are established the minimum thickness of pipes with different materials and with different diameters, for which do not exceed the permissible stresses values. Cylinder is in state of plane deformation, therefore are considered a two-dimensional boundary value problems for circular ring. Represented tables and graphs of minimum thickness of a circular ring when a) the normal constant stresses act at internal border, while the outer boundary is free of stresses and b) the normal constant stresses act at external border, while the inner boundary is free of stresses. To the numerical realization above mentioned problems are used solutions obtained by two means: the analytical solution obtained by method of separation of variables, and Lame’s solution.