concentrated force, elastostatics, singularity, three-dimensional problems, orb, the method of boundary state.

This article is devoted to the development of the method of boundary states into a class of problems of mechanics of a solid deformable body, including singularities of a physical nature. Many special solutions have been formed corresponding to concentrated force actions on the surface of a smooth three-dimensional body. Each special solution is included in the bases of spaces of internal and boundary states. As examples of the effectiveness of using special solutions using the boundary state method, stress-strain states of spherical bodies are constructed under the influence of concentrated forces.

Polikarpov Maxim Vladimirovich

e-mail: messiah142@gmail.com, graduate student, research assistant, Lipetsk state technical university, Lipetsk, Russia.

Penkov Viktor Borisovich

e-mail: vbpenkov@mail.ru, Dr. Sci. Phys. and Math, Professor, Lipetsk state technical university, Lipetsk, Russia.