The stress intensity factors in the corner cut-out area of the plane domain boundary

The increase of reliability and the robustness of structures and constructions with complex form boundary causing a singularity of the stress-strain state is the urgent task of engineering practice. The stress-strain state of structures and constructions with geometrically nonlinear shape borders (cuts and cutouts) is characterized by the occurrence of the stress concentration areas, as well as deformations with significant gradients and values. The practical relevance of the research is represented by the study of the stress state of composite constructions in the areas of conjugation of the elements made of materials with different mechanical properties under the action of forced deformations discontinuous along the contact line (surface) of the elements. The solution of the physically linear elasticity problem with a geometrically linearized formulation of boundary conditions is determined by infinite stresses and stress gradients at the vertex of the ideal cut or the corner cutout of the domain boundary. The concept of stress concentration at a singular point of the domain boundary becomes meaningless. The stress distribution in the neighborhood of the vertex of the boundary cut is determined by the intensity factors. In this paper, we consider the stress-strain state at the vertex of the corner cutout of the plane domain boundary; as in the case of an ideal theoretical cut, it is written using intensity factors. The output of expressions for stresses, deformations, and displacements in the neighborhood of the singular point of the plane domain boundary by means of the intensity factors determines the novelty of the obtained results. The stresses for the case of an ideal cut-out (cut) are defined as a particular case of the general expressions for the stress-strain state in the neighborhood of the corner cut-out of the plane domain boundary obtained by means of the intensity factors.