Homogeneous problems of elasticity theory for different boundary conditions in the region of the angular cut of the boundary

Abstract

Mathematical modeling of structures as complicated technical systems includes development of an experimental calculation method of problem solving for areas having different variants of structural shaping (special lines and points, e.g., reentering angles). The notion of stress concentration in an irregular point of the area boundary is losing its sense. Infinite stress and strain are determined in the area of the angular cut of the boundary as solution of homogeneous boundary problems. The singularity of a problem solution depends upon the type of homogeneous boundary conditions, mechanical specifications of the areas, apex angles of the boundary cut. The studies of power-mode strain and stress get especially vital during studies of the stress of multi-part structures in the areas of conjunction of elements made of materials with different mechanical properties in forced deflected mode with ruptural deformation along the contact line (surface) of the elements. The present paper reports on statements of homogeneous boundary problems for different types of homogeneous boundary conditions for a flat wedge-shaped area. A system determinant for determining of proper values is indicated, as well as proprietary solutions of the problem for different variants of the component areas of the wedge, mechanical properties and the cutout opening of the areas boundary.