Stress concentration around cavity in elastic half-space

Abstract

This paper presents an analytical method for studying stress concentration around slit like cavities. The method is based on the assumption that the influence of the cavity on the redistribution of internal forces can be modeled by including fictitious forces in the solution. To determine the stress-strain state, additional forces acting on the cavity surface are used. The magnitude of these forces is chosen on the basis of the value of stress tensor flow through the examined surfaces limiting the cavity volume. In calculating surface integrals, we use the replacement of the expressions for the stress tensor components by the polynomials of a low degree. Research of stress-strain state for the most general three-dimensional case is done; an elastic half-space with a cavity in the form of a «thin» rectangular parallelepiped under the action of a concentrated force applied to a free surface is considered. The obtained results are comprehensively compared with the solution of a similar problem by the finite element method. In addition, the stress concentration in the vicinity of the cavity in the form of a quadrangular pyramid is investigated, while the base of the pyramid coincides with the face of the cubic cavity. Distributions of the stress tensor components in the vicinity of these cavities are constructed. The solution used for the half-space gives acceptable results at the points located near the base of these cavities. The estimation of accuracy and efficiency of the proposed calculation model is made, the applicability boundary of the proposed solution is determined. Possible ways of improving the calculation method are given. It therefore seems promising to use the resource of structural materials advantageously. That is, creating a cavity system of the required shape and size in the bodies, one can reduce stresses at critical points, thereby increasing the strength of the product. Similar technique can be applied to redistribute stresses in the volume of the structure in order to level the bearing capacity of the material.