Cavity In Elastic Half-space Research Articles

Stress concentration around cavity in elastic half-space

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.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.