Stress-strain state of an elastic half-space with a cavity of arbitrary shape

Abstract

Background: Analytical method for studying stress concentration around arbitrary shape cavity is proposed. Methods: The method is based on the assumption that it is possible to simulate the influence of cavity on the redistribution of internal forces by including fictitious forces in the solution. To determine the stress-strain state, additional forces acting on 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 cavity volume. Results: Research of stress-strain state for the most general three-dimensional case is done: an elastic halfspace with a cubic shape cavity under action of a concentrated force applied to a free surface. The obtained results are comprehensively compared with the solution of a similar problem by the finite element method. Distributions of the stress tensor components in the vicinity of these cavities are constructed. The estimation of accuracy and efficiency of the proposed calculation model is made; the boundary of applicability of the proposed solution is determined. Conclusions: It seems promising to use the resource of structural materials advantageously, namely, creating in the bodies of the cavity system the required shape and size, to obtain stress reduction at critical points, thereby increasing the strength of the product.

Solving a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized Fourier method

“…Here, I m (λρ) and K m (λρ) are the modified Bessel's functions of the 1 st and 2 nd kind, m=0, ±1, ±2,…, are the parameters of λ, µ∈(-∞, ∞). The harmonic functions for a cylinder ( 8) and ( 9) are considered in work [21], and functions (7) An elastic half-space with an infinite cylindrical cavity parallel to its boundary is a two-connected body bounded by the canonical surfaces of the Cartesian and cylindrical coordinate systems. To solve the boundary problem of the theory of elasticity regarding this elastic body, a generalized Fourier method [11] has been used.…”

“…Reducing the problems related to the theory of elasticity to integral equations, described in works [5,6], is possible purely for the specified regions. An analytical method to study the concentration of stresses around the cavity of an arbitrary form is proposed in [7]. This method involves the possibility of modeling the effect of the cavity on the redistribution of internal forces by introducing fictitious forces acting on its surface.…”