Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle

A method is proposed to study the stress concentration around a shallow spheroidal crack in an infinite elastic body. The stress concentration is due to the diffraction of a low-frequency plane longitudinal wave by the crack. The direction of wave propagation is established in which the combined concentration of mode I and mode II stresses is maximum __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 70–77, January 2006.     

Boundary-integral formulation of dynamic nonstationary problems for an elastic space with a mathematical cut along a nonclosed Lyapunov surface

By satisfying the boundary conditions on the discontinuity surfaces using specially constructed integral representations of the solutions, we obtain a system of boundary integral equations for the functions of the opening of the cut.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 158–161.     

Boundary-integral formulation of three-dimensional problems of steady vibrations of an infinite body with a crack located on an open Lyapunov surface

We construct integral representations of the solutions of three-dimensional problems in the form of a combination of Helmholtz potentials [1] whose coefficients are determined in terms of the geometric parameters of the crack. By satisfying the boundary conditions we obtain two-dimensional integral equations in the displacement jumps on the opposite surfaces of the crack when it is loaded by harmonic forces. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 59–63.     

The interaction of coplanar cracks in an infinite body caused by steady external loads

We study the interaction of coplanar cracks in an infinite body such that the surfaces of the cracks are loaded with tensile and shear strains that vary harmonically with time. We give the graphs of the dependence of coefficients of intensity of the stresses on the frequency of oscillations of the external load in a wide range of variation. Five figures. Bibliography: 2 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 45–50.     

Opening-Function Simulation of the Three-Dimensional Nonstationary Interaction of Cracks in an Elastic Body

Integral relations between three-dimensional dynamic displacements (stresses) in an infinite elastic body with arbitrarily located plane cracks and discontinuities in the displacements of the opposite crack faces are presented. The influence of opening cracks on each other is considered in the problem on crack faces loaded by pulse forces. This problem is reduced to a system of boundary integral equations of the wave-potential type in a time domain. The dynamic mode I stress intensity factors are determined for two coplanar elliptic cracks under forces in the form of the Heaviside function     

Stress Concentration Near an Elliptic Crack in the Interface Between Elastic Bodies under Steady-State Vibrations

The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body consisting of two perfectly joined dissimilar half-spaces with an elliptic mode I crack located in one of the half-spaces normally to the interface. The problem is reduced to a boundary integral equation for the crack opening function. The integration domain of the equation is bounded by the crack domain, and the interaction between the crack and the interface is described by a regular kernel. The equation is solved using the mapping method. Numerical results are obtained for the case where the surfaces of the elliptic crack are subjected to harmonic loading with constant amplitude. The dependences of the stress intensity factors on the wave number are presented for various relationships among the mechanical constants that ensure the absence of near-surface waves