On solution of the first and second boundary problems dynamic elasticity theory of steady oscillations of half-space with elliptical cracks by biem

Abstract

The three-dimensional dynamic problem of elastic half-space with a plane elliptical crack is
considered. The cracks surface are under time-stationary discontinuous loads. Cases of free and
clamped half-space surfaces is considered. The problem is solved by boundary integral equations
(BIE) method. Using the Helmholtz potential, the problem is reduced to one BIE relatively
unknown crack opening function. With the solutions of the problem are obtained depending on the
dynamic stress intensity factors at different points of the contour of the defect on the frequency of
the applied load, the eccentricity of the ellipse, the depth of the cracks and the type of boundary
conditions on the half-space surface.