Three-Dimensional Dynamic Problems for an Elastic Body Containing a Shallow Crack

Abstract

By combining the methods of boundary integral equations and small parameter, we solve a three-dimensional problem of low-frequency harmonic loading of the surfaces of a shallow crack in an infinite elastic body. The functions of crack opening displacements and the stress intensity factors are obtained in the form of double convergent power series in the wave number and in a geometric parameter characterizing the curvature of the crack. We study the influence of inertial terms on the level of stresses in the vicinity of spheroidal cracks with various values of eccentricity under the action of uniform dynamic pressure with constant amplitude.