Dynamic Stress Concentration of a Cylindrical Cavity in Half-Plane Excited by Standing Goodier-Bishop Stress Wave

Abstract

AbstractBased on expansion technique, the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied in the paper. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by a series expansion, and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity. As a consequence, the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. The numerical technique based on the steepest descent method is used to calculate the integral representation of potential functions in wave-number domain. Numerical results for the dynamic hoop stresses around the wall of the cavity and the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.