SGBEM Analysis of Diffraction of P- and SV-Waves by a Plane Crack in an Infinite Domain

Abstract

Diffraction of elastic waves by a plane crack in an unbounded domain was investigated in this work using the symmetric Galerkin boundary element method (SGBEM) for elastodynamics in the frequency domain. The types of wave considered herein are the incident plane harmonic compressional wave (P-wave) and the incident plane harmonic shear wave (SV-wave). By using the scalar and vector potential functions of these incident waves, the wave displacement field and thereby, the wave traction field can be identified. To solve for the scattered field problem of these incoming waves on a crack in an infinite plate using the SGBEM, the crack faces were loaded with tractions equal and opposite to those produced at the same position by the incident waves. The scattering displacements and tractions found were then employed in a new boundary integral formula developed for computing the dynamic T-stress (DTS) for cracks in an infinite domain, while only the scattering displacements were needed for determining the dynamic stress intensity factors (DSIFs) by the displacement correlation technique. Numerous numerical examples were presented in this work. The SGBEM results for the DSIFs agreed very well with those obtained from using the integral transform method, and to the best knowledge of the authors, the SGBEM results for the DTS were presented for the first time in this work.