Cracks in three dimensions: A dynamic dual boundary element analysis

Abstract

In this paper the dual boundary integral equation for three-dimensional dynamic problems in Laplace space is presented for the first time. The dual boundary element method is used to calculate dynamic stress intensity factors for three-dimensional cracked structures. The application of Laplace transforms to the time-dependent equations of elasticity reduce the problem to a static one in Laplace space. The displacement and traction boundary integral equations for the transformed variables are established by Somigliana's identity. By applying the displacement integral equation on one of the crack surfaces and the traction boundary integral equation on the other, a general mixed-mode crack problem can be solved in a single region, in the same way as a static problem. The transformed mixed-mode stress intensity factors are calculated from the transformed displacement discontinuities near the crack tip. The dynamic stress intensity factors in the time domain are obtained by the use of Durbin's inversion method. The accuracy of this method is demonstrated by its application to embedded penny-shaped and elliptical cracks, and edge cracks.