Dynamic analysis of cracks using the SGBEM for elastodynamics in the Laplace-space frequency domain

Dynamic analysis of a system can be carried out either in the time or frequency domains. Time responses/histories of this system may be directly obtained using time-domain formulations. In the frequency domain, analysis can be performed in either the Fourier or Laplace spaces. The symmetric-Galerkin boundary element method (SGBEM) for 2-D elastodynamics in the Fourier-space frequency domain has been previously reported in the literature. In this paper, the SGBEM for elastodynamics in the Laplace-space frequency domain using the standard continuous quadratic element and its application to dynamic analysis of cracks is presented for the first time. The technique developed is employed together with the fast Laplace inverse transform by Durbin to obtain time-dependent results for several typical examples including both crack and non-crack problems. These results are highly accurate when compared to those obtained from other numerical techniques. It is shown in this work that the very same boundary element code can be utilized to perform frequency domain analysis in either the Fourier or Laplace spaces. However, if time responses are required, the accuracy and computational effectiveness of the analysis may depend on the type of space selected as it determines the type of transforms (inverse Fourier/Laplace transforms) needed for converting frequency solutions to the desired time responses.