A DR-BEM approach for analyzing the transient SH-wave scattering problems: A comparative study

In this paper, a new approach was presented for the transient analysis of SH-wave scattering problems by the dual reciprocity boundary element method (DR-BEM). In the use of static fundamental solutions and the concept of estimator functions, the effect of domain inertia integrals was applied in the boundary integral equations (BIEs). Then, the solvable form of the BIE was obtained by adding the free-field displacement to satisfy the stress-free boundary conditions on the surface. By implementing the formulation in a time-domain computer code, the accuracy and efficiency of the approach were evaluated by solving different examples including the embedded circular cavity, the semi-circular valley, and the twin hump hill subjected to obliquely propagating incident SH-wave. In this regard, a comprehensive comparative study was carried out with the half-space time-domain BEM (TD-BEM), previously presented by the corresponding author, to observe the accuracy of the results as well as the analysis time. The results showed that although the presented method had more complex models compared to the half-space TD-BEM, the analysis time was significantly reduced with the use of a simple formulation. This approach can be applied to prepare half-space models in the field of geotechnical earthquake engineering in substituting other time-consuming methods.