A new look at 2-D time-domain elastodynamic Green''s functions for general anisotropic solids

2-D time-domain elastodynamic displacement Green's functions for general anisotropic solids are obtained by a new method. This method is based on the use of a cosine transform with respect to time and exponential Fourier transforms with respect to both spatial coordinates. By use of a change of variables and the homogeneity and symmetry of the problem, the inverse transforms are reduced to an integral which can be evaluated by a simple use of redidue calculus. The solutions are expressed in terms of three wave fields. The field inside a wavefront corresponds to a complex root of a polynomial of order six with real coefficients. A simple relation between the spatial and time derivatives is found, and is used to reduce the corresponding stresses to a form that is directly applicable to the boundary element method. Numerical implementations are explained in some detail and are demonstrated by three examples.