2D and 3D dynamic Green's functions and time-domain BIE formulations for piezoelectric solids

Time transient 2D and 3D Green's functions for linear piezoelectric solids of general anisotropy are derived using Randon transform. Time-harmonic and Laplace transformed dynamic Green's functions are obtained by subsequent application of Fourier and Laplace transforms. The Green's functions are expressed as a summation of a singular static term and a regular dynamic term. The singular static terms correspond to the static Green's functions. The regular dynamic terms are given as integrals over a unit sphere for the 3D cases and a unit circle for the 2D cases. Time-domain boundary integral equation formulations are presented, where a regulation procedure of the hypersingular integrals is developed for the analysis of cracks.