Dynamics-based analytical solutions to singular integrals for elastodynamics by time domain boundary element method

The singularities in 2-D time domain boundary element (TD-BEM) formulation for elastodynamics are divided into three categories: the wave front singularity, the space singularity and the dual singularity. A fully analytical procedure for dealing with the three singularities is proposed by adopting the concept of the finite part of an integral (Hadamard principle integral). In order to reduce the computation time, the conventional numerical procedure is adopted for the non-singular integrals in 2-D TD-BEM formulation. Therefore, the algorithm including the fully analytical procedure for dealing with singular integrals and the numerical procedure for dealing with non-singular integrals is implemented in this study. Two examples, 1-D rod and 2-D cavity representing the problems for the finite domain and the infinite domain respectively, are chosen to verify the effectiveness of the proposed algorithm. It shows that the results obtained from the proposed algorithm agree with the analytical solutions with good accuracy, indicating that the proposed algorithm is applicable for elastodynamics in both finite and infinite domains.