A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics

Abstract

The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM.

Keywords

• time-space coordinate system
• time domain boundary element method (TD-BEM)
• Kutt’s quadrature
• time-space integration domain
• singular integrals