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

Xiaofei Qin, Youhua Fan, Hongjun Li and Weidong Lei
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Xiaofei Qin: School of Science, Harbin Institute of Technology, Shenzhen 518055, China
Youhua Fan: School of Science, Harbin Institute of Technology, Shenzhen 518055, China
Hongjun Li: Urban and Rural Construction Institute, Hebei Agricultural University, Baoding 071001, China
Weidong Lei: School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China

Mathematics, 2022, vol. 10, issue 2, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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