Analytical Expressions for the Singularities Treatment in the ‎Three-dimensional Elastostatic Boundary Element Method

Document Type : Research Paper

Authors
Leonardo Fellipe Prado Leite 1
Rodrigo Souza de Melo 2
Fabio Carlos Da Rocha 2
1 Department of Civil Engineering, Federal University of Sergipe, Avenida Marechal Rondon S/N, São Cristóvão, 49100-000, Brazil
2 Department of Civil Engineering, Federal University of Sergipe, Avenida Marechal Rondon S/N, São Cristóvão, 49100-000, Brazil‎
10.22055/jacm.2020.35017.2539
Abstract
The Boundary Element Method (BEM) is one of the most used numerical methods to solve engineering problems. This method has several advantages over other domain methods. However, BEM requires the use of the fundamental solution of the integral formulation that governs the problem under analysis. Furthermore, these fundamental solutions present, in their majority, singular and hyper-singular terms that impair the stability of the numerical solution when the source point is in the element to be integrated. In order to regularize unstable kernels present in the BEM's three-dimensional elastostatic formulation, the present work develops expressions, in Laurent's series, for treatment of the singularity. The precision of the developed expressions is verified on a standard curved triangular element. The results show excellent efficiency in the regularization of singular and hyper-singular kernels for the problem under analysis.
Keywords
Singular kernels
Hyper-singular kernels
Boundary Element Methods
Singularity subtraction technique
Laurent's series‎
Subjects
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Journal of Applied and Computational Mechanics
Volume 7, Issue 2
Spring 2021
Pages 739-751