Title of article :
Analytical Expressions for the Singularities Treatment in the Three-dimensional Elastostatic Boundary Element Method
Author/Authors :
Prado Leite, Leonardo Fellipe Department of Civil Engineering - Federal University of Sergipe, Avenida Marechal Rondon S/N, São Cristóvão, Brazil , Souza de Melo, Rodrigo Department of Civil Engineering - Federal University of Sergipe, Avenida Marechal Rondon S/N, São Cristóvão, Brazil , da Rocha, Fabio Carlos Department of Civil Engineering - Federal University of Sergipe, Avenida Marechal Rondon S/N, São Cristóvão, Brazil
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
Journal title :
Journal of Applied and Computational Mechanics
