Taha Hussein Abd Allah Mohamed
Lecturer
Computation of singular integrals in variational boundary element method
Computers and Mathematics with Applications • 2025
Publication Information
Authors
Naga, Taha HA and Rashed, Youssef F
Keywords
Boundary element method; Variational formulation; Stiffness matrix; Singular integrals; Elasticity problems; Taylor series expansion
Journal
Computers and Mathematics with Applications
Publisher
ELSEVIER
Volume
188
Issue
Not Available
Pages
244-26
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
This paper introduces a novel technique for addressing singular kernels in the variational
boundary element formulation. The study presents an expansion centered on two explicit singular
points, enabling the isolation of all relevant singular terms and extending the analytical capabilities to curved elements, thereby broadening the applicability of the formulation. The proposed
method comprehensively addresses all types of singularities and is validated through rigorous and
extensive numerical experimentation on examples with varied geometries, loading conditions,
and boundary conditions. The diversity and inclusivity of these examples highlight the reliability
and effectiveness of the proposed approach in solving two-dimensional elasticity problems.
boundary element formulation. The study presents an expansion centered on two explicit singular
points, enabling the isolation of all relevant singular terms and extending the analytical capabilities to curved elements, thereby broadening the applicability of the formulation. The proposed
method comprehensively addresses all types of singularities and is validated through rigorous and
extensive numerical experimentation on examples with varied geometries, loading conditions,
and boundary conditions. The diversity and inclusivity of these examples highlight the reliability
and effectiveness of the proposed approach in solving two-dimensional elasticity problems.