An Efficiency Study of the Radial Polynomial Expansion Method for Solv- ing Singular Integrals in the Dual-BEM

Resumo

In the Boundary Element Method (BEM), when the element which is being integrated contains the
source point, singularities arise in the integrals that govern the problem. Although several classical methods
have already been proposed and successfully used, their numerical implementation is laborious and often requires
particular codes for each type integral kernel. Recently, a method that allows the solution of integrals with different
singularity orders in a single numerical procedure has been proposed. It is based on the polynomial expansion
of the radial distance between the source and field points and it is called here as Radial Polynomial Expansion
Method (RPEM). The RPEM has its efficiency studied for application to the Dual-BEM. Elements with quadratic
interpolation functions are analyzed. The efficiency is verified in terms of the element distortion and the number
of terms needed in the expansion. For this, the method is implemented in a computational code in Fortran 95 and
the results are compared with other formulations, such as the singularity subtraction method. Once the reliability
and applicability of the method have been proven, it is intended to apply the solutions found in a Dual-BEM code,
for the analysis of fatigue crack propagation.