Analytic formulations for calculating nearly singular integrals in two-dimensional BEM

A natural stress boundary integral equation for calculating the near boundary stress field

“…The approaching degree e had been denoted by the author in Ref. [34] to describe the relative distance between the inner point and the integral boundary element, i.e.,…”

“…In this paper, based on the displacement derivative BIE [33], a new NSBIE was further deduced in which the boundary variable values are displacements, tractions and natural variables. Instead of the original nearly hyper-singularity, there is only the nearly strong singularity in the NSBIE, which can be effectively evaluated by the regularization method proposed by the authors [34].…”

A general algorithm for evaluating nearly singular integrals in anisotropic three-dimensional boundary element analysis

“…Apart from pure analytical integration, which has obvious limitations (low order elements), many other methods have been devised. The methods developed so far include, but are not limited to, element subdivision methods [15][16][17], semi-analytical methods [6,18,19] and various nonlinear transformations [20][21][22][23][24][25][26][27]. The element subdivision method is appealing, stable, and accurate but is costly because the number of sub-elements and their sizes are strongly dependent on the order of the near singularity and the dimension of the element.…”

Solution of Poisson’s equation by analytical boundary element integration

“…Accordingly, these singular integrals must be evaluated accurately. Much work has been performed in this regard to remove the singularities appearing in the boundary element integrals [13][14][15][16][17][18].…”