Analytic integration of kernel shape function product integrals in the boundary element method

Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems

“…Non-isoparametric elements are used to simplify integral kernel functions and Jacobean, in which geometry is interpolated using linear shape functions and only physical quantities are approximated by the higher order shape functions [11][12][13]33]. Alternatively, Taylor series expansion is used to treat the Jacobean and non-national kernel functions [36].…”

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.…”

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

“…In Ref. [29], all the integrals were evaluated exactly for straight boundaries in 2-D elastostatics, but a series approximation was adopted for curved boundaries. Semi-analytical or analytical integral formulas of nearly singular integrals were also developed to calculate the physical quantities at interior points very close to the boundary, for both 2-D elastic and potential problems [30,31].…”

“…In the method mentioned in Refs. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the nearly hyper-singular integral and the nearly strongly singular one are calculated separately.…”