TY - EJOU
AU - Zozulya, V.V.
TI - Divergent Integrals in Elastostatics: Regularization in 3-D Case
T2 - Computer Modeling in Engineering \& Sciences
PY - 2010
VL - 70
IS - 3
SN - 1526-1506
AB - In this article the divergent integrals, which arise when the boundary integral equation (BIE) methods are used for solution of the 3-D elastostatic problems is considered. The same approach for weakly singular, singular and hypersingular integral regularization is developed. The approach is based on theory of distribution and Green's theorems. This approach is applied for regularization of the divergent integrals over convex polygonal boundary elements (BE) in the case of piecewise constant approximation and over rectangular and triangular BE for piecewise linear approximation. The divergent integrals are transformed into the regular contour integrals that can be easily calculated analytically. Proposed methodology easy can be extended to other problems: elastodynamics, analytical calculation of the regular integrals, when collocation point situated outside the BE. Calculations of the divergent and regular integrals for square and triangle of the unit side are presented
KW - weakly singular
KW - singular
KW - hypersingular integrals
KW - regularization
KW - boundary integral equations
DO - 10.3970/cmes.2010.070.253