Open Access

ARTICLE

Divergent Integrals in Elastostatics: Regularization in 3-D Case

V.V. Zozulya¹

1 Centro de Investigacion Cientifica de Yucatan A.C., Calle 43, No 130, Colonia Chuburná de Hidalgo, C.P. 97200, Mérida, Yucatán, México. E-mail: zozulya@cicy.mx

Computer Modeling in Engineering & Sciences 2010, 70(3), 253-350. https://doi.org/10.3970/cmes.2010.070.253

Abstract

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

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Keywords

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