Regularization Of The Hypersingular Integrals In
3-D Problems Of Fracture Mechanics
Author(s)
V. V. Zozulya
Abstract
This article considers the hypersingular integrals, which arise when the boundary
integral equation (BIE) methods are used to solve fracture mechanics problems .
The methodology of hypersingular integral regularization developed in our
previous publications is based on theory of distribution and Green’s theorems. In
the case of piecewise constant and piecewise linear approximations the
hypersingular integrals are transformed into the regular contour integrals that can
be easily calculated analytically or numerically.
Keywords: weakly singular, singular, hypersingular integrals, boundary integral
equations, fracture mechanics.
1 Introduction
A huge amount of publications is devoted to the boundary integral equation
methods (BEM) and its application science and engineering. One of the main
problems arising in numerical solution of the BIE by the BEM is a calculation of
the divergent integrals. Different methods have been developed for regularization
of the divergent integrals [7]. The hypersingular integrals had been considered
by Hadamard in the sense of finite part (FP) in [4]. The theory of distributions
allows us to study the divergent integrals and integral operators with kernels
containing different kind of singularities in the same way as the regular integrals.
Analysis of the most known methods used for treatment of the different
divergent integrals has been done in our previous publications. It was shown that
theory of distributions provides a unified approach for the study of the divergent
integrals and integral operators with kernels containing different kind of
singularities. We applied the theory of distribution approach for the first time in
[8], then it was further developed in [9–11] and was applied for static and
Keywords
weakly singular, singular, hypersingular integrals, boundary integral
equations, fracture mechanics.
Related Book
Other papers in this volume
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