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On the Cauchy principal value of the surface integral in the boundary integral equation of 3D elasticity

Authors
Journal
Engineering Analysis with Boundary Elements
0955-7997
Publisher
Elsevier
Publication Date
Volume
12
Issue
4
Identifiers
DOI: 10.1016/0955-7997(93)90056-q
Keywords
  • Cauchy Principal Value
  • Strongly Singular Surface Integral
  • Boundary Integral Equations
  • Elasticity
  • Boundary Element Method

Abstract

Abstract A simple demonstration of the existence of the Cauchy principal value (CPV) of the strongly singular surface integral in the Somigliana Identity at a non-smooth boundary point is presented. First a regularization of the strongly singular integral by analytical integration of the singular term in the radial direction in pre-image planes of smooth surface patches is carried out. Then it is shown that the sum of the angular integrals of the characteristic of the tractions of the Kelvin fundamental solution is zero, a formula for the transformation of angles between the tangent plane of a suface patch and the pre-image plane at smooth mapping of the surface patch being derived for this purpose.

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