ON THE CAUCHY PRINCIPAL VALUE OF THE SURFACE INTEGRAL IN THE BOUNDARY INTEGRAL-EQUATION OF 3D ELASTICITY

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 surface patch and the pre-image plane at smooth mapping of the surface patch being derived for this purpose.