An asymptotic property of degenerate scales for multiple holes in plane elasticity

Abstract

The solution of an exterior Dirichlet boundary value problem of plane isotropic elasticity by the boundary integral equation of the first kind obtained from the Somigliana identity is considered. The logarithmic function appearing in the integral kernel may cause that the operator is non-invertible. Such a situation occurs if the size of the boundary coincides with a degenerate scale for a certain form of the fundamental solution used. A technique for the evaluation of the degenerate scales for an asymptotic case of an exterior domain with holes placed far one from another is discussed and analyzed. The examples provide results of particular cases and assess suitability of the proposed technique in relation to numerical calculation of degenerate scales by the Boundary Element Method.