Degenerate scales for boundary value problems in anisotropic elasticity

Abstract

Degenerate scales usually refer to a size effect which causes non-unique solutions of boundary integral equations for certain type of boundary value problems with a unique solution. They are closely connected to the presence of a logarithmic function in the integral kernel of the single-layer potential operator. The equations of the elasticity theory provide one of the known application fields where degenerate scales appear. The paper discusses conditions and formula for controlling and detection of the degenerate scales in the case of fully anisotropic analysis. No restrictions are considered for the material, only the loading should cause two-dimensional deformation of the anisotropic body. A technique for the evaluation of the degenerate scales is discussed and tested. The examples provide results of special simple cases and demonstrate suitability of the proposed technique in relation to calculation of degenerate scales by numerical solution of pertinent boundary integral equation by the boundary element method.