METHOD OF DISCRETE SINGULARITIES IN PLANE PROBLEMS OF THE THEORY OF ELASTICITY WITH NON-SMOOTH BOUNDARIES.

The numerical solution of a broad class of elasticity-theory problems is investigated, namely, plane problems with non-smooth boundaries by the method of discrete singularities (MDS). The MDS is the numerical solution of boundary value problems that is substantially the Tikhonov regularization method based on boundary singular integral equations. An elastic isotropic homogeneous medium is considered that occupies a simply-connected domain D with a piecewise-smooth closed contour T on a plane. The purpose of the paper is to study and give a foundation for what is new in the MDS for plane elasticity theory problems with non-smooth boundaries as compared with the smooth boundary case in question.