THE METHOD OF PROJECTION AND DECOMPOSITION OF ANALYTICAL FUNCTIONS IN BOUNDARY-VALUE-PROBLEMS OF ELASTICITY THEORY

A technique is proposed for reducing boundary-value problems of elasticity theory in multiply connected regions to a system of algebraic equations. The technique is based on the projection method for analytical functions of a complex variable combined with decomposition of the original region. The starting equations are provided by the Laurent series expansion of the necessary and sufficient condition of analyticity of functions. The coordinate functions are the terms of the Laurent series for the required potentials of elasticity theory in each of the subregions obtained from the original region by decomposition. The proposed method avoids the construction of integral equations, while preserving the advantages of the boundary-element method.