On some properties of the coefficients in the structural functions method

Some parameters of the structural functions method, which is used to construct an approximate solution to the elasticity problem for inhomogeneous solids, were analyzed. The equivalence of two existing approaches to computing structural functions was proved, and the set of known properties of structural functions was expanded. It was demonstrated that the method approximates the displacements in an inhomogeneous body by expressing them as a series involving derivatives of the displacements in a homogeneous (concomitant) body with the same geometry and loading. In practical applications, the series representation of the solution must be replaced by the partial sum of the series. For a specific class of approximate solutions to the concomitant problem, a relationship was established between the number of terms used in the partial sum of the series and the approximation order of the solution to the concomitant problem. Criteria for selecting elastic properties of the concomitant body were discussed.