In this paper, the approaches to the study of mathematical models of the theory of linear elasticity are developed. The general formulation of the 3-dimensional problem based on the representation of the fundamental solution in the form of V. P.
This article dwells upon the multiscale elastic structures consisting of matrix medium and thin coatings or inclusions. The matrix medium is described by the equations of classical elasticity theory, while Timoshenko shell theory is used for the description of the thin parts of the structure. On the interface between media, perfect contact conditions are assumed to hold. The coupled algorithm is developed, based on the boundary element method in the matrix part and on the high order finite element method in the thin parts of the structure. The two methods are coupled using a domain dec