Elasticity theory problem in terms of displacements for a cylindrical layer with strongly different characteristic sizes

An analysis of the principal terms of the general asymptotic expansions for the solutions to the 3D elasticity boundary value problem in terms of displacements (quasistatic case, compressibility) for a cylindrical layer is performed. A ratio of the layer thickness to the height of the cylinder is a natural asymptotic parameter. The radius of the cylinder's base can be of an arbitrary “intermediate”, including endpoints, order. Such a geometry is typical, e.g., for a cylindrical body with characteristic macro-, micro- and nanosizes in various directions.