Elasticity Theory Problem in Terms of Displacements for a Cylindrical Layer with Strongly Different Characteristic Sizes / Garyaeva T.I., Georgievskii D.V. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 3. P. 30-36 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 0].

An analysis of the principal terms of the general asymptotic expansions for the solutions to the three-dimensional Dirichlet 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 small asymptotic parameter. The radius of the cylinder may be intermediate between its height and the layer thickness. Such a geometry is typical, e.g., for a cylindrical body with characteristic macro-, micro-, and nanosizes in various directions.

Key words: elasticity, problem in terms of displacements, thin body, cylindrical layer, asymptotic solution, system of principal approximation.