Geodesic
Elasticity theory problem in terms of displacements for a cylindrical layer with strongly different characteristic sizes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 30-36

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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. 
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     author = {T. I. Garyaeva and D. V. Georgievskii},
     title = {Elasticity theory problem in terms of displacements for a cylindrical layer with strongly different characteristic sizes},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {30--36},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a5/}
}
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T. I. Garyaeva; D. V. Georgievskii. Elasticity theory problem in terms of displacements for a cylindrical layer with strongly different characteristic sizes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 30-36. http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a5/