Geodesic
Boundary layers and the hinge-support conditions for thin plates
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 228-287

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The boundary layer phenomenon is investigated for a thin three-dimensional plate. Arbitrary anisotropy of elastic properties and inhomogenuity in longitudinal and transversal directions are permitted. Some of initial asymptotic terms are constructed and a way to continue the asymptotic procedure is described. Precise estimates of the difference between the exact and approximate solutions are obtained for the energy norm. The amalgamated problem is formed that gives the two-term asymptotics of the displacement and stress fields at a distance from the lateral side of the plate while the edge effects are simulated by elastic clamping conditions containing integral characteristics of the boundary layer problem in the semi-strip. The hinge-support conditions which appear due to sufficiently narrow claming zone at plate's edge, are derived and justified, too. 
@article{ZNSL_1999_257_a14,
     author = {S. A. Nazarov},
     title = {Boundary layers and the hinge-support conditions for thin plates},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {228--287},
     publisher = {mathdoc},
     volume = {257},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a14/}
}
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S. A. Nazarov. Boundary layers and the hinge-support conditions for thin plates. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 228-287. http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a14/