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Asymptotic analysis of an \(L\)-shaped junction of two elastic beams. (English. Russian original) Zbl 1382.35297

J. Math. Sci., New York 216, No. 2, 279-312 (2016); translation from Probl. Mat. Anal. 84, 123-150 (2016).
Summary: We propose a one-dimensional asymptotic model of an \(L\)-shaped junction of two thin two-dimensional elastic beams subject to boundary conditions of different type at external bean ends. The beams are described by standard systems of the Kirchhoff ordinary differential equations, whereas the transmission conditions on coincident (internal) nodes essentially depend on the type of boundary conditions on the external beam ends. The transmission conditions are obtained by analyzing the boundary layer near internal nodes. The asymptotics is justified with the help of a weighted anisotropic Korn inequality.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K30 Junctions
35C20 Asymptotic expansions of solutions to PDEs
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
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