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## Asymptotics of the Deflection of a Cruciform Junction of Two Narrow Kirchhoff Plates

PIIS004446690000452-8-1
DOI10.31857/S004446690000452-8
Publication type Article
Status Published
Authors
Affiliation:
Petersburg State University
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Journal nameZhurnal vychislitelnoi matematiki i matematicheskoi fiziki
EditionVolume 58 Issue 7
Pages1197-1218
Abstract

Two two-dimensional plates with bending described by Sophie Germain’s equation with the biharmonic operator are joined in the form of a cross with clamped ends, but with free lateral sides outside the cross core. Asymptotics of the deflection of the junction with respect to the relative width of the plates regarded as a small parameter is constructed and justified. The variational-asymptotic model includes a system of two ordinary differential equations of the fourth and second orders with Dirichlet conditions at the endpoints of the one-dimensional cross and the Kirchhoff transmission conditions at its center. They are derived by analyzing the boundary layer near the crossing of the plates and mean that the deflection and the angles of rotation at the central point are continuous and that the total bending force and the principal torques vanish. Possible generalizations of the asymptotic analysis are discussed.

Keywordscruciform junction of narrow plates, asymptotics, one-dimensional model, boundary layer, Kirchhoff transmission conditions
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