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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 7, Pages 1197–1218 (Mi zvmmf10755)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotics of the deflection of a cruciform junction of two narrow Kirchhoff plates

S. A. Nazarovab

a Petersburg State University, St. Petersburg, Russia
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

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.

Key words: cruciform junction of narrow plates, asymptotics, one-dimensional model, boundary layer, Kirchhoff transmission conditions.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00325_а

DOI: https://doi.org/10.31857/S004446690000452-8

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1150–1171

Bibliographic databases:

UDC: 519.632
Received: 30.01.2017
Revised: 24.11.2017

Citation: S. A. Nazarov, “Asymptotics of the deflection of a cruciform junction of two narrow Kirchhoff plates”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1197–1218; Comput. Math. Math. Phys., 58:7 (2018), 1150–1171

Citation in format AMSBIB
\by S.~A.~Nazarov
\paper Asymptotics of the deflection of a cruciform junction of two narrow Kirchhoff plates
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 7
\pages 1197--1218
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 7
\pages 1150--1171

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    This publication is cited in the following articles:
    1. F. L. Bakharev, S. A. Nazarov, “Eigenvalue asymptotics of long Kirchhoff plates with clamped edges”, Sb. Math., 210:4 (2019), 473–494  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. S. A. Nazarov, “Homogenization of Kirchhoff plates with oscillating edges and point supports”, Izv. Math., 84:4 (2020), 722–779  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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