Premium
Reinforcement of a thin plate by a thin layer
Author(s) -
Rahmani Leila,
Vial Grégory
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.910
Subject(s) - mathematics , stiffness , remainder , asymptotic expansion , constant (computer programming) , bending stiffness , reinforcement , bending , mathematical analysis , boundary (topology) , thin layer , layer (electronics) , boundary layer , boundary value problem , scale (ratio) , structural engineering , computer science , mechanics , composite material , materials science , engineering , physics , arithmetic , quantum mechanics , programming language
Abstract We study the bending of a thin plate, stiffened with a thin elastic layer, of thickness δ. We describe the complete construction of an asymptotic expansion with respect to δ of the solution of the Kirchhoff–Love model and give optimal estimates for the remainder. We identify approximate boundary conditions, which take into account the effect of the stiffener at various orders. Thanks to the tools of multi‐scale analysis, we give optimal estimates for the error between the approximate problems and the original one. We deal with a layer of constant stiffness, as well as with a stiffness inδ −1 . Copyright © 2007 John Wiley & Sons, Ltd.