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Asymptotic Integration of One Narrow Plate Problem

  • Valentina O. Finiukova
  • Alexander M. Stolyar
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)

Abstract

The derivation of a narrow plate model is carried out in the paper. It has been based on the method of asymptotic integration in connection with the boundary layer method and applied to one non-linear dynamic problem. It allows to reduce the solution of the given problem to a sequence of linear or nonlinear one-dimensional initial boundary-value problems (as a result of the first iteration process) and a sequence of two-dimensional linear problems (second order process) and get the solution of a given problem with high accuracy. The small parameter is equal to the relation of the lengths of adjacent sides of the plate. It has been obtained that the main term of the asymptotic expansion satisfies the known equation of a beam theory. Some examples are calculated in order to find the limits of asymptotics obtained.

Keywords

Asymptotic integration Narrow plate 

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Valentina O. Finiukova
    • 1
  • Alexander M. Stolyar
    • 1
  1. 1.Southern Federal University,Rostov-on-DonRussia

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