Approximate solution to the Föppl-Kármán-Marguerre equations
type: Item
instance of: scholarly article
title: Approximate solution to the Föppl-Kármán-Marguerre equations
zbMATH Open document ID: 0657.73036
DOI: 10.1016/0093-6413(89)90010-4
author: Z. Sadovský
published in: Mechanics Research Communications
publication date: 1989-01-01T00:00:00Z
review text: From the engineering point of view it is of interest to know a simple and yet sufficiently precise approximate solution to the thin plate equation when initial deflection has the form of buckling mode and load ranges from zero up to few times the bucklng load. We review: (i) the formula based on classical small solution expansion near the critical load (Koiter's initial postbuckling analysis), (ii) solution of one Galerkin equation assuming initial as well as the overall deflection in the form of the buckling mode, (iii) the formal correction to (ii) suggested by \textit{A. C. Walker} [The postbuckling behaviour of simply supported square plates. Aeron. Q. 20, 203-222 (1969)]. Our aim is to combine the power of small solution analysis with the practical usefulness of approximate solution (ii) by a consistent approach. We realize it taking the Galerkin equation (ii) as an equality constraint into a constructive small solution analysis. Although derived in a neighbourhood of the buckling load the resulting formula yields an exact deflection function at zero load value. Illustrative numerical results are given.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 4074622
zbMATH Keywords: linearized eigenvalue problem
zbMATH Keywords: linear boundary value problem
zbMATH Keywords: small solution expansion near the critical load
zbMATH Keywords: approximate solution
zbMATH Keywords: Galerkin equation
zbMATH Keywords: equality constraint
zbMATH Keywords: exact deflection function at zero load
MaRDI profile type: Publication
full work available at URL: 0093-6413(89)90010-4
OpenAlex ID: W2056711306
description: scientific article; zbMATH DE number 4074622