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An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells
Author(s) -
Azrar L.,
Cochelin B.,
Damil N.,
PotierFerry M.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360802
Subject(s) - mathematics , bifurcation , buckling , finite element method , shell (structure) , numerical analysis , polynomial , stiffness , square (algebra) , convergence (economics) , mathematical analysis , geometry , structural engineering , nonlinear system , engineering , physics , civil engineering , quantum mechanics , economics , economic growth
In this paper, we apply an asymptotic‐numerical method for computing the postbuckling behaviour of plate and shell structures. The bifurcating branch is sought in the form of polynomial expansions, and it is determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can easily be computed by using recurrent formulas. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. However, the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point. In the present form, the method should be viewed as a cheap and automatic way of completing a linear buckling analysis. It is illustrated in two examples: a square plate under in‐plane compression and a cylindrical shell under pressure.