Asymptotic study of the elastic postbuckling behavior of structures by the finite element method

Abstract

Within the framework of finite element analysis, an asymptotic method is presented for the study of geometrically nonlinear static behavior of thin structures under one-parameter conservative loading. The method can be applied when the prebuckling behavior is moderately non-linear so that the bifurcation analysis is no longer accurate enough. An iterative process makes it possible to find suitable deformation modes which enable a good approximation of the structural behavior around the buckling point. As in the Rayleigh-Ritz approach, a reduced energy can be formulated with only a small number of generalized degrees of freedom. The influence of small initial imperfections on the buckling load can easily be analyzed as in Koiter's asymptotic method. A comprehensive treatment and several improvements of this asymptotic iterative method are given and selected examples illustrate the basic features of the method.