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.

[1]  Raphael T. Haftka,et al.  Adaption of Koiter's method to finite element analysis of snap-through buckling behavior† , 1971 .

[2]  Arnold D. Kerr,et al.  The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads , 1969 .

[3]  W. T. Koiter.  THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[4]  David Bushnell.  Buckling of shells - Pitfall for designers , 1980 .

[5]  D. Nagy,et al.  Buckling analysis with the aska program system , 1978 .

[6]  R. T. Haftka,et al.  Progress in nonlinear finite element analysis using asymptotic solution techniques. , 1972 .

[7]  E. Carnoy.  Asymptotic study of the postbuckling behavior of thin-type structures by the finite element method , 1981 .

[8]  Effective Use of the Incremental Stiffness Matrices in Nonlinear Geometric Analysis. , 1970 .

[9]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .

[10]  E. Carnoy,et al.  Postbuckling analysis of elastic structures by the finite element method , 1980 .

[11]  F. A. Brogan,et al.  Bifurcation Buckling as an Approximation of the Collapse Load for General Shells , 1972 .

[12]  John Argyris,et al.  A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems , 1977 .

[13]  M. König,et al.  Geometrically nonlinear finite element behaviour using buckling mode superposition , 1979 .

[14]  Ahmed K. Noor,et al.  Reduced basis technique for collapse analysis of shells , 1981 .

[15]  A.M.C. Holmes,et al.  Buckling of shells with cutouts, experiment and analysis☆ , 1972 .

[16]  E. Carnoy.  Mixed finite elements based upon marguerre theory for the study of geometrically nonlinear behavior of thin shells , 1981 .

[17]  P. Stehlin,et al.  Use of global functions for improvement in efficiency of nonlinear analysis. [in computer structural displacement estimation , 1981 .

[18]  L. J. Ernst,et al.  Geometrical and physical nonlinearities some developments in the netherlands , 1979 .

[19]  P. Stern,et al.  Automatic choice of global shape functions in structural analysis , 1978 .

[20]  R. Leicester.  Finite Deformations of Shallow Shells , 1968 .