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The purpose of this paper is to derive sufficient and necessary conditions for zero‐stiffness postbuckling which is bound up with a favorable form of transition from imperfection sensitivity to imperfection insensitivity in the course of sensitivity analysis of the initial postbuckling path. Zero‐stiffness postbuckling as such is shown to be imperfection insensitive. Choosing Koiter's initial postbuckling analysis as the vehicle for answering the question of predictability of zero‐stiffness postbuckling seems, at first sight, to be a contradiction in terms, since zero‐stiffness postbuckling includes the entire postbuckling path whereas Koiter's initial postbuckling analysis is practically restricted to the neighborhood of the bifurcation point. The theoretical findings presented in this work are verified numerically.

SUMMARY A membrane stress state may be considered as a general stress state in which mechanical constraints have been imposed. Therefore, it would appear that there are mathematical subsidiary conditions for bifurcation buckling from such a stress state. In this work, such conditions are derived in the frame of the Finite Element Method. The basic condition follows from disintegration of the second derivative of the mathematical formulation of the so‐called consistently linearized eigenproblem with respect to a dimensionless load parameter. It is used for deriving another condition, characterized by the vanishing of a particular bilinear form. Linear stability analysis and bifurcation buckling from linear prebuckling paths are two special cases for which this condition is satisfied. Sensitivity analysis of bifurcation buckling of a two‐hinged arch, subjected to a uniformly distributed static load, by varying the geometric form of its axis serves the purpose of non‐trivial verification of the derived condition for the special case of a thrust‐line arch. Copyright © 2011 John Wiley & Sons, Ltd.

No abstract

In the course of sensitivity analysis of the initial postbuckling behavior of elastic structures, a special case may occur which is referred to as zero-stiffness postbuckling. The purpose of this paper is to present sufficient and necessary conditions for this special case which is associated with a favorable form of transition from imperfection sensitivity to imperfection insensitivity in the course of sensitivity analysis of the initial postbuckling path. Koiter's initial postbuckling analysis is chosen as the vehicle for quantification of the initial postbuckling behavior.