In case of loss of stability by means of symmetric bifurcation, a qualitative improvement of the postbuckling behavior of originally imperfection-sensitive elastic structures is their conversion into imperfection-insensitive structures by means of modifications of the original design.
The search for specific modes of stiffening that result in the aforementioned conversion is of fundamental as well as of practical importance.
Koiter's initial postbuckling analysis is applied in the framework of the FEM to deduce mathematical relations associated with the transition from imperfection sensitivity to insensitivity.
This mode of analysis primarily serves the purpose of deducing important theoretical results which facilitate the verification of specific numerical results.
Most of the structural analyses reported in this work are performed by means of the FEM, but without regard for Koiter's initial postbuckling analysis.
New mathematical conditions for symmetric bifurcation from nonlinear prebuckling paths are presented.
For the special case of linear prebuckling paths, these conditions are satisfied trivially.
The completeness of the set of solutions from Koiter's initial postbuckling analysis that involve the vanishing of a specific load parameter as a necessary (but not sufficient) condition for the conversion into imperfection insensitivity is demonstrated.
Attempts to achieve the aforementioned conversion include the increase of the thickness and of the stiffness of a spring attached to the structure, respectively, and the reduction of the rise of the undeformed structure.
The results of this investigation include different modes of conversion from imperfection-sensitive into imperfection-insensitive structures as well as failure to achieve such a conversion