Conversion from imperfection-sensitive into imperfection-insensitive elastic structures

Abstract

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.<br />The search for specific modes of stiffening that result in the aforementioned conversion is of fundamental as well as of practical importance.<br />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.<br />This mode of analysis primarily serves the purpose of deducing important theoretical results which facilitate the verification of specific numerical results.<br />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.<br />New mathematical conditions for symmetric bifurcation from nonlinear prebuckling paths are presented.<br />For the special case of linear prebuckling paths, these conditions are satisfied trivially.<br />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.<br />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.<br />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