Sensitivity of post-critical states to changes in design parameters

Abstract

Sensitivity of post-buckling paths is studied in the context of the general theory of elastic stability of discrete structural systems. It is assumed that the sensitivity of the critical state itself has been computed and a formulation is developed to account for sensitivity of the curvature of the post-critical states when there are changes in design parameters. A linear fundamental path is considered. Explicit expressions are obtained for the sensitivities and they take the form of perturbation expansions. Only first order sensitivity of post-critical paths has been developed. A simple example of an angle section column with deformable cross-section illustrates that although a critical state may be insensitive to changes in certain design parameters, the post-critical response may be highly sensitive. In the first example presented (an axially loaded angle section column), the postbuckling response even changes from stable to unstable depending on the values of the design parameter considered.