Design of beneficial geometric imperfections for elastic collapse of thin-walled box columns

Abstract

This paper deals with the design of beneficial geometric imperfections for elastic collapse of thin-walled box columns of square cross-section under axial compression. From the point of view of high elastic post-collapse stiffness, it is desirable to force the column to collapse with a larger number of axial half-waves than with the preferred wave number which is approximately equal to the aspect ratio. By introducing a beneficial geometric imperfection with such a larger wave number and if the magnitude of such imperfection exceeds the transitional value, it is found that the column will collapse in the beneficial mode in the initial postbuckling (assume to be elastic) finite-deflection regime. Equilibrium paths of typical box columns are plotted and analyzed. The two-mode potential energy is found to fall into the category of a double-cusp catastrophe.