Global Stability of a Thick Solid Supported by Elastica Columns

Abstract

The global critical load is an extremely useful index for flexible structures under large disturbances. The present technical note determines this index for a two-dimensional rigid solid supported by two flexible columns. The buckling and postbuckling problem is solved by a homotopy algorithm applied to a Galerkin formulation of the nonlinear elastica equations. The present results show the bifurcation curve is quite sensitive to an elevated mass center. The global buckling load is greatly reduced although the critical buckling load of linear stability analysis remains the same, showing that the linear stability index or bifurcation load is entirely erroneous in predicting the safe load under finite disturbances for flexible structures with elevated mass centers.