Effect of Elevated Mass Center on the Global Stability of a Solid Supported by Elastica Columns

Recently we advocated a new stability index, the global critical load, for very elastic structures. This index is extremely useful for flexible structures under large disturbances such as earthquakes. The present note determines this index for a two-dimensional rigid solid supported by two flexible columns. Using the nonlinear elastica equations the buckling and postbuckling problem is solved by a homotopy nonlinear system solver. The present results show the bifurcation curve is quite sensitive to the elevated mass center. The global buckling load is drastically reduced although the critical buckling load of linear stability analysis is the same. An explanation is given through the study of a solid supported by one column.