Bifurcation buckling eigenvector characteristics for structures exhibiting buckling mode interactions

Abstract Since the recognition that local buckling of plate elements can significantly reduce the column buckling load of thin walled beams and columns, significant research has established a firm basis for understanding the interplay between buckling modes in classical built-up structures. Recent work on a modal projection procedure for representing the results of both static and dynamic nonlinear collapse computations has demonstrated that for structures whose collapse process includes a predominantly linear prebuckling domain, the failure process can be well understood by tracking the growth of the bifurcation eigenvectors in the solution. It has recently been observed that for structures which exhibit mode coupling characteristics, the bifurcation eigenvectors by themselves do not form a set of orthogonal functions when their inner product is evaluated. For complex structures or structures exhibiting complex multi-modal postbuckling behavior, this procedure provides an approach to evaluate the design basis for buckling mode interactions. Examples are shown illustrating this for collapse analyses involving both the classical case of geometric imperfections and material imperfections such as delaminations in composite structures.