Modal identification for shell finite element models of thin-walled members in nonlinear collapse analysis

The objective of this paper is to provide a method for applying modal identification (i.e. the separation of general deformations into fundamental modal deformation classes: local, distortional, global, shear, and transverse extension) to the collapse analysis of thin-walled members modeled using material and geometric nonlinear shell finite element analysis. The advantage of such a modal identification is the ability to categorize and reduce the complicated deformations that occur in a shell finite element model—and ultimately to (a) quantitatively associate failures with particular classes, e.g. state a model as a local failure, and (b) track the evolution of the classes, e.g., mixed local and distortional buckling leading to a distortional failure in a given model. Ultimately, this capability will aid Specification development, which must simplify complicated behavior down to strength predictions in isolated buckling-induced limit states. The modal identification method is enabled by creating a series of base vectors, consistent with the fundamental deformation classes, that are used to categorize the general finite element displacements. The base vectors are constructed using the constrained finite strip method for general end boundary conditions, previously developed by the authors. A fairly sizeable minimization problem is required for assigning the contributions to the fundamental deformation classes. The procedure is illustrated with shell finite element examples of cold-formed steel members modeled to collapse with geometric or/and material nonlinearity. The failure modes of the member are tracked (i.e., identified as a function of displacement), and the collapse mechanism is investigated. The provided examples provide both proof of concept for the modal identification and demonstrate the potential of using such information to better understand the behavior of thin-walled members.