Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Secondary modes, orthogonality, examples

In this paper the generalization of the constrained finite strip method (cFSM) is provided. cFSM is an extension of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied to enforce the thin-walled member to deform in accordance with desired deformations, e.g., to buckle in flexural, lateral-torsional, distortional, or local buckling mode. This paper is a companion to [1], where the method is introduced and where the primary modes are defined, i.e., modes that are associated with minimal cross-section discretization, when nodal lines are located at folds and ends only. In this paper the so-called secondary modes are defined, i.e., those with no displacements at folds and edges, which thus exist only if flat plates are discretized into multiple strips. Moreover, some practical aspects are also discussed, including how the individual base vector of the deformation spaces can be defined in a practically useful and meaningful manner. The applicability of the method is demonstrated by numerical examples.